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Sample records for bioheat transfer equation

  1. A new bioheat equation and its application to peripheral tissue and whole limb heat transfer

    International Nuclear Information System (INIS)

    Weinbaum, S.

    1987-01-01

    Much of the mathematical modeling of heat transfer in perfused tissue over the past three decades has been based on the Pennes bioheat equation. This equation assumes that blood at the local arterial supply temperature reaches the capillaries where the primary thermal equilibration occurs because of the large surface area available for heat exchange. While this argument is correct for gas, water and solute transport, recent theoretical and experimental studies have shown that virtually no heat exchange occurs in vessels under 100 μm and that the primary mechanism for microvascular heat exchange is the imperfect heat exchange between the larger paired countercurrent microvessels that occur 3 to 6 generations prior to the capillaries. A new fundamental bioheat equations has been derived to describe this heat transfer mechanism. This equation contains a basic new expression for the thermal conductivity of perfused tissue which depends on the geometry and flow in the largest microvessels of the local tissue element and the direction of the vessels relative to the local tissue temperature gradient. Although the new equation appears to be complicated, it is shown that it can be applied with relative ease to a host of problems previously treated by the Pennes equation

  2. Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

    Science.gov (United States)

    Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.

    2017-05-01

    In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.

  3. Analysis of the dual phase lag bio-heat transfer equation with constant and time-dependent heat flux conditions on skin surface

    Directory of Open Access Journals (Sweden)

    Ziaei Poor Hamed

    2016-01-01

    Full Text Available This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer, hyperbolic (thermal wave and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.

  4. Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

    Science.gov (United States)

    Kumar, Dinesh; Kumar, P; Rai, K N

    2017-11-01

    This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

  5. Triangular node for Transmission-Line Modeling (TLM) applied to bio-heat transfer.

    Science.gov (United States)

    Milan, Hugo F M; Gebremedhin, Kifle G

    2016-12-01

    Transmission-Line Modeling (TLM) is a numerical method used to solve complex and time-domain bio-heat transfer problems. In TLM, rectangles are used to discretize two-dimensional problems. The drawback in using rectangular shapes is that instead of refining only the domain of interest, a large additional domain will also be refined in the x and y axes, which results in increased computational time and memory space. In this paper, we developed a triangular node for TLM applied to bio-heat transfer that does not have the drawback associated with the rectangular nodes. The model includes heat source, blood perfusion (advection), boundary conditions and initial conditions. The boundary conditions could be adiabatic, temperature, heat flux, or convection. A matrix equation for TLM, which simplifies the solution of time-domain problems or solves steady-state problems, was also developed. The predicted results were compared against results obtained from the solution of a simplified two-dimensional problem, and they agreed within 1% for a mesh length of triangular faces of 59µm±9µm (mean±standard deviation) and a time step of 1ms. Copyright © 2016 Elsevier Ltd. All rights reserved.

  6. A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment.

    Science.gov (United States)

    Kumar, P; Kumar, Dinesh; Rai, K N

    2015-01-01

    The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τT. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications. Copyright © 2015 Elsevier Ltd. All rights reserved.

  7. Bio-heat transfer model of electroconvulsive therapy: Effect of biological properties on induced temperature variation.

    Science.gov (United States)

    de Oliveira, Marilia M; Wen, Paul; Ahfock, Tony

    2016-08-01

    A realistic human head model consisting of six tissue layers was modelled to investigate the behavior of temperature profile and magnitude when applying electroconvulsive therapy stimulation and different biological properties. The thermo-electrical model was constructed with the use of bio-heat transfer equation and Laplace equation. Three different electrode montages were analyzed as well as the influence of blood perfusion, metabolic heat and electric and thermal conductivity in the scalp. Also, the effect of including the fat layer was investigated. The results showed that temperature increase is inversely proportional to electrical and thermal conductivity increase. Furthermore, the inclusion of blood perfusion slightly drops the peak temperature. Finally, the inclusion of fat is highly recommended in order to acquire more realistic results from the thermo-electrical models.

  8. The effect of the shape and size of gold seeds irradiated with ultrasound on the bio-heat transfer in tissue.

    Science.gov (United States)

    Gkigkitzis, Ioannis; Austerlitz, Carlos; Haranas, Ioannis; Campos, Diana

    2015-01-01

    The aim of this report is to propose a new methodology to treat prostate cancer with macro-rod-shaped gold seeds irradiated with ultrasound and develop a new computational method for temperature and thermal dose control of hyperthermia therapy induced by the proposed procedure. A computer code representation, based on the bio-heat diffusion equation, was developed to calculate the heat deposition and temperature elevation patterns in a gold rod and in the tissue surrounding it as a result of different therapy durations and ultrasound power simulations. The numerical results computed provide quantitative information on the interaction between high-energy ultrasound, gold seeds and biological tissues and can replicate the pattern observed in experimental studies. The effect of differences in shapes and sizes of gold rod targets irradiated with ultrasound is calculated and the heat enhancement and the bio-heat transfer in tissue are analyzed.

  9. Tetrahedral node for Transmission-Line Modeling (TLM) applied to Bio-heat Transfer.

    Science.gov (United States)

    Milan, Hugo F M; Gebremedhin, Kifle G

    2016-12-01

    Transmission-Line Modeling (TLM) is a numerical method used to solve complex and time-domain bio-heat transfer problems. In TLM, parallelepipeds are used to discretize three-dimensional problems. The drawback in using parallelepiped shapes is that instead of refining only the domain of interest, a large additional domain would also have to be refined, which results in increased computational time and memory space. In this paper, we developed a tetrahedral node for TLM applied to bio-heat transfer that does not have the drawback associated with the parallelepiped node. The model includes heat source, blood perfusion, boundary conditions and initial conditions. The boundary conditions could be adiabatic, temperature, heat flux, or convection. The predicted temperature and heat flux were compared against results from an analytical solution and the results agreed within 2% for a mesh size of 69,941 nodes and a time step of 5ms. The method was further validated against published results of maximum skin-surface temperature difference in a breast with and without tumor and the results agreed within 6%. The published results were obtained from a model that used parallelepiped TLM node. An open source software, TLMBHT, was written using the theory developed herein and is available for download free-of-charge. Copyright © 2016 Elsevier Ltd. All rights reserved.

  10. Lattice Boltzmann method for solving the bioheat equation

    International Nuclear Information System (INIS)

    Zhang Haifeng

    2008-01-01

    In this work, we develop the lattice Boltzmann method (LBM) as a potential solver for the bioheat problems. The accuracy of the present LBM algorithm is validated through comparison with the analytical solution and the finite element simulation. The results show that the LBM can give a precise prediction of the temperature distribution, and it is efficient to deal with the space- and time-dependent heat source, which are often encountered in the treatment planning of tumor hyperthermia. (note)

  11. Fourier and non-Fourier bio-heat transfer models to predict ex vivo temperature response to focused ultrasound heating

    Science.gov (United States)

    Li, Chenghai; Miao, Jiaming; Yang, Kexin; Guo, Xiasheng; Tu, Juan; Huang, Pintong; Zhang, Dong

    2018-05-01

    Although predicting temperature variation is important for designing treatment plans for thermal therapies, research in this area is yet to investigate the applicability of prevalent thermal conduction models, such as the Pennes equation, the thermal wave model of bio-heat transfer, and the dual phase lag (DPL) model. To address this shortcoming, we heated a tissue phantom and ex vivo bovine liver tissues with focused ultrasound (FU), measured the temperature response, and compared the results with those predicted by these models. The findings show that, for a homogeneous-tissue phantom, the initial temperature increase is accurately predicted by the Pennes equation at the onset of FU irradiation, although the prediction deviates from the measured temperature with increasing FU irradiation time. For heterogeneous liver tissues, the predicted response is closer to the measured temperature for the non-Fourier models, especially the DPL model. Furthermore, the DPL model accurately predicts the temperature response in biological tissues because it increases the phase lag, which characterizes microstructural thermal interactions. These findings should help to establish more precise clinical treatment plans for thermal therapies.

  12. Simulation of temperature field for temperature-controlled radio frequency ablation using a hyperbolic bioheat equation and temperature-varied voltage calibration: a liver-mimicking phantom study.

    Science.gov (United States)

    Zhang, Man; Zhou, Zhuhuang; Wu, Shuicai; Lin, Lan; Gao, Hongjian; Feng, Yusheng

    2015-12-21

    This study aims at improving the accuracy of temperature simulation for temperature-controlled radio frequency ablation (RFA). We proposed a new voltage-calibration method in the simulation and investigated the feasibility of a hyperbolic bioheat equation (HBE) in the RFA simulation with longer durations and higher power. A total of 40 RFA experiments was conducted in a liver-mimicking phantom. Four mathematical models with multipolar electrodes were developed by the finite element method in COMSOL software: HBE with/without voltage calibration, and the Pennes bioheat equation (PBE) with/without voltage calibration. The temperature-varied voltage calibration used in the simulation was calculated from an experimental power output and temperature-dependent resistance of liver tissue. We employed the HBE in simulation by considering the delay time τ of 16 s. First, for simulations by each kind of bioheat equation (PBE or HBE), we compared the differences between the temperature-varied voltage-calibration and the fixed-voltage values used in the simulations. Then, the comparisons were conducted between the PBE and the HBE in the simulations with temperature-varied voltage calibration. We verified the simulation results by experimental temperature measurements on nine specific points of the tissue phantom. The results showed that: (1) the proposed voltage-calibration method improved the simulation accuracy of temperature-controlled RFA for both the PBE and the HBE, and (2) for temperature-controlled RFA simulation with the temperature-varied voltage calibration, the HBE method was 0.55 °C more accurate than the PBE method. The proposed temperature-varied voltage calibration may be useful in temperature field simulations of temperature-controlled RFA. Besides, the HBE may be used as an alternative in the simulation of long-duration high-power RFA.

  13. Novel conformal technique to reduce staircasing artifacts at material boundaries for FDTD modeling of the bioheat equation

    Energy Technology Data Exchange (ETDEWEB)

    Neufeld, E [Foundation for Research on Information Technologies in Society (IT' IS), ETH Zurich, 8092 Zurich (Switzerland); Chavannes, N [Foundation for Research on Information Technologies in Society (IT' IS), ETH Zurich, 8092 Zurich (Switzerland); Samaras, T [Radiocommunications Laboratory, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Kuster, N [Foundation for Research on Information Technologies in Society (IT' IS), ETH Zurich, 8092 Zurich (Switzerland)

    2007-08-07

    The modeling of thermal effects, often based on the Pennes Bioheat Equation, is becoming increasingly popular. The FDTD technique commonly used in this context suffers considerably from staircasing errors at boundaries. A new conformal technique is proposed that can easily be integrated into existing implementations without requiring a special update scheme. It scales fluxes at interfaces with factors derived from the local surface normal. The new scheme is validated using an analytical solution, and an error analysis is performed to understand its behavior. The new scheme behaves considerably better than the standard scheme. Furthermore, in contrast to the standard scheme, it is possible to obtain with it more accurate solutions by increasing the grid resolution.

  14. An advanced computational bioheat transfer model for a human body with an embedded systemic circulation.

    Science.gov (United States)

    Coccarelli, Alberto; Boileau, Etienne; Parthimos, Dimitris; Nithiarasu, Perumal

    2016-10-01

    In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat

  15. Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

    Energy Technology Data Exchange (ETDEWEB)

    Kudryashov, Nikolay A.; Shilnikov, Kirill E. [National Research Nuclear University MEPhI, Department of Applied Mathematics, Moscow (Russian Federation)

    2016-06-08

    Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumor tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.

  16. Modelling the impact of blood flow on the temperature distribution in the human eye and the orbit: fixed heat transfer coefficients versus the Pennes bioheat model versus discrete blood vessels

    Energy Technology Data Exchange (ETDEWEB)

    Flyckt, V M M; Raaymakers, B W; Lagendijk, J J W [Department of Radiotherapy, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands)

    2006-10-07

    Prediction of the temperature distribution in the eye depends on how the impact of the blood flow is taken into account. Three methods will be compared: a simplified eye anatomy that applies a single heat transfer coefficient to describe all heat transport mechanisms between the sclera and the body core, a detailed eye anatomy in which the blood flow is accounted for either by the bioheat approach, or by including the discrete vasculature in the eye and the orbit. The comparison is done both for rabbit and human anatomies, normo-thermally and when exposed to homogeneous power densities. The first simplified model predicts much higher temperatures than the latter two. It was shown that the eye is very hard to heat when taking physiological perfusion correctly into account. It was concluded that the heat transfer coefficient describing the heat transport from the sclera to the body core reported in the literature for the first simplified model is too low. The bioheat approach is appropriate for a first-order approximation of the temperature distribution in the eye when exposed to a homogeneous power density, but the discrete vasculature down to 0.2 mm in diameter needs to be taken into account when the heterogeneity of the temperature distribution at a mm scale is of interest.

  17. Modelling the impact of blood flow on the temperature distribution in the human eye and the orbit: fixed heat transfer coefficients versus the Pennes bioheat model versus discrete blood vessels

    International Nuclear Information System (INIS)

    Flyckt, V M M; Raaymakers, B W; Lagendijk, J J W

    2006-01-01

    Prediction of the temperature distribution in the eye depends on how the impact of the blood flow is taken into account. Three methods will be compared: a simplified eye anatomy that applies a single heat transfer coefficient to describe all heat transport mechanisms between the sclera and the body core, a detailed eye anatomy in which the blood flow is accounted for either by the bioheat approach, or by including the discrete vasculature in the eye and the orbit. The comparison is done both for rabbit and human anatomies, normo-thermally and when exposed to homogeneous power densities. The first simplified model predicts much higher temperatures than the latter two. It was shown that the eye is very hard to heat when taking physiological perfusion correctly into account. It was concluded that the heat transfer coefficient describing the heat transport from the sclera to the body core reported in the literature for the first simplified model is too low. The bioheat approach is appropriate for a first-order approximation of the temperature distribution in the eye when exposed to a homogeneous power density, but the discrete vasculature down to 0.2 mm in diameter needs to be taken into account when the heterogeneity of the temperature distribution at a mm scale is of interest

  18. 3D discrete angiogenesis dynamic model and stochastic simulation for the assessment of blood perfusion coefficient and impact on heat transfer between nanoparticles and malignant tumors.

    Science.gov (United States)

    Yifat, Jonathan; Gannot, Israel

    2015-03-01

    Early detection of malignant tumors plays a crucial role in the survivability chances of the patient. Therefore, new and innovative tumor detection methods are constantly searched for. Tumor-specific magnetic-core nano-particles can be used with an alternating magnetic field to detect and treat tumors by hyperthermia. For the analysis of the method effectiveness, the bio-heat transfer between the nanoparticles and the tissue must be carefully studied. Heat diffusion in biological tissue is usually analyzed using the Pennes Bio-Heat Equation, where blood perfusion plays an important role. Malignant tumors are known to initiate an angiogenesis process, where endothelial cell migration from neighboring vasculature eventually leads to the formation of a thick blood capillary network around them. This process allows the tumor to receive its extensive nutrition demands and evolve into a more progressive and potentially fatal tumor. In order to assess the effect of angiogenesis on the bio-heat transfer problem, we have developed a discrete stochastic 3D model & simulation of tumor-induced angiogenesis. The model elaborates other angiogenesis models by providing high resolution 3D stochastic simulation, capturing of fine angiogenesis morphological features, effects of dynamic sprout thickness functions, and stochastic parent vessel generator. We show that the angiogenesis realizations produced are well suited for numerical bio-heat transfer analysis. Statistical study on the angiogenesis characteristics was derived using Monte Carlo simulations. According to the statistical analysis, we provide analytical expression for the blood perfusion coefficient in the Pennes equation, as a function of several parameters. This updated form of the Pennes equation could be used for numerical and analytical analyses of the proposed detection and treatment method. Copyright © 2014 Elsevier Inc. All rights reserved.

  19. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

    Science.gov (United States)

    Murase, Kenya

    2016-01-01

    Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

  20. ANALYSIS OF NON-FOURIER THERMAL BEHAVIOUR FOR MULTI-LAYER SKIN MODEL

    Directory of Open Access Journals (Sweden)

    Kuo-Chi Liu

    2011-01-01

    Full Text Available This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

  1. The theoretical and experimental evaluation of the heat balance in perfused tissue

    NARCIS (Netherlands)

    Crezee, J.; Mooibroek, J.; Lagendijk, J. J.; van Leeuwen, G. M.

    1994-01-01

    Accurate treatment planning is necessary for the successful application of hyperthermia in the clinic. The validity of four different bioheat models or combinations of models is evaluated: the conventional bioheat transfer equation, the limited effective conductivity model, a mixed heat

  2. Potential for PET scanning as an aid to heat transfer modeling

    International Nuclear Information System (INIS)

    Samulski, T.V.; Harris, C.; Winget, J.M.; Dewhirst, M.W.

    1987-01-01

    Positron Emission Tomography (PET) using /sup 68/Ga labelled microspheres (15μ diam.) for quantitative imaging of perfusion is being investigated for its potential to aid in verification of parameter estimation techniques. Such techniques have been used in bioheat transfer modeling where direct measurement of perfusion has not been possible. Perfusion is needed, to utilize bioheat transfer to predict temperatures between measured points during hyperthermia therapy. A preliminary study showing that PET could be used for verification of parameter estimation was done by heating a melanoma in a dog in which multiple thermometry catheters were placed in a central plane. Microspheres were injected at the end of a one hour heat treatment session before power down. CT and PET images of the same plane were aligned so that relative counts/pixel in 2 cm regions of interest of the PET image were measured along several catheter tracks. In all tracks measured an inverse correlation was shown between relative perfusion and temperature along the catheter during thermal steady state. These data strongly imply that PET scans obtained in the manner described bear relevance to bioheat transfer and for verification of perfusion in heated tissues as estimated by heat transfer modeling

  3. Electron transfer dynamics: Zusman equation versus exact theory

    International Nuclear Information System (INIS)

    Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

    2009-01-01

    The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

  4. Effects of microwave heating on the thermal states of biological tissues

    African Journals Online (AJOL)

    A mathematical analysis of microwave heating equations in one-dimensional multi-layer model has been discussed. Maxwell's equations and transient bioheat transfer equation were numerically calculated by using finite difference method to predict the effects of thermal physical properties on the transient temperature of ...

  5. Effects of microwave heating on the thermal states of biological tissues

    African Journals Online (AJOL)

    Effects of microwave heating on the thermal states of biological tissues. Nabil TM El-dabe, Mona AA Mohamed, Asma F El-Sayed. Abstract. A mathematical analysis of microwave heating equations in one-dimensional multi-layer model has been discussed. Maxwell's equations and transient bioheat transfer equation were ...

  6. Numerical analysis for the conjugate heat transfer of skin under various temperature conditions of contrast therapy

    Energy Technology Data Exchange (ETDEWEB)

    Park, Da Ae; Oh, Han Nah; Choi, Hyoung Gwon [Dept. of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of); Jeon, Byoung Jin; Kim, Eun Jeoung; Lee, Seung Deok [Yonsei University, Seoul (Korea, Republic of)

    2015-11-15

    In this paper, the contrast therapy of skin was numerically investigated by solving the conjugate heat transfer problem. A finite volume method based on the SIMPLE algorithm was adopted to solve the axisymmetric incompressible Navier-Stokes equations, coupled with an energy equation. These equations are strongly coupled with the Pennes bio-heat equation in order to consider the effect of blood perfusion rate. We investigated the thermal response of skin at some selected depths for various input temperature profiles of a stimulator for contrast therapy. From the numerical simulations, the regions with cold/hot threshold temperatures were found for five input temperature profiles. It was shown that the temperature varies mildly for different input profiles as the depth increases, owing to the Pennes effect. The input temperatures for effective hot/cold stimulation of dermis layer were found to be 47 degrees C and 7 degrees C, respectively. The present numerical results will be used for finding an optimal temperature profile of a stimulator for contrast therapy.

  7. Modeling skin cooling using optical windows and cryogens during laser induced hyperthermia in a multilayer vascularized tissue

    International Nuclear Information System (INIS)

    Singh, Rupesh; Das, Koushik; Okajima, Junnosuke; Maruyama, Shigenao; Mishra, Subhash C.

    2015-01-01

    This article deals with the spatial and the temporal evolution of tissue temperature during skin surface cooled laser induced hyperthermia. Three different skin surface cooling methodologies viz., optical window contact cooling, cryogenic spray cooling and cryogen cooled optical window contact cooling are considered. Sapphire, yttrium aluminum garnet, lithium tantalate, and magnesium oxide doped lithium niobate are the considered optical windows. The cryogens considered are liquid CO_2 and R1234yf. Heat transfer in the multilayer skin tissue embedded with thermally significant blood vessels pairs is modeled using the Pennes and Weinbaum–Jiji bioheat equations. Weinbaum–Jiji bioheat equation is used for the vascularized tissue. Laser transport in the tissue is modeled using the radiative transfer equation. Axial and radial (skin surface) temperature distributions for different combinations of optical windows and cryogens are analyzed. Liquid CO_2 cooled yttrium aluminum garnet is found to be the best surface cooling mechanism. - Highlights: • Skin surface cooled laser induced hyperthermia is studied. • A multi-layer 2-D cylindrical tissue geometry is considered. • Both Pennes and Weinbaum–Jiji bioheat models are considered. • Laser transport in the tissue is modeled using discrete ordinate method. • Results for 4 optical windows and 2 cryogens for skin cooling are presented.

  8. Bioheat model evaluations of laser effects on tissues: role of water evaporation and diffusion

    Science.gov (United States)

    Nagulapally, Deepthi; Joshi, Ravi P.; Thomas, Robert J.

    2011-03-01

    A two-dimensional, time-dependent bioheat model is applied to evaluate changes in temperature and water content in tissues subjected to laser irradiation. Our approach takes account of liquid-to-vapor phase changes and a simple diffusive flow of water within the biotissue. An energy balance equation considers blood perfusion, metabolic heat generation, laser absorption, and water evaporation. The model also accounts for the water dependence of tissue properties (both thermal and optical), and variations in blood perfusion rates based on local tissue injury. Our calculations show that water diffusion would reduce the local temperature increases and hot spots in comparison to simple models that ignore the role of water in the overall thermal and mass transport. Also, the reduced suppression of perfusion rates due to tissue heating and damage with water diffusion affect the necrotic depth. Two-dimensional results for the dynamic temperature, water content, and damage distributions will be presented for skin simulations. It is argued that reduction in temperature gradients due to water diffusion would mitigate local refractive index variations, and hence influence the phenomenon of thermal lensing. Finally, simple quantitative evaluations of pressure increases within the tissue due to laser absorption are presented.

  9. Improved numerical modelling of heat transfer in human tissue exposed to RF

    International Nuclear Information System (INIS)

    Prishvin, Mikheil; Zaridze, Revaz; Bit-Babik, Georgi; Faraone, Antonio

    2010-01-01

    Full text: A novel numerical model to simulate thermal response of human body tissues exposed to RF energy is presented in this article. It is based on a new algorithm for the construction of a realistic blood vessel network, a new model of blood flow velocity distribution and an approach to solve the bio-heat equation in human tissue with variable and initially unknown blood temperature distribution. The algorithm generates a discrete 3D representation of both arterial and venous vascular networks and a continuous blood velocity vector field for arbitrary enclosed geome tries required to represent the complex anatomy of human body and blood flow. The results obtained in this article by applying the developed method to realistic exposure con ditions demonstrates relative difference in thermal response of the exposed tissue compared to results obtained by conventional bio-heat equation with constant blood perfusion and temperature. The developed technique may provide more accurate and realistic modelling in thermal dosimetry studies of human body RF exposure.

  10. Some fundamental considerations of the equation of radiative transfer

    International Nuclear Information System (INIS)

    Kuriyan, J.G.; Sudarshan, E.C.G.

    1978-10-01

    The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references

  11. Interference-exact radiative transfer equation

    DEFF Research Database (Denmark)

    Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani

    2017-01-01

    Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....

  12. Bioenergy for District Bioheating System (DBS) from eucalyptus residues in a European coal-producing region

    International Nuclear Information System (INIS)

    Paredes-Sánchez, José P.; López-Ochoa, Luis M.; López-González, Luis M.; Xiberta-Bernat, Jorge

    2016-01-01

    Highlights: • The paper introduces a combined method to evaluate bioenergy. • Forest biomass needs to be studied as a fuel supplier and carbon sink. • The forests under study produce about 28 kt dry and 0.15 Mt CO 2 per year. • Examined a District Bioheating System (DBS) with the available biomass. - Abstract: Since forest biomass can substitute for CO 2 -emitting fossil fuels in the energy sector, forest management can greatly affect the global carbon cycle. Eucalyptus globulus has adapted very well in the coal region of the Principality of Asturias (Northwestern Spain) and has become highly regarded as a valuable raw material for the pulp and paper industry. In the present work, the Eucalyptus globulus is studied as a key natural energy source in order to improve existing methods and develop new ways of optimizing the evaluation and use of both forest biomass and woody residue in energy systems, in accordance with sustainable forestry industry safety and environmental requirements. The feasibility of utilizing forest biomass instead of natural gas in a District Bioheating System (DBS) has been examined based on an analysis of its economical and environmental impacts.

  13. Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface.

    Science.gov (United States)

    Ezzat, Magdy A; El-Bary, Alaa A; Al-Sowayan, Noorah S

    2016-10-01

    A fractional model of Bioheat equation for describing quantitatively the thermal responses of skin tissue under sinusoidal heat flux conditions on skin surface is given. Laplace transform technique is used to obtain the solution in a closed form. The resulting formulation is applied to one-dimensional application to investigate the temperature distribution in skin with instantaneous surface heating for different cases. According to the numerical results and its graphs, conclusion about the fractional bioheat transfer equation has been constructed. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature. The comparisons are made with the results obtained in the case of the absence of time-fractional order. © 2016 Japanese Society of Animal Science. © 2016 Japanese Society of Animal Science.

  14. A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

    Science.gov (United States)

    Haisch, B. M.

    1976-01-01

    A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

  15. Methods for the solution of the two-dimensional radiation-transfer equation

    International Nuclear Information System (INIS)

    Weaver, R.; Mihalas, D.; Olson, G.

    1982-01-01

    We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed

  16. Radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems

    International Nuclear Information System (INIS)

    Liu, L.H.; Zhang, L.; Tan, H.P.

    2006-01-01

    In graded index medium, the ray goes along a curved path determined by Fermat principle, and the curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectory, the methods not based on ray-tracing technique need to be developed for the solution of radiative transfer in graded index medium. For this purpose, in this paper the streaming operator along a curved ray trajectory in original radiative transfer equation for graded index medium is transformed and expressed in spatial and angular ordinates and the radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems are derived. The conservative and the non-conservative forms of radiative transfer equation for three-dimensional graded index medium are given, which can be used as base equations to develop the numerical simulation methods, such as finite volume method, discrete ordinates method, and finite element method, for radiative transfer in graded index medium in cylindrical and spherical coordinate systems

  17. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    Science.gov (United States)

    Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

    2018-01-01

    In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  18. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    Directory of Open Access Journals (Sweden)

    Azmat Ullah

    Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  19. Thermal non-equilibrium heat transfer in a porous cavity in the presence of bio-chemical heat source

    Directory of Open Access Journals (Sweden)

    Nazari Mohsen

    2015-01-01

    Full Text Available This paper is concerned with thermal non-equilibrium natural convection in a square cavity filled with a porous medium in the presence of a biomass which is transported in the cavity. The biomass can consume a secondary moving substrate. The physics of the presented problem is related to the analysis of heat and mass transfer in a composting process that controlled by internal heat generation. The intensity of the bio-heat source generated in the cavity is equal to the rate of consumption of the substrate by the biomass. It is assumed that the porous medium is homogeneous and isotropic. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. A simplified Monod model is introduced along with the governing equations to describe the consumption of the substrate by the biomass. In other word, the transient biochemical heat source which is dependent on a solute concentration is considered in the energy equations. Investigation of the biomass activity and bio-chemical heat generation in the case of thermal non-equilibrium assumption has not been considered in the literature and they are open research topics. The effects of thermal non-equilibrium model on heat transfer, flow pattern and biomass transfer are investigated. The effective parameters which have a direct impact on the generated bio-chemical heat source are also presented. The influences of the non-dimensional parameters such as fluid-to-solid conductivity ratio on the temperature distribution are presented.

  20. A computational procedure for finding multiple solutions of convective heat transfer equations

    International Nuclear Information System (INIS)

    Mishra, S; DebRoy, T

    2005-01-01

    In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations

  1. The potential demand for bioenergy in residential heating applications (bio-heat) in the UK based on a market segment analysis

    International Nuclear Information System (INIS)

    Jablonski, S.; Pantaleo, A.; Bauen, A.; Pearson, P.; Panoutsou, C.; Slade, R.

    2008-01-01

    How large is the potential demand for bio-heat in the UK? Whilst most research has focused on the supply of biomass for energy production, an understanding of the potential demand is crucial to the uptake of heat from bioenergy. We have designed a systematic framework utilising market segmentation techniques to assess the potential demand for biomass heat in the UK. First, the heat market is divided into relevant segments, characterised in terms of their final energy consumption, technological and fuel supply options. Second, the key technical, economic and organisational factors that affect the uptake of bioenergy in each heat segment are identified, classified and then analysed to reveal which could be strong barriers, which could be surmounted easily, and for which bioenergy heat represents an improvement compared to alternatives. The defined framework is applied to the UK residential sector. We identify provisionally the most promising market segments for bioenergy heat, and their current levels of energy demand. We find that, depending on the assumptions, the present potential demand for bio-heat in the UK residential sector ranges between 3% (conservative estimate) and 31% (optimistic estimate) of the total energy consumed in the heat market. (author)

  2. A User-Friendly Software Package for HIFU Simulation

    Science.gov (United States)

    Soneson, Joshua E.

    2009-04-01

    A freely-distributed, MATLAB (The Mathworks, Inc., Natick, MA)-based software package for simulating axisymmetric high-intensity focused ultrasound (HIFU) beams and their heating effects is discussed. The package (HIFU_Simulator) consists of a propagation module which solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and a heating module which solves Pennes' bioheat transfer (BHT) equation. The pressure, intensity, heating rate, temperature, and thermal dose fields are computed, plotted, the output is released to the MATLAB workspace for further user analysis or postprocessing.

  3. Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.

    Science.gov (United States)

    Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

    2017-01-02

    Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.

  4. A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, J.M., E-mail: jmzhao@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); Tan, J.Y., E-mail: tanjy@hit.edu.cn [School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China); Liu, L.H., E-mail: lhliu@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China)

    2013-01-01

    A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

  5. Laser radiation in active amplifying media treated as a transport problem - Transfer equation derived and exactly solved

    Science.gov (United States)

    Gupta, S. R. D.; Gupta, Santanu D.

    1991-10-01

    The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein's A, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the 'rate equations' to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

  6. Spatial discretizations for self-adjoint forms of the radiative transfer equations

    International Nuclear Information System (INIS)

    Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

    2006-01-01

    There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

  7. General Eulerian formulation of the comoving-frame equation of radiative transfer

    International Nuclear Information System (INIS)

    Riffert, H.

    1986-01-01

    For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. 9 references

  8. Application of the Radiative Transfer Equation (RTE) to Scattering by ...

    African Journals Online (AJOL)

    Application of the Radiative Transfer Equation (RTE) to Scattering by a Dust Aerosol Layer. ... Incident radiation in its journey through the atmosphere before reaching the earth surface encounters particles of different sizes and composition such as dust aerosols resulting in interactions that lead to absorption and scattering.

  9. On similarity and scaling of the radiative transfer equation

    International Nuclear Information System (INIS)

    Mitrescu, C.; Stephens, G.L.

    2004-01-01

    The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced

  10. Global existence of a generalized solution for the radiative transfer equations

    International Nuclear Information System (INIS)

    Golse, F.; Perthame, B.

    1984-01-01

    We prove global existence of a generalized solution of the radiative transfer equations, extending Mercier's result to the case of a layer with an initially cold area. Our Theorem relies on the results of Crandall and Ligett [fr

  11. Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

    International Nuclear Information System (INIS)

    Rozanov, Vladimir V.; Vountas, Marco

    2014-01-01

    Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented

  12. Application research of computational mass-transfer differential equation in MBR concentration field simulation.

    Science.gov (United States)

    Li, Chunqing; Tie, Xiaobo; Liang, Kai; Ji, Chanjuan

    2016-01-01

    After conducting the intensive research on the distribution of fluid's velocity and biochemical reactions in the membrane bioreactor (MBR), this paper introduces the use of the mass-transfer differential equation to simulate the distribution of the chemical oxygen demand (COD) concentration in MBR membrane pool. The solutions are as follows: first, use computational fluid dynamics to establish a flow control equation model of the fluid in MBR membrane pool; second, calculate this model by adopting direct numerical simulation to get the velocity field of the fluid in membrane pool; third, combine the data of velocity field to establish mass-transfer differential equation model for the concentration field in MBR membrane pool, and use Seidel iteration method to solve the equation model; last but not least, substitute the real factory data into the velocity and concentration field model to calculate simulation results, and use visualization software Tecplot to display the results. Finally by analyzing the nephogram of COD concentration distribution, it can be found that the simulation result conforms the distribution rule of the COD's concentration in real membrane pool, and the mass-transfer phenomenon can be affected by the velocity field of the fluid in membrane pool. The simulation results of this paper have certain reference value for the design optimization of the real MBR system.

  13. On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

    International Nuclear Information System (INIS)

    Zhao, J.M.; Tan, J.Y.; Liu, L.H.

    2012-01-01

    Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

  14. In Vivo Radiofrequency Heating in Swine in a 3T (123.2 MHz) Birdcage Whole-Body Coil

    Science.gov (United States)

    Shrivastava, Devashish; Utecht, Lynn; Tian, Jinfeng; Hughes, John; Vaughan, J. Thomas

    2014-01-01

    Purpose To study in vivo radiofrequency (RF) heating produced due to power deposition from a 3T (Larmour frequency = 123.2 MHz), birdcage, whole-body coil. Methods The RF heating was simulated in a digital swine by solving the mechanistic generic bioheat transfer model (GBHTM) and the conventional, empirical Pennes bioheat transfer equation for the following two cases: (1) when the porcine head was in the isocenter, and (2) when the porcine trunk was in the isocenter. The simulation results were validated by making direct fluoroptic temperature measurements in the skin, brain, simulated hot regions, and rectum of ten swine (Case 1, N= 5, mean animal weight = 84.03 ± 6.85 kg, Whole-body average SAR = 2.65 ± 0.22 W/kg; Case 2, N= 5, mean animal weight = 81.59 ± 6.23 kg, Whole-body average SAR = 2.77 ± 0.26 W/kg) during one hour of exposure to a turbo spin echo sequence. Results The GBHTM simulated the RF heating more accurately compared to the Pennes equation. In vivo temperatures exceeded safe temperature thresholds with allowable SAR exposures. Hot regions may be produced deep inside the body, away from the skin. Conclusion SAR exposures to produce safe temperature thresholds may need re-investigation. PMID:24259413

  15. Exact traveling wave solutions for a new nonlinear heat transfer equation

    Directory of Open Access Journals (Sweden)

    Gao Feng

    2017-01-01

    Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

  16. Transfer equations for spectral densities of inhomogeneous MHD turbulence

    International Nuclear Information System (INIS)

    Tu, C.-Y.; Marsch, E.

    1990-01-01

    On the basis of the dynamic equations governing the evolution of magnetohydrodynamic fluctuations expressed in terms of Elsaesser variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented describing the evolutions of the energy spectrum e ± and of the residual energy spectra e R and e S of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e ± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for e R the triple correlations do not correspond to an 'energy' conserving process, but also represent a nonlinear source term for e R . If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations. (author)

  17. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

    International Nuclear Information System (INIS)

    Sun, Wenjun; Jiang, Song; Xu, Kun

    2015-01-01

    The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach

  18. A non linear half space problem for radiative transfer equations. Application to the Rosseland approximation

    International Nuclear Information System (INIS)

    Sentis, R.

    1984-07-01

    The radiative transfer equations may be approximated by a non linear diffusion equation (called Rosseland equation) when the mean free paths of the photons are small with respect to the size of the medium. Some technical assomptions are made, namely about the initial conditions, to avoid any problem of initial layer terms

  19. Anomalous properties of heat diffusion in living tissue caused by branching artery network. Qualitative description

    OpenAIRE

    Lubashevsky, I. A.; Gafiychuk, V. V.; Datsko, B. Y.

    2002-01-01

    We analyze the effect of blood flow through large arteries of peripheral circulation on heat transfer in living tissue. Blood flow in such arteries gives rise to fast heat propagation over large scales, which is described in terms of heat superdiffusion. The corresponding bioheat heat equation is derived. In particular, we show that under local strong heating of a small tissue domain the temperature distribution inside the surrounding tissue is affected substantially by heat superdiffusion.

  20. Time-dependent simplified PN approximation to the equations of radiative transfer

    International Nuclear Information System (INIS)

    Frank, Martin; Klar, Axel; Larsen, Edward W.; Yasuda, Shugo

    2007-01-01

    The steady-state simplified P N approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified P N (SP N ) equations (up to N = 3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SP N equations. Second, we use an approach similar to the original derivation of the steady-state SP N equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium, Ann. Nucl. Energy 24 (1997) 1035-1055.

  1. About Navier-Stokes Equation in the Theory of Convective Heat Transfer

    Science.gov (United States)

    Davidzon, M. Y.

    2017-10-01

    A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).

  2. Towards a General Equation for the Survival of Microbes Transferred between Solar System Bodies

    Science.gov (United States)

    Fries, M.; Steele, A.

    2014-01-01

    It should be possible to construct a general equation describing the survival of microbes transferred between Solar System bodies. Such an equation will be useful for constraining the likelihood of transfer of viable organisms between bodies throughout the lifetime of the Solar System, and for refining Planetary Protection constraints placed on future missions. We will discuss the construction of such an equation, present a plan for definition of pertinent factors, and will describe what research will be necessary to quantify those factors. Description: We will examine the case of microbes transferred between Solar System bodies as residents in meteorite material ejected from one body (the "intial body") and deposited on another (the "target body"). Any microbes transferred in this fashion will experience four distinct phases between their initial state on the initial body, up to the point where they colonize the target body. Each of these phases features phenomena capable of reducing or exterminating the initial microbial population. They are: 1) Ejection: Material is ejected from the initial body, imparting shock followed by rapid desiccation and cooling. 2) Transport: Material travels through interplanetary space to the target body, exposing a hypothetical microbial population to extended desiccation, irradiation, and temperature extremes. 3) Infall: Material is deposited on the target body, diminishing the microbial population through shock, mass loss, and heating. 4) Adaptation: Any microbes which survive the previous three phases must then adapt to new chemophysical conditions of the target body. Differences in habitability between the initial and target bodies dominate this phase. A suitable general-form equation can be assembled from the above factors by defining the initial number of microbes in an ejected mass and applying multiplicitive factors based on the physical phenomena inherent to each phase. It should be possible to present the resulting equation

  3. Simplified equations for transient heat transfer problems at low Fourier numbers

    DEFF Research Database (Denmark)

    Christensen, Martin Gram; Adler-Nissen, Jens

    2015-01-01

    and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...

  4. Optimization and real-time control for laser treatment of heterogeneous soft tissues.

    Science.gov (United States)

    Feng, Yusheng; Fuentes, David; Hawkins, Andrea; Bass, Jon M; Rylander, Marissa Nichole

    2009-01-01

    Predicting the outcome of thermotherapies in cancer treatment requires an accurate characterization of the bioheat transfer processes in soft tissues. Due to the biological and structural complexity of tumor (soft tissue) composition and vasculature, it is often very difficult to obtain reliable tissue properties that is one of the key factors for the accurate treatment outcome prediction. Efficient algorithms employing in vivo thermal measurements to determine heterogeneous thermal tissues properties in conjunction with a detailed sensitivity analysis can produce essential information for model development and optimal control. The goals of this paper are to present a general formulation of the bioheat transfer equation for heterogeneous soft tissues, review models and algorithms developed for cell damage, heat shock proteins, and soft tissues with nanoparticle inclusion, and demonstrate an overall computational strategy for developing a laser treatment framework with the ability to perform real-time robust calibrations and optimal control. This computational strategy can be applied to other thermotherapies using the heat source such as radio frequency or high intensity focused ultrasound.

  5. Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy.

    Science.gov (United States)

    Kumar, Dinesh; Rai, K N

    2017-07-01

    In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy. Copyright © 2017 Elsevier Ltd. All rights reserved.

  6. A study on the boundary condition for analysis of bio-heat equation according to light irradiation

    Energy Technology Data Exchange (ETDEWEB)

    Ko, Dong Guk; Bae, Sung Woo; Im, Ik Tae [Chunbuk Natinal University, Junju (Korea, Republic of)

    2015-11-15

    In this study, the temperature change in an imitational biological tissue, when its surface is irradiated with bio-light, was measured by experiments. Using the experimental data, an equation for temperature as a function of time was developed in order to use it as a boundary condition in numerical studies for the model. The temperature profile was measured along the depth for several wavelengths and distances of the light source from the tissue. It was found that the temperature of the tissue increased with increasing wavelength and irradiation time; however, the difference in the temperatures with red light and near infrared light was not large. The numerical analysis results obtained by using the developed equation as boundary condition show good agreement with the measured temperatures.

  7. Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

    Science.gov (United States)

    Zhang, Chuang; Guo, Zhaoli; Chen, Songze

    2017-12-01

    An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

  8. In vivo radiofrequency heating in swine in a 3T (123.2-MHz) birdcage whole body coil.

    Science.gov (United States)

    Shrivastava, Devashish; Utecht, Lynn; Tian, Jinfeng; Hughes, John; Vaughan, J Thomas

    2014-10-01

    To study in vivo radiofrequency (RF) heating produced due to power deposition from a 3T (Larmour frequency = 123.2 MHz), birdcage, whole body coil. The RF heating was simulated in a digital swine by solving the mechanistic generic bioheat transfer model (GBHTM) and the conventional, empirical Pennes bioheat transfer equation for two cases: 1) when the swine head was in the isocenter and 2) when the swine trunk was in the isocenter. The simulation results were validated by making direct fluoroptic temperature measurements in the skin, brain, simulated hot regions, and rectum of 10 swine (case 1: n = 5, mean animal weight = 84.03 ± 6.85 kg, whole body average SAR = 2.65 ± 0.22 W/kg; case 2: n = 5, mean animal weight = 81.59 ± 6.23 kg, whole body average SAR = 2.77 ± 0.26 W/kg) during 1 h of exposure to a turbo spin echo sequence. The GBHTM simulated the RF heating more accurately compared with the Pennes equation. In vivo temperatures exceeded safe temperature thresholds with allowable SAR exposures. Hot regions may be produced deep inside the body, away from the skin. SAR exposures that produce safe temperature thresholds need reinvestigation. Copyright © 2013 Wiley Periodicals, Inc.

  9. The impact of thermal wave characteristics on thermal dose distribution during thermal therapy: A numerical study

    International Nuclear Information System (INIS)

    Shih, T.-C.; Kou, H.-S.; Liauh, C.-T.; Lin, W.-L.

    2005-01-01

    The aim of this study was to investigate the effects of the propagation speed of a thermal wave in terms of the thermal relaxation time on the temperature/thermal dose distributions in living tissue during thermal therapies. The temperature field in tissue was solved by the finite difference method, and the thermal dose was calculated from the formulation proposed by Sapareto and Dewey [Int. J. Radiat. Oncol. Biol. Phys. 10, 787-800 (1984)]. Under the same total deposited energy, for a rapid heating process the time lagging behavior of the peak temperature became pronounced and the level of the peak temperature was decreased with increasing the thermal relaxation time. When the heating duration was longer than the thermal relaxation time of tissues, there was no significant difference between the thermal dose distributions with/without considering the effect of the thermal relaxation time. In other words, when the heating duration is comparable to or shorter than the thermal relaxation time of tissue, the results of the wave bioheat transfer equation (WBHTE) are fully different from that of the Pennes' bioheat transfer equation (PBHTE). Besides, for a rapid heating process the dimension of thermal lesion was still significantly affected by perfusion, because this is what is predicted by the WBHTE but not by the PBHTE, i.e., the wave feature of the temperature field cannot fully be predicted by the PBHTE

  10. Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations

    Energy Technology Data Exchange (ETDEWEB)

    Iles-Smith, Jake, E-mail: Jakeilessmith@gmail.com [Controlled Quantum Dynamics Theory, Imperial College London, London SW7 2PG (United Kingdom); Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Department of Photonics Engineering, DTU Fotonik, Ørsteds Plads, 2800 Kongens Lyngby (Denmark); Dijkstra, Arend G. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Lambert, Neill [CEMS, RIKEN, Saitama 351-0198 (Japan); Nazir, Ahsan, E-mail: ahsan.nazir@manchester.ac.uk [Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom)

    2016-01-28

    We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.

  11. A new perspective on the electron transfer: recovering the Butler-Volmer equation in non-equilibrium thermodynamics.

    Science.gov (United States)

    Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger

    2016-09-28

    Electron transfer reactions are commonly described by the phenomenological Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Although the general structure of the equation is well accepted, for modern electrochemical systems like batteries and fuel cells there is still intensive discussion about the specific dependencies of the coefficients. A general guideline for the derivation of Butler-Volmer type equations is missing in the literature. We derive very general relations of Butler-Volmer structure which are based on a rigorous non-equilibrium thermodynamic model and allow for adaption to a wide variety of electrochemical systems. We discuss the application of the new thermodynamic approach to different scenarios like the classical electron transfer reactions at metal electrodes and the intercalation process in lithium-iron-phosphate electrodes. Furthermore we show that under appropriate conditions also adsorption processes can lead to Butler-Volmer equations. We illustrate the application of our theory by a strongly simplified example of electroplating.

  12. Thermal interaction of short-pulsed laser focused beams with skin tissues

    International Nuclear Information System (INIS)

    Jiao Jian; Guo Zhixiong

    2009-01-01

    Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.

  13. Thermal interaction of short-pulsed laser focused beams with skin tissues

    Energy Technology Data Exchange (ETDEWEB)

    Jiao Jian; Guo Zhixiong [Department of Mechanical and Aerospace Engineering, Rutgers, State University of New Jersey, Piscataway, NJ 08854 (United States)], E-mail: guo@jove.rutgers.edu

    2009-07-07

    Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.

  14. Excitation transfer pathways in excitonic aggregates revealed by the stochastic Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Abramavicius, Vytautas, E-mail: vytautas.ab@gmail.com; Abramavicius, Darius, E-mail: darius.abramavicius@ff.vu.lt [Faculty of Physics, Department of Theoretical Physics, Vilnius University, Saulėtekio 9, LT-10222 Vilnius (Lithuania)

    2014-02-14

    We derive the stochastic Schrödinger equation for the system wave vector and use it to describe the excitation energy transfer dynamics in molecular aggregates. We suggest a quantum-measurement based method of estimating the excitation transfer time. Adequacy of the proposed approach is demonstrated by performing calculations on a model system. The theory is then applied to study the excitation transfer dynamics in a photosynthetic pigment-protein Fenna-Matthews-Olson (FMO) aggregate using both the Debye spectral density and the spectral density obtained from earlier molecular dynamics simulations containing strong vibrational high-frequency modes. The obtained results show that the excitation transfer times in the FMO system are affected by the presence of the vibrational modes; however, the transfer pathways remain the same.

  15. Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

    International Nuclear Information System (INIS)

    Tarvainen, Tanja; Vauhkonen, Marko; Kolehmainen, Ville; Arridge, Simon R; Kaipio, Jari P

    2005-01-01

    In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model

  16. Fire Intensity Data for Validation of the Radiative Transfer Equation

    Energy Technology Data Exchange (ETDEWEB)

    Blanchat, Thomas K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jernigan, Dann A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-01-01

    A set of experiments and test data are outlined in this report that provides radiation intensity data for the validation of models for the radiative transfer equation. The experiments were performed with lightly-sooting liquid hydrocarbon fuels that yielded fully turbulent fires 2 m diameter). In addition, supplemental measurements of air flow and temperature, fuel temperature and burn rate, and flame surface emissive power, wall heat, and flame height and width provide a complete set of boundary condition data needed for validation of models used in fire simulations.

  17. Effects of Thermal Resistance on One-Dimensional Thermal Analysis of the Epidermal Flexible Electronic Devices Integrated with Human Skin

    Science.gov (United States)

    Li, He; Cui, Yun

    2017-12-01

    Nowadays, flexible electronic devices are increasingly used in direct contact with human skin to monitor the real-time health of human body. Based on the Fourier heat conduction equation and Pennes bio-heat transfer equation, this paper deduces the analytical solutions of one - dimensional heat transfer for flexible electronic devices integrated with human skin under the condition of a constant power. The influence of contact thermal resistance between devices and skin is considered as well. The corresponding finite element model is established to verify the correctness of analytical solutions. The results show that the finite element analysis agrees well with the analytical solution. With bigger thermal resistance, temperature increase of skin surface will decrease. This result can provide guidance for the design of flexible electronic devices to reduce the negative impact that exceeding temperature leave on human skin.

  18. Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

    Energy Technology Data Exchange (ETDEWEB)

    Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

    2017-04-01

    The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

  19. Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

    Science.gov (United States)

    Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

    2018-04-01

    An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

  20. The response matrix discrete ordinates solution to the 1D radiative transfer equation

    International Nuclear Information System (INIS)

    Ganapol, Barry D.

    2015-01-01

    The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey–Greenstein scattering as an example. - Highlights: • Presents a new solution to the RTE called the response matrix DOM (RM/DOM). • Solution representations avoid the instability common in exponential solutions. • Explicit form in terms of matrix hyperbolic functions. • Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks. • Provides a more transparent numerical evaluation than found previously

  1. Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

    Science.gov (United States)

    Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

    2018-03-01

    In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

  2. Generalized solutions of the radiative transfer equations in a singular case

    International Nuclear Information System (INIS)

    Golse, F.; Perthame, B.

    1985-07-01

    This paper is devoted to the study of the radiative transfer equations (TR). First, we prove a global existence theorem, which allows a blow-up of the opacity σsub(ν)(E) when E → 0. Thus, it extends Mercier's previous result. This proof relies mainly on a non linear version of Hille-Yosida theorem. Then, we prove the uniqueness of the semigroup solving (TR), and some regularity results (in the class of functions with bounded variation). Finally, we prove the convergence of some splitting algorithms associated to (TR)

  3. State equation approximation of transfer matrices and its application to the phase domain calculation of electromagnetic transients

    International Nuclear Information System (INIS)

    Soysal, A.O.; Semlyen, A.

    1994-01-01

    A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time

  4. Solution of the time-dependent inertial-frame equation of radiative transfer in moving media to O(v/c)

    International Nuclear Information System (INIS)

    Mihalas, D.; Klein, R.I.

    1982-01-01

    A stable and efficient mixed-frame method has been formulated for the solution of the time-dependent equation of radiative transfer with full retention of all velocity dependent terms to O(ν/c). The method retains the simplicity of the differential operator found in the inertial frame while transforming the absorption and emission coefficients to the comoving frame keeping them isotropic. The method is ideally suited to continuum calculations. To correctly treat the time dependence of the radiation field over fluid-flow time increments, the velocity-dependent terms on the right-hand side of both the transfer and moment equations must be retained for consistency

  5. A Direct Radiative Transfer Equation Solver for Path Loss Calculation of Underwater Optical Wireless Channels

    KAUST Repository

    Li, Changping; Park, Ki-Hong; Alouini, Mohamed-Slim

    2014-01-01

    In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.

  6. A Direct Radiative Transfer Equation Solver for Path Loss Calculation of Underwater Optical Wireless Channels

    KAUST Repository

    Li, Changping

    2014-11-10

    In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.

  7. About application of the 'rough' net method for decision of the neutron transfer transient equation

    International Nuclear Information System (INIS)

    Seleznev, E.F.; Tarasenko, V.V.

    1995-01-01

    Method of the decision of a transient equation of the neutrons transfer is developed, which at preservation of necessary accuracy permits considerably to speed up a finding of the decision up to modeling of processes in reactor in real time. The transient equation of neutrons transfer in one-group diffusion approximation is decided by the finite-difference method. The calculating model of reactor is divided into rather large zones, where the currents on internal borders are away, and on external borders ones are a sum of currents on the borders of small-sized zones. For the decision of an equation in finite-difference kind the numerical scheme 'Time - integrate' is used, which permits to search the decision in a half-explicit kind with rather large temporary step. The decision for density of neutrons flux is determine by the SOR method. Under the conducted preliminary analysis of an algorithm efficiency it is possible to conclude, that the time of the decision on a computer can be reduced in 3 and more times, in depending on 'roughness' of a calculated net in comparison with computation on a complete net. The realized algorithm can be used as for scientific researches, and as neutron-physical block of the simulator. 6 refs., 1 fig

  8. Study on the key technologies of the Transfer Equipment Cask for Tokamak Equator Port Plug

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Buyun, E-mail: ayun@iim.ac.cn [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Gao, Lifu [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Cao, Huibin; Sun, Jian [Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Sun, Yuxiang; Song, Quanjun; Ma, Chengxue; Chang, Li; Shuang, Feng [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China)

    2014-12-15

    Highlights: • Design on Intelligent Air Transfer System (IATS) for Transfer Equipment Cask (TECA). • A rhombic-like parallel robot for docking with minimum misalignment. • Design on electro-hydraulic servo system of the TECA for Tokamak Equator Port Plug (TEPP) manipulation. • A control architecture with several algorithms and information acquired from sensors could be used by the TECA for Remote Handling (RH). - Abstract: The Transfer Equipment Cask (TECA) is a key solution for Remote Handling (RH) in Tokamak Equator Port Plug (TEPP) operations. From the perspectives of both engineering and technical designs of effective experiments on the TEPP, key technologies on these topics covering the TECA are required. According to conditions in ITER (International Thermonuclear Experimental Reactor) and features of the TEPP, this paper introduces the design of an Intelligent Air Transfer System (IATS) with an adaptive attitude and high precision positioning that transports a cask system of more than 30 tons from the Tokamak Building (TB) to the Hot Cell Building (HCB). Additionally, different actuators are discussed, and the hydraulic power drive is eventually selected and designed. A rhombic-like parallel robot is capable of being used for docking with minimum misalignment. Practical mechanisms of the cask system are presented for hostile environments. A control architecture with several algorithms and information acquired from sensors could be used by the TECA. These designs yield realistic and extended applications for the RH of ITER.

  9. Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

    Directory of Open Access Journals (Sweden)

    Sun Huan

    2016-01-01

    Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

  10. Testing the transferability of regression equations derived from small sub-catchments to a large area in central Sweden

    Directory of Open Access Journals (Sweden)

    C. Xu

    2003-01-01

    Full Text Available There is an ever increasing need to apply hydrological models to catchments where streamflow data are unavailable or to large geographical regions where calibration is not feasible. Estimation of model parameters from spatial physical data is the key issue in the development and application of hydrological models at various scales. To investigate the suitability of transferring the regression equations relating model parameters to physical characteristics developed from small sub-catchments to a large region for estimating model parameters, a conceptual snow and water balance model was optimised on all the sub-catchments in the region. A multiple regression analysis related model parameters to physical data for the catchments and the regression equations derived from the small sub-catchments were used to calculate regional parameter values for the large basin using spatially aggregated physical data. For the model tested, the results support the suitability of transferring the regression equations to the larger region. Keywords: water balance modelling,large scale, multiple regression, regionalisation

  11. Modeling Xenon Tank Pressurization using One-Dimensional Thermodynamic and Heat Transfer Equations

    Science.gov (United States)

    Gilligan, Ryan P.; Tomsik, Thomas M.

    2017-01-01

    As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.

  12. On the steady state temperature profiles of biological tissues during ...

    African Journals Online (AJOL)

    The Maxwell equations are solved together with the Pennes Bio-heat equation analytically. The procedure of solution is provoked by the solution to the Maxwell equation. The result revealed the effect of the model parameters such as: the thermal conductivity, blood perfusion coefficient, and the thickness of the tissues and ...

  13. Heat transfer due to electroconvulsive therapy: Influence of anisotropic thermal and electrical skull conductivity.

    Science.gov (United States)

    Menezes de Oliveira, Marilia; Wen, Peng; Ahfock, Tony

    2016-09-01

    This paper focuses on electroconvulsive therapy (ECT) and head models to investigate temperature profiles arising when anisotropic thermal and electrical conductivities are considered in the skull layer. The aim was to numerically investigate the threshold for which this therapy operates safely to the brain, from the thermal point of view. A six-layer spherical head model consisting of scalp, fat, skull, cerebro-spinal fluid, grey matter and white matter was developed. Later on, a realistic human head model was also implemented. These models were built up using the packages from COMSOL Inc. and Simpleware Ltd. In these models, three of the most common electrode montages used in ECT were applied. Anisotropic conductivities were derived using volume constraint and included in both spherical and realistic head models. The bio-heat transferring problem governed by Laplace equation was solved numerically. The results show that both the tensor eigenvalues of electrical conductivity and the electrode montage affect the maximum temperature, but thermal anisotropy does not have a significant influence. Temperature increases occur mainly in the scalp and fat, and no harm is caused to the brain by the current applied during ECT. The work assures the thermal safety of ECT and also provides a numerical method to investigate other non-invasive therapies. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  14. Computer simulation of heating of biological tissue during laser radiation

    International Nuclear Information System (INIS)

    Bojanic, S.; Sreckovic, M.

    1995-01-01

    Computer model is based on an implicit finite difference scheme to solve the diffusion equation for light distribution and the bio-heat equation. A practical application of the model is to calculate the temperature distributions during thermal coagulation of prostate by radiative heating. (author)

  15. A finite element solution to conjugated heat transfer in tissue using magnetic resonance angiography to measure the in vitro velocity field

    Science.gov (United States)

    Dutton, Andrew William

    1993-12-01

    A combined numerical and experimental system for tissue heat transfer analysis was developed. The goal was to develop an integrated set of tools for studying the problem of providing accurate temperature estimation for use in hyperthermia treatment planning in a clinical environment. The completed system combines (1) Magnetic Resonance Angiography (MRA) to non-destructively measure the velocity field in situ, (2) the Streamwise Upwind Petrov-Galerkin finite element solution to the 3D steady state convective energy equation (CEE), (3) a medical image based automatic 3D mesh generator, and (4) a Gaussian type estimator to determine unknown thermal model parameters such as thermal conductivity, blood perfusion, and blood velocities from measured temperature data. The system was capable of using any combination of three thermal models (1) the Convective Energy Equation (CEE), (2) the Bioheat Transfer Equation (BHTE), and (3) the Effective Thermal Conductivity Equation (ETCE) Incorporation of the theoretically correct CEE was a significant theoretical advance over approximate models made possible by the use of MRA to directly measure the 3D velocity field in situ. Experiments were carried out in a perfused alcohol fixed canine liver with hyperthermia induced through scanned focused ultrasound Velocity fields were measured using Phase Contrast Angiography. The complete system was then used to (1) develop a 3D finite element model based upon user traced outlines over a series of MR images of the liver and (2) simulate temperatures at steady state using the CEE, BHTE, and ETCE thermal models in conjunction with the gauss estimator. Results of using the system on an in vitro liver preparation indicate the need for improved accuracy in the MRA scans and accurate spatial registration between the thermocouple junctions, the measured velocity field, and the scanned ultrasound power No individual thermal model was able to meet the desired accuracy of 0.5 deg C, the resolution

  16. A flux transfer event observed at the magnetopause by the Equator-S spacecraft and in the ionosphere by the CUTLASS HF radar

    Directory of Open Access Journals (Sweden)

    D. A. Neudegg

    1999-06-01

    Full Text Available Observations of a flux transfer event (FTE have been made simultaneously by the Equator-S spacecraft near the dayside magnetopause whilst corresponding transient plasma flows were seen in the near-conjugate polar ionosphere by the CUTLASS Finland HF radar. Prior to the occurrence of the FTE, the magnetometer on the WIND spacecraft ~226 RE upstream of the Earth in the solar wind detected a southward turning of the interplanetary magnetic field (IMF which is estimated to have reached the subsolar magnetopause ~77 min later. Shortly afterwards the Equator-S magnetometer observed a typical bipolar FTE signature in the magnetic field component normal to the magnetopause, just inside the magnetosphere. Almost simultaneously the CUTLASS Finland radar observed a strong transient flow in the F region plasma between 78° and 83° magnetic latitude, near the ionospheric region predicted to map along geomagnetic field lines to the spacecraft. The flow signature (and the data set as a whole is found to be fully consistent with the view that the FTE was formed by a burst of magnetopause reconnection.Key words. Interplanetary physics (ionosphere-magnetosphere interaction · Magnetospheric physics (magnetopause · cusp · and boundary layers; solar wind-magnetosphere interactions

  17. Modeling ARRM Xenon Tank Pressurization Using 1D Thermodynamic and Heat Transfer Equations

    Science.gov (United States)

    Gilligan, Patrick; Tomsik, Thomas

    2016-01-01

    As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.

  18. A multi-phase ferrofluid flow model with equation of state for thermomagnetic pumping and heat transfer

    Energy Technology Data Exchange (ETDEWEB)

    Aursand, Eskil, E-mail: eskil.aursand@sintef.no; Gjennestad, Magnus Aa.; Yngve Lervåg, Karl; Lund, Halvor

    2016-03-15

    A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base fluid. The magnetization model is based on statistical mechanics, taking into account non-uniform particle size distributions. An implementation of the proposed model is validated against experiments from the literature, and found to give good predictions for the thermomagnetic pumping performance. However, the results reveal a very large sensitivity to uncertainties in heat transfer coefficient predictions. - Highlights: • A multi-phase flow model for thermomagnetically pumped ferrofluid is proposed. • An implementation is validated against experiments from the literature. • Predicted thermomagnetic pumping effect agrees with experiments. • However, a very large sensitivity to heat transfer coefficient is revealed.

  19. Discrete ordinate solution of the radiative transfer equation in the 'polarization normal wave representation'

    Science.gov (United States)

    Kylling, A.

    1991-01-01

    The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.

  20. The Effect of Off-Farm Employment on Forestland Transfers in China: A Simultaneous-Equation Tobit Model Estimation

    Directory of Open Access Journals (Sweden)

    Han Zhang

    2017-09-01

    Full Text Available China’s new round tenure reform has devolved collective forests to individuals on an egalitarian basis. To balance the equity–efficiency dilemma, forestland transfers are highly advocated by policymakers. However, the forestland rental market is still inactive after the reform. To examine the role of off-farm employment in forestland transfers, a simultaneous Tobit system of equations was employed to account for the endogeneity, interdependency, and censoring issues. Accordingly, the Nelson–Olson two-stage procedure, embedded with a multivariate Tobit estimator, was applied to a nationally representative dataset. The estimation results showed that off-farm employment plays a significantly negative role in forestland rent-in, at the 5% risk level. However, off-farm activities had no significant effect on forestland rent-out. Considering China’s specific situation, a reasonable explanation is that households hold forestland as a crucial means of social security against the risk of unemployment. In both rent-in and rent-out equations, high transaction costs are one of the main obstacles impeding forestland transfer. A remarkable finding was that forestland transactions occurred with a statistically significant factor equalization effect, which would be helpful to adjust the mismatched labor–land ratio and improve the land-use efficiency.

  1. Application of stochastic Liouville–von Neumann equation to electronic energy transfer in FMO complex

    International Nuclear Information System (INIS)

    Imai, Hajime; Ohtsuki, Yukiyoshi; Kono, Hirohiko

    2015-01-01

    Highlights: • Stochastic Liouville–von Neumann equation is applied to energy transfer dynamics. • Noise generation methods for dealing with exciton in FMO complexes are proposed. • Structured spectral densities could better support coherent population dynamics. - Abstract: A stochastic Liouville–von Neumann approach to solving a spin-boson model is applied to electronic energy transfer in Fenna–Matthews–Olson (FMO) complexes as a case study of the dynamics in biological systems. We modify a noise generation method to treat an experimentally obtained highly structured spectral density. By considering the population dynamics in a two-site system with a model structured spectral density, we numerically observe two kinds of coherent motions associated with inter-site coupling and system–bath coupling, the latter of which is mainly attributed to the peak structure of the spectral density

  2. Technical characterization of dialysis fluid flow and mass transfer rate in dialyzers with various filtration coefficients using dimensionless correlation equation.

    Science.gov (United States)

    Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka

    2017-06-01

    The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.

  3. The relationship between vapour pressure, vaporization enthalpy, and enthalpy of transfer from solution to gas: An extension of the Martin equation

    International Nuclear Information System (INIS)

    Srisaipet, A.; Aryusuk, K.; Lilitchan, S.; Krisnangkura, K.

    2007-01-01

    Martin's equation, Δ sln g G=Δ sln g G o +zδ sln g G, is extended to cover vaporization free energy (Δ l g G). The extended equation is further expanded in terms of enthalpy and entropy and then used to correlate vaporization enthalpy (Δ l g H) and enthalpy of transfer from solution to gas (Δ sln g H). Data available in the literatures are used to validate and support the speculations derived from the proposed equation

  4. Effects of geometry discretization aspects on the numerical solution of the bioheat transfer equation with the FDTD technique

    Energy Technology Data Exchange (ETDEWEB)

    Samaras, T; Christ, A; Kuster, N [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Foundation for Research on Information Technologies in Society (IT' IS Foundation), Swiss Federal Institute of Technology (ETH), CH-8004 Zurich (Switzerland)

    2006-06-07

    In this work, we highlight two issues that have to be taken into consideration for accurate thermal modelling with the finite-difference time-domain (FDTD) method, namely the tissue interfaces and the staircasing effect. The former appears less critical in the overall accuracy of the results, whereas the latter may have an influence on the worst-case approach used in numerical dosimetry of non-ionizing radiation. (note)

  5. Effects of geometry discretization aspects on the numerical solution of the bioheat transfer equation with the FDTD technique

    International Nuclear Information System (INIS)

    Samaras, T; Christ, A; Kuster, N

    2006-01-01

    In this work, we highlight two issues that have to be taken into consideration for accurate thermal modelling with the finite-difference time-domain (FDTD) method, namely the tissue interfaces and the staircasing effect. The former appears less critical in the overall accuracy of the results, whereas the latter may have an influence on the worst-case approach used in numerical dosimetry of non-ionizing radiation. (note)

  6. Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

    Directory of Open Access Journals (Sweden)

    Martin Gregory T

    2004-11-01

    Full Text Available Abstract Background Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. Methods We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1 surface contact heating and (2 spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42°C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. Results The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45°C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. Conclusions The heat transport system model of the

  7. New developments in the discrete ordinate method for the resolution of the radiative transfer equation

    International Nuclear Information System (INIS)

    Ben Jaffel, L.; Vidal-Madjar, A.

    1989-01-01

    The discrete ordinate method for the resolution of the radiative transfer equation is developed. We show that the construction of a quasi-analytical solution to the corresponding matrix diagonalization problem reduces the time calculation and allows the use of more dense discrete frequency and angle grids. Comparison with previous work is made, showing that the present method reduces by more than a factor of ten the computational time, and is more appropriate in all cases

  8. Test plan for validation of the radiative transfer equation.

    Energy Technology Data Exchange (ETDEWEB)

    Ricks, Allen Joseph; Grasser, Thomas W.; Kearney, Sean Patrick; Jernigan, Dann A.; Blanchat, Thomas K.

    2010-09-01

    As the capabilities of numerical simulations increase, decision makers are increasingly relying upon simulations rather than experiments to assess risks across a wide variety of accident scenarios including fires. There are still, however, many aspects of fires that are either not well understood or are difficult to treat from first principles due to the computational expense. For a simulation to be truly predictive and to provide decision makers with information which can be reliably used for risk assessment the remaining physical processes must be studied and suitable models developed for the effects of the physics. A set of experiments are outlined in this report which will provide soot volume fraction/temperature data and heat flux (intensity) data for the validation of models for the radiative transfer equation. In addition, a complete set of boundary condition measurements will be taken to allow full fire predictions for validation of the entire fire model. The experiments will be performed with a lightly-sooting liquid hydrocarbon fuel fire in the fully turbulent scale range (2 m diameter).

  9. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Jiang, Song, E-mail: jiang@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong (China); Li, Shu, E-mail: li_shu@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)

    2015-12-01

    This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP

  10. Equations of macrotransport in reactor fuel assemblies

    International Nuclear Information System (INIS)

    Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.

    1986-01-01

    The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given

  11. Accuracy of the solution of the transfer equation for a plane layer of high optical thickness with strongly anisotropic scattering

    International Nuclear Information System (INIS)

    Konovalov, N.V.

    The accuracy of the calculation of the characteristics of a radiation field in a plane layer is investigated by solving the transfer equation in dependence on the error in the specification of the scattering indicatrix. It is shown that a small error in the specification of the indicatrix can lead to a large error in the solution at large optical depths. An estimate is given for the region of optical thicknesses for which the emission field can be determined with sufficient degree of accuracy from the transfer equation with a known error in the specification of the indicatrix. For an estimation of the error involved in various numerical methods, and also for a determination of the region of their applicability, the results of calculations of problems with strongly anisotropic indicatrix are given

  12. The forward and inverse problem in tissue optics based on the radiative transfer equation: A brief review

    International Nuclear Information System (INIS)

    Klose, Alexander D.

    2010-01-01

    This note serves as an introduction to two papers by Klose et al. and provides a brief review of the latest developments in optical tomography of scattering tissue. We discuss advancements made in solving the forward model for light propagation based on the radiative transfer equation, in reconstructing scattering and absorption cross sections of tissue, and in molecular imaging of luminescent sources.

  13. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  14. Scattering of lower-hybrid waves by drift-wave density fluctuations: solutions of the radiative transfer equation

    International Nuclear Information System (INIS)

    Andrews, P.L.; Perkins, F.W.

    1983-01-01

    The investigation of the scattering of lower-hybrid waves by density fluctuations arising from drift waves in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. The propagation of the lower-hybrid waves is well represented by a radiative transfer equation when the scale size of the density fluctuations is small compared to the overall plasma size. The radiative transfer equation is solved in two limits: first, the forward scattering limit, where the scale size of density fluctuations is large compared to the lower-hybrid perpendicular wavelength, and second, the large-angle scattering limit, where this inequality is reversed. The most important features of these solutions are well represented by analytical formulas derived by simple arguments. Based on conventional estimates for density fluctuations arising from drift waves and a parabolic density profile, the optical depth tau for scattering through a significant angle, is given by tauroughly-equal(2/N 2 /sub parallel/) (#betta#/sub p/i0/#betta#) 2 (m/sub e/c 2 /2T/sub i/)/sup 1/2/ [c/α(Ω/sub i/Ω/sub e/)/sup 1/2/ ], where #betta#/sub p/i0 is the central ion plasma frequency and T/sub i/ denotes the ion temperature near the edge of the plasma. Most of the scattering occurs near the surface. The transmission through the scattering region scales as tau - 1 and the emerging intensity has an angular spectrum proportional to cos theta, where sin theta = k/sub perpendicular/xB/sub p//(k/sub perpendicular/B/sub p/), and B/sub p/ is the poloidal field

  15. A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor

    Directory of Open Access Journals (Sweden)

    B. Godongwana

    2010-01-01

    Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.

  16. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  17. Solution of the comoving-frame equation of transfer in spherically symmetric flows. III. Effect of aberration and advection terms

    International Nuclear Information System (INIS)

    Mihalas, D.; Kunasz, P.B.; Hummer, D.G.

    1976-01-01

    We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/cvery-much-less-than1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V (r) approx.r/subn/(n=0,1,2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5V/c relative to the solution with these terms omitted. In stellar winds V/capproximately-less-than0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres

  18. Behavior of Poisson Bracket Mapping Equation in Studying Excitation Energy Transfer Dynamics of Cryptophyte Phycocyanin 645 Complex

    International Nuclear Information System (INIS)

    Lee, Weon Gyu; Kelly, Aaron; Rhee, Young Min

    2012-01-01

    Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic light harvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density

  19. Diffusion and mass transfer

    CERN Document Server

    Vrentas, James S

    2013-01-01

    The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedime...

  20. Adjoint Sensitivity Analysis of Radiative Transfer Equation: Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Scattering Atmospheres in Thermal IR

    Science.gov (United States)

    Ustinov, E.

    1999-01-01

    Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.

  1. A Parallel 2D Numerical Simulation of Tumor Cells Necrosis by Local Hyperthermia

    International Nuclear Information System (INIS)

    Reis, R F; Loureiro, F S; Lobosco, M

    2014-01-01

    Hyperthermia has been widely used in cancer treatment to destroy tumors. The main idea of the hyperthermia is to heat a specific region like a tumor so that above a threshold temperature the tumor cells are destroyed. This can be accomplished by many heat supply techniques and the use of magnetic nanoparticles that generate heat when an alternating magnetic field is applied has emerged as a promise technique. In the present paper, the Pennes bioheat transfer equation is adopted to model the thermal tumor ablation in the context of magnetic nanoparticles. Numerical simulations are carried out considering different injection sites for the nanoparticles in an attempt to achieve better hyperthermia conditions. Explicit finite difference method is employed to solve the equations. However, a large amount of computation is required for this purpose. Therefore, this work also presents an initial attempt to improve performance using OpenMP, a parallel programming API. Experimental results were quite encouraging: speedups around 35 were obtained on a 64-core machine

  2. Modeling methanol transfer in the mesoporous catalyst for the methanol-to-olefins reaction by the time-fractional diffusion equation

    Science.gov (United States)

    Zhokh, Alexey A.; Strizhak, Peter E.

    2018-04-01

    The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.

  3. LEAST SQUARE APPROACH FOR ESTIMATING OF LAND SURFACE TEMPERATURE FROM LANDSAT-8 SATELLITE DATA USING RADIATIVE TRANSFER EQUATION

    Directory of Open Access Journals (Sweden)

    Y. Jouybari-Moghaddam

    2017-09-01

    Full Text Available Land Surface Temperature (LST is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE. However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11 and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

  4. Least Square Approach for Estimating of Land Surface Temperature from LANDSAT-8 Satellite Data Using Radiative Transfer Equation

    Science.gov (United States)

    Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.

    2017-09-01

    Land Surface Temperature (LST) is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE). However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11) and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI) and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE) is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

  5. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  6. Optical properties reconstruction using the adjoint method based on the radiative transfer equation

    Science.gov (United States)

    Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir

    2018-01-01

    An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

  7. Self-similar solution for coupled thermal electromagnetic model ...

    African Journals Online (AJOL)

    An investigation into the existence and uniqueness solution of self-similar solution for the coupled Maxwell and Pennes Bio-heat equations have been done. Criteria for existence and uniqueness of self-similar solution are revealed in the consequent theorems. Journal of the Nigerian Association of Mathematical Physics ...

  8. A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

    Energy Technology Data Exchange (ETDEWEB)

    Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

    2016-02-20

    We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

  9. Notes on the infinity Laplace equation

    CERN Document Server

    Lindqvist, Peter

    2016-01-01

    This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

  10. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  11. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  12. Tissue lesion created by HIFU in continuous scanning mode

    Science.gov (United States)

    Fan, Tingbo; Liu, Zhenbo; Zhang, Dong

    2012-09-01

    The lesion formation was numerically and experimentally investigated by the continuous scanning mode. Simulations were presented based on the combination of Khokhlov-Zabolotskaya-Kuznetov (KZK) equation and bio-heat equation. Measurements were performed on porcine liver tissues using a 1.01 MHz single-element focused transducer at various acoustic powers, confirmed the predicted results. Controlling of the peak temperature and lesion by the scanning speed may be exploited for improvement of efficiency in HIFU therapy.

  13. THE REGULARITY OF INFLUENCE OF TRAFFIC PARAMETERS ON THE PROBABILITY OF REALISATION OF PLANNED PASSENGER TRANSFER AT TRANSFER NODES

    Directory of Open Access Journals (Sweden)

    G. Samchuk

    2017-06-01

    Full Text Available The article deals with the definition of traffic parameters that ensure the minimum value of the transfer waiting time for passengers. On the basis of experimental studies results, a regression equation to determine the probability of realisation of the planned transfer between a pair of vehicles was proposed. Using the identified regression equation, the transfer waiting time can be assessed for any headway exceeding 7,5 min.

  14. Neutronics methods for thermal radiative transfer

    International Nuclear Information System (INIS)

    Larsen, E.W.

    1988-01-01

    The equations of thermal radiative transfer are time discretized in a semi-implicit manner, yielding a linear transport problem for each time step. The governing equation in this problem has the form of a neutron transport equation with fission but no scattering. Numerical methods are described, whose origins lie in neutron transport, and that have been successfully adapted to this new problem. Acceleration methods that have been developed specifically for the radiative transfer problem, but may have generalizations applicable in neutronics problems, are also discussed

  15. Discretisation of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements

    Directory of Open Access Journals (Sweden)

    E. D. Resende

    2007-09-01

    Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.

  16. Application of Quasi-Heat-Pulse Solutions for Luikov’s Equations of Heat and Moisture Transfer for Calibrating and Utilizing Thermal Properties Apparatus

    Science.gov (United States)

    Mark A. Dietenberger; Charles R. Boardman

    2014-01-01

    Several years ago the Laplace transform solutions of Luikov’s differential equations were presented for one-dimensional heat and moisture transfer in porous hydroscopic orthotropic materials for the boundary condition of a gradual heat pulse applied to both surfaces of a flat slab. This paper presents calibration methods and data for the K-tester 637 (Lasercomp),...

  17. On the Use of a Direct Radiative Transfer Equation Solver for Path Loss Calculation in Underwater Optical Wireless Channels

    KAUST Repository

    Li, Changping; Park, Kihong; Alouini, Mohamed-Slim

    2015-01-01

    In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.

  18. On the Use of a Direct Radiative Transfer Equation Solver for Path Loss Calculation in Underwater Optical Wireless Channels

    KAUST Repository

    Li, Changping

    2015-07-22

    In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.

  19. Turbulence modeling for mass transfer enhancement by separation and reattachment with two-equation eddy-viscosity models

    International Nuclear Information System (INIS)

    Xiong Jinbiao; Koshizuka, Seiichi; Sakai, Mikio

    2011-01-01

    Highlights: → We selected and evaluated five two-equation eddy-viscosity turbulence models for modeling the separated and reattaching flow. → The behavior of the models in the simple flow is not consistent with that in the separated and reattaching flow. → The Abe-Kondoh-Nagano model is the best one among the selected model. → Application of the stress limiter and the Kato-Launder modification in the Abe-Kondoh-Nagano model helps to improve prediction of the peak mass transfer coefficient in the orifice flow. → The value of turbulent Schmidt number is investigated. - Abstract: The prediction of mass transfer rate is one of the key elements for estimation of the flow accelerated corrosion (FAC) rate. Three low Reynolds number (LRN) k-ε models (Lam-Bremhorst (LB), Abe-Kondoh-Nagano (AKN) and Hwang-Lin (HL)), one LRN k-ω (Wilcox, WX) model and the k-ω SST model are tested for the computation of the high Schmidt number mass transfer, especially in the flow through an orifice. The models are tested in the computation of three types of flow: (1) the fully developed pipe flow, (2) the flow over a backward facing step, (3) the flow through an orifice. The HL model shows a good performance in predicting mass transfer in the fully developed pipe flow but fails to give reliable prediction in the flow through an orifice. The WX model and the k-ω SST model underpredict the mass transfer rate in the flow types 1 and 3. The LB model underestimates the mass transfer in the flow type 1, but shows abnormal behavior at the reattaching point in type 3. Synthetically evaluating all the models in all the computed case, the AKN model is the best one; however, the prediction is still not satisfactory. In the evaluation in the flow over a backward facing step shows k-ω SST model shows superior performance. This is interpreted as an implication that the combination of the k-ε model and the stress limiter can improve the model behavior in the recirculation bubble. Both the

  20. Fem Formulation of Heat Transfer in Cylindrical Porous Medium

    Science.gov (United States)

    Azeem; Khaleed, H. M. T.; Soudagar, Manzoor Elahi M.

    2017-08-01

    Heat transfer in porous medium can be derived from the fundamental laws of flow in porous region ass given by Henry Darcy. The fluid flow and energy transport inside the porous medium can be described with the help of momentum and energy equations. The heat transfer in cylindrical porous medium differs from its counterpart in radial and axial coordinates. The present work is focused to discuss the finite element formulation of heat transfer in cylindrical porous medium. The basic partial differential equations are derived using Darcy law which is the converted into a set of algebraic equations with the help of finite element method. The resulting equations are solved by matrix method for two solution variables involved in the coupled equations.

  1. Thermal-mechanical deformation modelling of soft tissues for thermal ablation.

    Science.gov (United States)

    Li, Xin; Zhong, Yongmin; Jazar, Reza; Subic, Aleksandar

    2014-01-01

    Modeling of thermal-induced mechanical behaviors of soft tissues is of great importance for thermal ablation. This paper presents a method by integrating the heating process with thermal-induced mechanical deformations of soft tissues for simulation and analysis of the thermal ablation process. This method combines bio-heat transfer theories, constitutive elastic material law under thermal loads as well as non-rigid motion dynamics to predict and analyze thermal-mechanical deformations of soft tissues. The 3D governing equations of thermal-mechanical soft tissue deformation are discretized by using the finite difference scheme and are subsequently solved by numerical algorithms. Experimental results show that the proposed method can effectively predict the thermal-induced mechanical behaviors of soft tissues, and can be used for the thermal ablation therapy to effectively control the delivered heat energy for cancer treatment.

  2. Improved coupling of the conduction and flow equations in TRAC

    International Nuclear Information System (INIS)

    Addessio, F.L.

    1981-01-01

    Recent nuclear-reactor-systems modeling efforts have been directed toward the development of computer codes capable of simulating transients in short computational times. For this reason, a stability enhancing two-stem method (SETS) has been applied to the two-phase flow equations in the Transient Reactor Analysis Code (TRAC) allowing the Courant limit to be violated. Unfortunately, the coupling between the wall conduction equation and the fluid-dynamics equations is performed semi-implicitly, that is, the wall-heat transfer term, is evaluated using old-time heat-transfer coefficients and wall temperatures and new-time coolant temperatures. This coupling may lead to numerical instabilities at large time steps because of large variations in the heat-transfer coefficient in certain regimes of the boiling curve. Consequently, simply using new-time wall temperatures is not sufficient. A technique that also incorporates new-time heat-transfer coefficients must be used

  3. An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers

    Directory of Open Access Journals (Sweden)

    Vasyl Chekurin

    2017-01-01

    Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.

  4. Extending generalized Kubelka-Munk to three-dimensional radiative transfer.

    Science.gov (United States)

    Sandoval, Christopher; Kim, Arnold D

    2015-08-10

    The generalized Kubelka-Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one (DP1) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an 8×8 system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

  5. Integration of Chandrasekhar's integral equation

    International Nuclear Information System (INIS)

    Tanaka, Tasuku

    2003-01-01

    We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness

  6. Formulation and validation of applied engineering equations for heat transfer processes in the food industry

    DEFF Research Database (Denmark)

    Christensen, Martin Gram

    The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of food engineering such as equipment manufacture the use of predictive...... calculations, modelling activities and simulations for improved design is employed to a high degree. In food manufacture the use process calculations are seldom applied. Even though, the calculation of thermal processes is not a challenging task in academia; this is not the case for food manufacture. However......; the calculations need fundamental validation and a generality that ensures a wide application, thus also the development of simplified approximations and engineering equations have to be conducted in academia. The focus group for the utilization of the presented work is; food manufacture, authorities ensuring food...

  7. High-order solution methods for grey discrete ordinates thermal radiative transfer

    Energy Technology Data Exchange (ETDEWEB)

    Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

    2016-12-15

    This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

  8. Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

    Science.gov (United States)

    Cross, M. F.

    2011-01-01

    A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

  9. Simultaneous Heat and Mass Transfer Model for Convective Drying of Building Material

    Science.gov (United States)

    Upadhyay, Ashwani; Chandramohan, V. P.

    2018-04-01

    A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss-Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

  10. Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability

    Science.gov (United States)

    Janett, Gioele; Paganini, Alberto

    2018-04-01

    Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented.

  11. A Photon Free Method to Solve Radiation Transport Equations

    International Nuclear Information System (INIS)

    Chang, B

    2006-01-01

    The multi-group discrete-ordinate equations of radiation transfer is solved for the first time by Newton's method. It is a photon free method because the photon variables are eliminated from the radiation equations to yield a N group XN direction smaller but equivalent system of equations. The smaller set of equations can be solved more efficiently than the original set of equations. Newton's method is more stable than the Semi-implicit Linear method currently used by conventional radiation codes

  12. Numerical Modeling of Conjugate Heat Transfer in Fluid Network

    Science.gov (United States)

    Majumdar, Alok

    2004-01-01

    Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

  13. Linear orbit parameters for the exact equations of motion

    International Nuclear Information System (INIS)

    Parzen, G.

    1995-01-01

    This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

  14. Convective heat transfer

    CERN Document Server

    Kakac, Sadik; Pramuanjaroenkij, Anchasa

    2014-01-01

    Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....

  15. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  16. Conjugate Heat Transfer of Mixed Convection for Viscoelastic Fluid Past a Stretching Sheet

    Directory of Open Access Journals (Sweden)

    Kai-Long Hsiao

    2007-01-01

    Full Text Available A conjugate heat transfer problem of a second-grade viscoelastic fluid past a stretching sheet has been studied. Governing equations include heat conduction equation of a stretching sheet, continuity equation, momentum equation, and energy equation of a second-grade fluid, analyzed by a combination of a series expansion method, the similarity transformation, and a second-order accurate finite-difference method. These solutions are used to iterate with the heat conduction equation of the stretching sheet to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. Ranges of dimensionless parameters, the Prandtl number Pr, the elastic number E and the conduction-convection coefficient Ncc are from 0.001 to 10, 0.0001 to 0.01, and 0.5 to 2.0, respectively. A parameter G, which is used to represent the dominance of the buoyant effect, is present in governing equations. Results indicated that elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a stretching sheet. In addition, same as the results from Newtonian fluid flow and conduction analysis of a stretching sheet, a better heat transfer is obtained with a larger Ncc, G, and E.

  17. Non-Fourier thermal transport induced structural hierarchy and damage to collagen ultrastructure subjected to laser irradiation.

    Science.gov (United States)

    Sahoo, Nilamani; Narasimhan, Arunn; Dhar, Purbarun; Das, Sarit K

    2018-05-01

    Comprehending the mechanism of thermal transport through biological tissues is an important factor for optimal ablation of cancerous tissues and minimising collateral tissue damage. The present study reports detailed mapping of the rise in internal temperature within the tissue mimics due to NIR (1064 nm) laser irradiation, both for bare mimics and with gold nanostructures infused. Gold nanostructures such as mesoflowers and nanospheres have been synthesised and used as photothermal converters to enhance the temperature rise, resulting in achieving the desired degradation of malignant tissue in targeted region. Thermal history was observed experimentally and simulated considering non-Fourier dual phase lag (DPL) model incorporated Pennes bio-heat transfer equation using COMSOL Multiphysics software. The gross deviation in temperature i.e. rise from the classical Fourier model for bio-heat conduction suggests additional effects of temperature rise on the secondary structures and morphological and physico-chemical changes to the collagen ultrastructures building the tissue mass. The observed thermal denaturation in the collagen fibril morphologies have been explained based on the physico-chemical structure of collagen and its response to thermal radiation. The large shift in frequency of amides A and B is pronounced at a depth of maximum temperature rise compared with other positions in tissue phantom. Observations for change in band of amide I, amide II, and amide III are found to be responsible for damage to collagen ultra-structure. Variation in the concentration of gold nanostructures shows the potentiality of localised hyperthermia treatment subjected to NIR radiation through a proposed free radical mechanism.

  18. Investigation of two and three parameter equations of state for cryogenic fluids

    International Nuclear Information System (INIS)

    Jenkins, S.L.; Majumdar, A.K.; Hendricks, R.C.

    1990-01-01

    Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point. 13 refs

  19. Principles of the radiosity method versus radiative transfer for canopy reflectance modeling

    Science.gov (United States)

    Gerstl, Siegfried A. W.; Borel, Christoph C.

    1992-01-01

    The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.

  20. Adaptive integral equation methods in transport theory

    International Nuclear Information System (INIS)

    Kelley, C.T.

    1992-01-01

    In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented

  1. Spectral element method for vector radiative transfer equation

    International Nuclear Information System (INIS)

    Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

    2010-01-01

    A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

  2. Thermal performance analysis of heat exchanger for closed wet cooling tower using heat and mass transfer analogy

    International Nuclear Information System (INIS)

    Yoo, Seong Yeon; Han, Kyu Hyun; Kim, Jin Hyuck

    2010-01-01

    In closed wet cooling towers, the heat transfer between the air and external tube surfaces can be composed of the sensible heat transfer and the latent heat transfer. The heat transfer coefficient can be obtained from the equation for external heat transfer of tube banks. According to experimental data, the mass transfer coefficient was affected by the air velocity and spray water flow rate. This study provides the correlation equation for mass transfer coefficient based on the analogy of the heat and mass transfer and the experimental data. The results from this correlation equation showed fairly good agreement with experimental data. The cooling capacity and thermal efficiency of the closed wet cooling tower were calculated from the correlation equation to analyze the performance of heat exchanger for the tower

  3. Optimal control penalty finite elements - Applications to integrodifferential equations

    Science.gov (United States)

    Chung, T. J.

    The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

  4. Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

    Directory of Open Access Journals (Sweden)

    Umer Saeed

    2014-01-01

    Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

  5. An Implementation of Interfacial Transport Equation into the CUPID code

    Energy Technology Data Exchange (ETDEWEB)

    Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

    2009-11-15

    A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region.

  6. An Implementation of Interfacial Transport Equation into the CUPID code

    International Nuclear Information System (INIS)

    Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

    2009-11-01

    A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region

  7. Fem Formulation for Heat and Mass Transfer in Porous Medium

    Science.gov (United States)

    Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

    2017-08-01

    Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

  8. Equation of State for Phospholipid Self-Assembly

    DEFF Research Database (Denmark)

    Marsh, Derek

    2016-01-01

    Phospholipid self-assembly is the basis of biomembrane stability. The entropy of transfer from water to self-assembled micelles of lysophosphatidylcholines and diacyl phosphatidylcholines with different chain lengths converges to a common value at a temperature of 44°C. The corresponding enthalpies...... of transfer converge at ∼-18°C. An equation of state for the free energy of self-assembly formulated from this thermodynamic data depends on the heat capacity of transfer as the sole parameter needed to specify a particular lipid. For lipids lacking calorimetric data, measurement of the critical micelle...

  9. The Enskog Equation for Confined Elastic Hard Spheres

    Science.gov (United States)

    Maynar, P.; García de Soria, M. I.; Brey, J. Javier

    2018-03-01

    A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

  10. Modelling conjugation with stochastic differential equations

    DEFF Research Database (Denmark)

    Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

    2010-01-01

    Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

  11. Experimental study of natural convective heat transfer in a vertical hexagonal sub channel

    International Nuclear Information System (INIS)

    Tandian, Nathanael P.; Umar, Efrizon; Hardianto, Toto; Febriyanto, Catur

    2012-01-01

    The development of new practices in nuclear reactor safety aspects and optimization of recent nuclear reactors, including the APWR and the PHWR reactors, needs a knowledge on natural convective heat transfer within sub-channels formed among several nuclear fuel rods or heat exchanger tubes. Unfortunately, the currently available empirical correlation equations for such heat transfer modes are limited and researches on convective heat transfer within a bundle of vertical cylinders (especially within the natural convection modes) are scarcely done. Although boundary layers around the heat exchanger cylinders or fuel rods may be dominated by their entry regions, most of available convection correlation equations are for fully developed boundary layers. Recently, an experimental study on natural convective heat transfer in a subchannel formed by several heated parallel cylinders that arranged in a hexagonal configuration has been being done. The study seeks for a new convection correlation for the natural convective heat transfer in the sub-channel formed among the hexagonal vertical cylinders. A new convective heat transfer correlation equation has been obtained from the study and compared to several similar equations in literatures.

  12. MRI feedback temperature control for focused ultrasound surgery

    International Nuclear Information System (INIS)

    Vanne, A; Hynynen, K

    2003-01-01

    A temperature feedback controller routine using a physical model for temperature evolution was developed for use with focused ultrasound surgery. The algorithm for the controller was a multi-input, single-output linear quadratic regulator (LQR) derived from Pennes' bioheat transfer equation. The controller was tested with simulated temperature data that had the same characteristics as those obtained with magnetic resonance imaging (MRI). The output of the controller was the appropriate power level to be used by the transducer. Tissue parameters estimated prior to the simulated treatments were used to determine the controller parameters. The controller performance was simulated in three dimensions with varying system parameters, and sufficient temperature tracking was achieved. The worst-case overshoot was 7 deg. C and the steady-state error was 5 deg. C. The simulated behaviour of the controller suggests satisfactory performance and that the controller may be useful in controlling the power output during MRI-monitored ultrasound surgery

  13. Biothermomechanical behavior of skin tissue

    Institute of Scientific and Technical Information of China (English)

    F.Xu; T.J.Lu; K.A.Seffen

    2008-01-01

    Advances in laser,microwave and similar tech nologies have led to recent developments of thermal treatments involving skin tissue.The effectiveness of these treatments is governed by the coupled thermal,mechanical,biological and neural responses of the affected tissue:a favorable interaction results in a procedure with relatively little pain and no lasting side effects.Currently,even though each behavioral facet is to a certain extent established and understood,none exists to date in the interdisciplinarv area.A highly interdisciplinary approach is required for studying the biothermomechanical behavior of skin,involving bioheat transfer.biomechanics and physiology.A comprehensive literature review penrtinent to the subject is presented in this paper,covering four subject areas:(a)skin structure,(b)skin bioheat transfer and thermal damage,(c)skin biomechanics,and(d)skin biothermomechanics.The major problems,issues,and topics for further studies are also outlined.This review finds that significant advances in each of these aspects have been achieved in recent years.Although focus is placed upon the biothermomechanical behavior of skin tissue,the fundamental concepts and methodologies reviewed in this paper may also be applicable for studying other soft tissues.

  14. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  15. Numerical solution of the kinetic equation in reactor shielding

    International Nuclear Information System (INIS)

    Germogenova, T.A.

    1975-01-01

    A review is made of methods of solving marginal problems of multi-group systems of equations of neutron and γ radiation transfer. The first stage of the solution - the quantification of the basic task, is determined by the qualitative behaviour of the solution - is the nature of its performance and asymptotics. In the second stage - solution of the approximating system, various modifications of the iterative method are as a rule used. A description is given of the features of the major Soviet complexes of programmes (ROZ and RADUGA) for the solution of multi-group systems of transfer equations and some methodological research findings are presented. (author)

  16. Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

    Science.gov (United States)

    Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

    2016-11-01

    The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

  17. An improved nucleate boiling design equation

    International Nuclear Information System (INIS)

    Basu, D.K.; Pinder, K.L.

    1976-01-01

    The effect of varying ΔT, the primary variable, on the value of heat transfer coefficient (h) in nucleate boiling is discussed. The three-parameter quadratic equation, h=P 1 + P 2 (ΔT) + P 3 (ΔT) 2 (where the constants, P 1 ,P 2 ,P 3 are functions of pressure, liquid properties and surface properties of the heater) is suggested. Ten sets of data at atmospheric pressure from six different workers and two more sets for pressure variation have been tested. The above quadratic equation fits the experimental data better than the existing two-parameter power relation, h=C(ΔT)sup(n) (where C is constant). The values of the three coeffcients in the quadratic equations are dependent on pressure, liquid properties and surface properties. A generalized empirical equation has been derived, which fits the selected pressure data well. (author)

  18. Kalman filtered MR temperature imaging for laser induced thermal therapies.

    Science.gov (United States)

    Fuentes, D; Yung, J; Hazle, J D; Weinberg, J S; Stafford, R J

    2012-04-01

    The feasibility of using a stochastic form of Pennes bioheat model within a 3-D finite element based Kalman filter (KF) algorithm is critically evaluated for the ability to provide temperature field estimates in the event of magnetic resonance temperature imaging (MRTI) data loss during laser induced thermal therapy (LITT). The ability to recover missing MRTI data was analyzed by systematically removing spatiotemporal information from a clinical MR-guided LITT procedure in human brain and comparing predictions in these regions to the original measurements. Performance was quantitatively evaluated in terms of a dimensionless L(2) (RMS) norm of the temperature error weighted by acquisition uncertainty. During periods of no data corruption, observed error histories demonstrate that the Kalman algorithm does not alter the high quality temperature measurement provided by MR thermal imaging. The KF-MRTI implementation considered is seen to predict the bioheat transfer with RMS error 10 sec.

  19. On the precise connection between the GRW master equation and master equations for the description of decoherence

    Energy Technology Data Exchange (ETDEWEB)

    Vacchini, Bassano [Dipartimento di Fisica dell' Universita di Milano, Via Celoria 16, 20133 Milan (Italy); Istituto Nazionale di Fisica Nucleare, sezione di Milano, Via Celoria 16, 20133 Milan (Italy)

    2007-03-09

    We point out that the celebrated GRW master equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master equations. Such master equations are typically used for the description of decoherence due to momentum transfers between the system and environment. Building on this analogy we show the exact relationship between the GRW master equation and decoherence master equations, further providing a collisional decoherence model formally equivalent to the GRW master equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications.

  20. Heat transfer from rough surfaces

    International Nuclear Information System (INIS)

    Dalle Donne, M.

    1977-01-01

    Artificial roughness is often used in nuclear reactors to improve the thermal performance of the fuel elements. Although these are made up of clusters of rods, the experiments to measure the heat transfer and friction coefficients of roughness are performed with single rods contained in smooth tubes. This work illustrated a new transformation method to obtain data applicable to reactor fuel elements from these annulus experiments. New experimental friction data are presented for ten rods, each with a different artificial roughness made up of two-dimensional rectangular ribs. For each rod four tests have been performed, each in a different outer smooth tube. For two of these rods, each for two different outer tubes, heat transfer data are also given. The friction and heat transfer data, transformed with the present method, are correlated by simple equations. In the paper, these equations are applied to a case typical for a Gas Cooled Fast Reactor fuel element. (orig.) [de

  1. Non-equilibrium reaction rates in chemical kinetic equations

    Science.gov (United States)

    Gorbachev, Yuriy

    2018-05-01

    Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

  2. An evaluation of analytical heat transfer area with various boiling heat transfer correlations in steam generator thermal sizing

    International Nuclear Information System (INIS)

    Jung, B. R.; Park, H. S.; Chung, D. M.; Baik, S. J.

    1999-01-01

    The computer program SAFE has been used to size and analyze the performance of a steam generator which has two types of heat transfer regions in Korean Standard Nuclear Power Plants (KSNP) and Korean Next Generation Reactor (KNGR) design. The SAFE code calculates the analytical boiling heat transfer area using the modified form of the saturated nucleate pool boiling correlation suggested by Rohsenow. The predicted heat transfer area in the boiling region is multiplied by a constant to obtain a final analytical heat transfer area. The inclusion of the multiplier in the analytical calculation has some disadvantage of loss of complete correlation by the governing heat transfer equation. Several comparative analyses have been performed quantitatively to evaluate the possibility of removing the multiplier in the analytical calculation in the SAFE code. The evaluation shows that the boiling correlation and multiplier used in predicting the boiling region heat transfer area can be replaced with other correlations predicting nearly the same heat transfer area. The removal of multiplier included in the analytical calculation will facilitate a direct use of a set of concerned analytical sizing values that can be exactly correlated by the governing heat transfer equation. In addition this will provide more reasonable basis for the steam generator thermal sizing calculation and enhance the code usability without loss of any validity of the current sizing procedure. (author)

  3. A 1D radiative transfer benchmark with polarization via doubling and adding

    Science.gov (United States)

    Ganapol, B. D.

    2017-11-01

    Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

  4. Radiation and combined heat transfer in channels

    International Nuclear Information System (INIS)

    Tamonis, M.

    1986-01-01

    This book presents numerical methods of calculation of radiative and combined heat transfer in channel flows of radiating as well as nonradiating media. Results obtained in calculations for flow conditions of combustion products from organic fuel products are given and methods used in determining the spectral optical properties of molecular gases are analyzed. The book presents applications of heat transfer in solving problems. Topic covered are as follows: optical properties of molecular gases; transfer equations for combined heat transfer; experimental technique; convective heat transfer in heated gas flows; radiative heat transfer in gaseous media; combined heat transfer; and radiative and combined heat transfer in applied problems

  5. Spin–transfer torque oscillator in magnetic tunneling junction with short–wavelength magnon excitation

    Directory of Open Access Journals (Sweden)

    Shizhu Qiao

    2018-05-01

    Full Text Available Bloch–Bloembergen–Slonczewski (BBS equation is established by extending Bloch–Bloembergen equation, and it is used to study magnetization oscillation in the free magnetic layer of a magnetic tunneling junction. Since both short–wavelength magnon excitation and spin–transfer torque are taken into account in the BBS equation, it is distinguished from Landau–Lifshitz–Gilbert–Slonczewski equation. The macro–spin BBS model predicts that the transverse relaxation time in free magnetic layer should be long enough, as compared with the longitudinal relaxation time, to achieve stable magnetization oscillation for spin–transfer torque oscillator application. Moreover, field–like torque favors the tolerance of fast transverse relaxation, which makes magnetic tunneling junction a better choice than spin valve for the spin–transfer torque oscillator application.

  6. Heat transfer between adsorbate and laser-heated hot electrons

    International Nuclear Information System (INIS)

    Ueba, H; Persson, B N J

    2008-01-01

    Strong short laser pulses can give rise to a strong increase in the electronic temperature at metal surfaces. Energy transfer from the hot electrons to adsorbed molecules may result in adsorbate reactions, e.g. desorption or diffusion. We point out the limitations of an often used equation to describe the heat transfer process in terms of a friction coupling. We propose a simple theory for the energy transfer between the adsorbate and hot electrons using a newly introduced heat transfer coefficient, which depends on the adsorbate temperature. We calculate the transient adsorbate temperature and the reaction yield for a Morse potential as a function of the laser fluency. The results are compared to those obtained using a conventional heat transfer equation with temperature-independent friction. It is found that our equation of energy (heat) transfer gives a significantly lower adsorbate peak temperature, which results in a large modification of the reaction yield. We also consider the heat transfer between different vibrational modes excited by hot electrons. This mode coupling provides indirect heating of the vibrational temperature in addition to the direct heating by hot electrons. The formula of heat transfer through linear mode-mode coupling of two harmonic oscillators is applied to the recent time-resolved study of carbon monoxide and atomic oxygen hopping on an ultrafast laser-heated Pt(111) surface. It is found that the maximum temperature of the frustrated translation mode can reach high temperatures for hopping, even when direct friction coupling to the hot electrons is not strong enough

  7. Discontinuous Galerkin for the Radiative Transport Equation

    KAUST Repository

    Guermond, Jean-Luc

    2013-10-11

    This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

  8. Discontinuous Galerkin for the Radiative Transport Equation

    KAUST Repository

    Guermond, Jean-Luc; Kanschat, Guido; Ragusa, Jean C.

    2013-01-01

    This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

  9. Heat transfer of laminar mixed convection of liquid

    CERN Document Server

    Shang, De-Yi

    2016-01-01

    This book presents a new algorithm to calculate fluid flow and heat transfer of laminar mixed convection. It provides step-by-step tutorial help to learn quickly how to set up the theoretical and numerical models of laminar mixed convection, to consider the variable physical properties of fluids, to obtain the system of numerical solutions, to create a series of formalization equations for the convection heat transfer by using a curve-fitting approach combined with theoretical analysis and derivation. It presents the governing ordinary differential equations of laminar mixed convection, equivalently transformed by an innovative similarity transformation with the description of the related transformation process. A system of numerical calculations of the governing ordinary differential equations is presented for the water laminar mixed convection. A polynomial model is induced for convenient and reliable treatment of variable physical properties of liquids. The developed formalization equations of mixed convec...

  10. An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)

    2017-04-01

    In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

  11. Interfacial area and interfacial transfer in two-phase systems. DOE final report

    Energy Technology Data Exchange (ETDEWEB)

    Ishii, Mamoru; Hibiki, T.; Revankar, S.T.; Kim, S.; Le Corre, J.M.

    2002-07-01

    In the two-fluid model, the field equations are expressed by the six conservation equations consisting of mass, momentum and energy equations for each phase. The existence of the interfacial transfer terms is one of the most important characteristics of the two-fluid model formulation. The interfacial transfer terms are strongly related to the interfacial area concentration and to the local transfer mechanisms such as the degree of turbulence near interfaces. This study focuses on the development of a closure relation for the interfacial area concentration. A brief summary of several problems of the current closure relation for the interfacial area concentration and a new concept to overcome the problem are given.

  12. Stochastic differential equations used to model conjugation

    DEFF Research Database (Denmark)

    Philipsen, Kirsten Riber; Christiansen, Lasse Engbo

    Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...

  13. Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation

    International Nuclear Information System (INIS)

    Wu Guocheng

    2011-01-01

    Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  14. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

    KAUST Repository

    Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto

    2017-01-01

    Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

  15. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

    KAUST Repository

    Festa, Adriano

    2017-03-22

    Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

  16. Retrieval of water cloud characteristic from active sensor data using the analytical solution of radiative transfer equation

    International Nuclear Information System (INIS)

    Cai, W.; Gayen, S.K.

    2010-01-01

    An analytical forward model and numerical algorithm for retrieving the parameters of water cloud of earth atmosphere from optical measurements carried out by satellite-based lidars is presented. The forward model, based on the analytical solution of the radiative transfer equation, is used to fit the temporal profile of the laser light pulses backscattered from the cloud layers. The cloud parameters extracted from the analysis at each position on earth include the transport mean free path, the average radius of water drops, the density of drops, the scattering length, the scattering cross section, the anisotropy factor, and the altitude of top level of major clouds. Also estimated is the possible thickness of cloud layers. The efficacy of the approach is demonstrated by generating parameters of water cloud using the data collected by NASA's cloud-aerosol lidar and infrared pathfinder satellite observations (CALIPSO) satellite when it passed through North America on August 7, 2007.

  17. Finite element simulation of heat transfer

    CERN Document Server

    Bergheau, Jean-Michel

    2010-01-01

    This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re

  18. Theoretical and numerical study of heat transfer deterioration in HPLWR

    International Nuclear Information System (INIS)

    Palko, D.; Anglart, H.

    2007-01-01

    A numerical investigation of the Heat Transfer Deterioration (HTD) phenomena is performed using the low-Re k - ω turbulence model. Steady state Reynolds-averaged Navier-Stokes equations are solved together with equations for the transport of enthalpy and turbulence. Equations are solved for the supercritical water flow at different pressures, using water properties from the standard IAPWS tables. All cases are extensively validated against experimental data. The influence of buoyancy on the HTD is demonstrated for different mass flow rates in the heated pipes. Numerical results prove that the RANS low-Re turbulence modeling approach is fully capable to simulate the heat transfer in pipes with the water flow at supercritical pressures. A study of buoyancy influence shows that for the low mass flow rates of coolant, the influence of buoyancy forces on the heat transfer in heated pipes is significant. For the high flow rates, buoyancy influence could be neglected and there are clearly other mechanisms causing the decrease in heat transfer at high coolant flow rates. (author)

  19. Application of a pressure based CFD code with mass transfer model based on the Rayleigh equation for the numerical simulation of the cavitating flow around a hydrofoil with circular leading edge

    Directory of Open Access Journals (Sweden)

    Deimel Christian

    2014-03-01

    Full Text Available The most common method for simulating cavitating flows is using the governing flow equations in a form with a variable density and treats both phases as incompressible in combination with a transport equation for the vapour volume fraction. This approach is commonly referred to as volume of fluid method (VoF. To determine the transition of the liquid phase to vapour and vice versa, a relation for the mass transfer is needed. Several models exist, based on slightly differing physical assumptions, for example derivation from the dynamics of single bubbles or large bubble clusters. In our simulation, we use the model of Sauer and Schnerr which is based on the Rayleigh equation. One common problem of all mass transfer models is the use of model constants which often need to be tuned with regard to the examined problem. Furthermore, these models often overpredict the turbulent dynamic viscosity in the two-phase region which counteracts the development of transient shedding behaviour and is compensated by the modification proposed by Reboud. In the presented study, we vary the parameters of the Sauer-Schnerr model with Reboud modification that we implemented into an OpenFOAM solver to match numerical to experimental data.

  20. Numerical simulations of a coupled radiative?conductive heat transfer model using a modified Monte Carlo method

    KAUST Repository

    Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

    2012-01-01

    Radiative-conductive heat transfer in a medium bounded by two reflecting and radiating plane surfaces is considered. This process is described by a nonlinear system of two differential equations: an equation of the radiative heat transfer

  1. Study of the stochastic point reactor kinetic equation

    International Nuclear Information System (INIS)

    Gotoh, Yorio

    1980-01-01

    Diagrammatic technique is used to solve the stochastic point reactor kinetic equation. The method gives exact results which are derived from Fokker-Plank theory. A Green's function dressed with the clouds of noise is defined, which is a transfer function of point reactor with fluctuating reactivity. An integral equation for the correlation function of neutron power is derived using the following assumptions: 1) Green's funntion should be dressed with noise, 2) The ladder type diagrams only contributes to the correlation function. For a white noise and the one delayed neutron group approximation, the norm of the integral equation and the variance to mean-squared ratio are analytically obtained. (author)

  2. Thermal radiation heat transfer in participating media by finite volume discretization using collimated beam incidence

    Science.gov (United States)

    Harijishnu, R.; Jayakumar, J. S.

    2017-09-01

    The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.

  3. Direct numerical simulations of fluid flow, heat transfer and phase changes

    Science.gov (United States)

    Juric, D.; Tryggvason, G.; Han, J.

    1997-01-01

    Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

  4. Separate effects tests for GOTHIC condensation and evaporative heat transfer models

    International Nuclear Information System (INIS)

    George, T.L.; Singh, A.

    1994-01-01

    The GOTHIC computer program, under development at EPRI/NAI, is a general purpose thermal hydraulics computer program for design, licensing, safety and operating analysis of nuclear containments and other confinement buildings. The code solves a nine equation model for three dimensional multiphase flow with separate mass, momentum and energy equations for vapor, liquid and drop phases. The vapor phase can be a gas mixture of steam and non-condensing gases. The phase balance equations are coupled by mechanistic and empirical models for interface mass, energy and momentum transfer that cover the entire flow regime from bubbly flow to film/drop flow. A variety of heat transfer correlations are available to model the fluid coupling to active and passive solid conductors. This paper focuses on the application of GOTHIC to two separate effects tests; condensation heat transfer on a vertical flat plate with varying bulk velocity, steam concentration and temperature, and evaporative heat transfer from a hot pool to a dry (superheated) atmosphere. Comparisons with experimental data is included for both tests. Results show the validity of two condensation heat transfer correlations as incorporated into GOTHIC and the interfacial heat and mass transfer models for the range of the experimental test conditions. Comparisons are also made for lumped versus multidimensional modeling for buoyancy controlled flow with evaporative heat transfer. (author). 13 refs., 1 tab., 10 figs

  5. Separate effects tests for GOTHIC condensation and evaporative heat transfer models

    International Nuclear Information System (INIS)

    George, T.L.; Singh, A.

    1996-01-01

    The GOTHIC computer program, under development at NAI for EPRI, is a general purpose thermal hydraulics computer program for design, licensing, safety and operating analysis of nuclear containments and other confinement buildings. The code solves a nine-equation model for three-dimensional multiphase flow with separate mass, momentum and energy equations for vapor, liquid and drop phases. The vapor phase can be a gas mixture of steam and non-condensing gases. The phase balance equations are coupled by mechanistic and empirical models for interface mass, energy and momentum transfer that cover the entire flow regime from bubbly flow to film-drop flow. A variety of heat transfer correlations are available to model the fluid coupling to active and passive solid conductors. This paper focuses on the application of GOTHIC to two separate effects tests: condensation heat transfer on a vertical flat plate with varying bulk velocity, steam concentration and temperature, and evaporative heat transfer from a hot pool to a dry (superheated) atmosphere. Comparisons with experimental data are included for both tests. Results show the validity of two condensation heat transfer correlations as incorporated into GOTHIC and the interfacial heat and mass transfer models for the range of the experimental test conditions. Comparisons are also made for lumped vs. multidimensional modeling for buoyancy-controlled flow with evaporative heat transfer. (orig.)

  6. Analysis of heat transfer in plain carbon steels

    International Nuclear Information System (INIS)

    Han, Heung Nam; Lee, Kyung Jong

    1999-01-01

    During cooling of steels, the heat transfer was controlled by radiation, convection, conduction and heat evolution from phase transformation. To analyze the heat transfer during cooling precisely, the material constants such as density, heat capacity and the heat evolved during transformation were obtained as functions of temperature and chemical composition for each phase observed in plain carbon steel using a thermodynamic analysis based on the sublattice model of Fe-C-Mn system. The results were applied to 0.049 wt% and 0.155 wt% carbon steels with an austenitic stainless steel as reference by developing a proper heat transfer governing equation. The equation was solved using the lumped system method. In addition, using a transformation dilatometer with adequate experimental conditions to clarify the individual heat transfer effect, the transformation heat evolved during cooling and the transformation behavior as well as the temperature change were observed. The predicted temperature profiles during cooling were well agreed with the measured ones

  7. Low-Flow Film Boiling Heat Transfer on Vertical Surfaces

    DEFF Research Database (Denmark)

    Munthe Andersen, J. G.; Dix, G. E.; Leonard, J. E.

    1976-01-01

    The phenomenon of film boiling heat transfer for high wall temperatures has been investigated. Based on the assumption of laminar flow for the film, the continuity, momentum, and energy equations for the vapor film are solved and a Bromley-type analytical expression for the heat transfer...... length, an average film boiling heat transfer coefficient is obtained....

  8. Screening of exciplex formation by distant electron transfer.

    Science.gov (United States)

    Fedorenko, S G; Khokhlova, S S; Burshtein, A I

    2012-01-12

    The excitation quenching by reversible exciplex formation, combined with irreversible but distant electron transfer, is considered by means of the integral encounter theory (IET). Assuming that the quenchers are in great excess, the set of IET equations for the excitations, free ions, and exciplexes is derived. Solving these equations gives the Laplace images of all these populations, and these are used to specify the quantum yields of the corresponding reaction products. It appears that diffusion facilitates the exciplex production and the electron transfer. On the other hand the stronger the electron transfer is, the weaker is the exciplex production. At slow diffusion the distant quenching of excitations by ionization prevents their reaching the contact where they can turn into exciplexes. This is a screening effect that is most pronounced when the ionization rate is large.

  9. Heat transfer, condensation and fog formation in crossflow plastic heat exchangers

    NARCIS (Netherlands)

    Brouwers, H.J.H.

    1996-01-01

    In this paper heat transfer of air-water-vapour mixtures in plastic crossflow heat exchangers is studied theoretically and experimentally. First, a model for heat transfer without condensation is derived, resulting in a set of classical differential equations. Subsequently, heat transfer with wall

  10. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model

  11. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

  12. Spatial evolution equation of wind wave growth

    Institute of Scientific and Technical Information of China (English)

    WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)

    2003-01-01

    Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.

  13. Stability test for a parabolic partial differential equation

    NARCIS (Netherlands)

    Vajta, Miklos

    2001-01-01

    The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer.

  14. Mixed Convection Heat Transfer on the Outside of a Vertical Cylinder

    Energy Technology Data Exchange (ETDEWEB)

    Bhattacharyya, A

    1965-10-15

    An experimental study was made of turbulent heat transfer from a vertical cylinder placed in a square channel. The flow medium was water flowing upwards. Basic differential equations governing the mixed flow heat transfer phenomena in a vertical annulus are presented. A dimensional analysis is done to find the dimensionless variables affecting the relative magnitude of the effect of buoyancy on forced convection heat transfer. Dimensionless equations correlating the experimental data ana incorporating a buoyancy parameter of the form Gr/Re{sup 2} are presented. Reynolds number range covered is 690 to 129,500 and the Rayleigh num- ber range covered is 10{sup 9} to 4.2 x 10{sup 13} . Effect of different length parameters, like hydraulic diameter and distance of the measuring point from the inlet of the test section, on dimensionless equations are studied.

  15. Simultaneous heat and moisture transfer in porous elements: transfer function method

    International Nuclear Information System (INIS)

    Souza, H.A. de.

    1985-01-01

    The presence of moisture in a porous element may strongly affect the transfer of heat through this element due to the processes which occur associated with the phase changes at the boundary surfaces and internally in the wall body. In addition, the structural properties of the element may also be meaningfully affected. The formulation of mathematical models for the simultaneous heat and mass transfer in porous elements results in a pair of nonlinear coupled equations for the temperature and moisture content distributions, in the material. It is supposed, in this work, that the actual variation of the properties of the porous medium is small in the range of variables which describe the specific problem to be analyzed. This enables us to work with linearized equations, making possible the use of linear solution methods. In this context, the present work deals with a linear procedure for the solution of simultaneous heat and moisture transfer problems in porous elements, sujected to arbitrary boundary conditions. This results in a linear relation between the heat and mass flux densities through the boundary surfaces of the elements and their associated potentials. It is shown that the model is consistent in asymptotical limiting cases; the model is then used for analyzing the drying process of a porous element, subjected to ambient actual conditions. (Author) [pt

  16. Computation of single- and two-phase heat transfer rates suitable for water-cooled tubes and subchannels

    International Nuclear Information System (INIS)

    Groeneveld, D.C.; Leung, L.K.H.; Cheng, S.C.; Nguyen, C.

    1989-01-01

    A computational method for predicting heat transfer, valid for a wide range of flow conditions (from pool boiling and laminar flow conditions to highly turbulent flow), has been developed. It correctly identifies the heat transfer modes and predicts the heat transfer rates as well as transition points (such as the critical heat flux point) on the boiling curve. The computational heat transfer method consists of a combination of carefully chosen heat transfer equations for each heat transfer mode. Each of these equations has been selected because of their accuracy, wide range of application, and correct asymptotic trends. Using a mechanistically-based heat transfer logic, these equations have been combined in a convenient software package suitable for PC or mainframe application. The computational method has been thoroughly tested against many sets of experimental data. The parametric and asymptotic trends of the prediction method have been examined in detail. Correction factors are proposed for extending the use of individual predictive techniques to various geometric configurations and upstream conditions. (orig.)

  17. Scattering and emission from inhomogeneous vegetation canopy and alien target beneath by using three-dimensional vector radiative transfer (3D-VRT) equation

    International Nuclear Information System (INIS)

    Jin Yaqiu; Liang Zichang

    2005-01-01

    To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed

  18. Solution of the comoving-frame equation of transfer in spherically symmetric flows. IV. Frequency-dependent source functions for scattering by atoms and electrons

    International Nuclear Information System (INIS)

    Mihalas, D.; Kunasz, P.B.; Hummer, D.G.

    1976-01-01

    A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles

  19. Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

    International Nuclear Information System (INIS)

    Bourdon, A; Pasko, V P; Liu, N Y; Celestin, S; Segur, P; Marode, E

    2007-01-01

    This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP 3 ) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by Segur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 O 2 O 2 is the partial pressure of molecular oxygen in air in units of Torr ( p O 2 = 150 Torr) at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP 3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of

  20. International symposium on radiative heat transfer: Book of abstracts

    International Nuclear Information System (INIS)

    1995-01-01

    The international symposium on radiative heat transfer was held on 14-18 August 1995 Turkey. The specialists discussed radiation transfer in materials processing and manufacturing, solution of radiative heat transfer equation, transient radiation problem and radiation-turbulence interactions, raditive properties of gases, atmospheric and stellar radiative transfer , radiative transfer and its applications, optical and radiative properties of soot particles, inverse radiation problems, partticles, fibres,thermophoresis and waves and modelling of comprehensive systems at the meeting. Almost 79 papers were presented in the meeting

  1. Modeling of the heat transfer in bypass transitional boundary-layer flows

    Science.gov (United States)

    Simon, Frederick F.; Stephens, Craig A.

    1991-01-01

    A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.

  2. Social Support and Motivation to Transfer as Predictors of Training Transfer: Testing Full and Partial Mediation Using Meta-Analytic Structural Equation Modelling

    Science.gov (United States)

    Reinhold, Sarah; Gegenfurtner, Andreas; Lewalter, Doris

    2018-01-01

    Social support and motivation to transfer are important components in conceptual models on transfer of training. Previous research indicates that both support and motivation influence transfer. To date, however, it is not yet clear if social support influences transfer of training directly, or if this influence is mediated by motivation to…

  3. A new approach to radiative transfer theory using Jones's vectors. I

    International Nuclear Information System (INIS)

    Fymat, A.L.; Vasudevan, R.

    1975-01-01

    Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)

  4. Elementary heat transfer analysis

    CERN Document Server

    Whitaker, Stephen; Hartnett, James P

    1976-01-01

    Elementary Heat Transfer Analysis provides information pertinent to the fundamental aspects of the nature of transient heat conduction. This book presents a thorough understanding of the thermal energy equation and its application to boundary layer flows and confined and unconfined turbulent flows. Organized into nine chapters, this book begins with an overview of the use of heat transfer coefficients in formulating the flux condition at phase interface. This text then explains the specification as well as application of flux boundary conditions. Other chapters consider a derivation of the tra

  5. Heat transfer in plate heat exchanger channels: Experimental validation of selected correlation equations

    Directory of Open Access Journals (Sweden)

    Cieśliński Janusz T.

    2016-09-01

    Full Text Available This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx. The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.

  6. Mode-to-mode energy transfers in convective patterns

    Indian Academy of Sciences (India)

    Abstract. We investigate the energy transfer between various Fourier modes in a low- dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical ...

  7. Standard electrode potential, Tafel equation, and the solvation thermodynamics.

    Science.gov (United States)

    Matyushov, Dmitry V

    2009-06-21

    Equilibrium in the electronic subsystem across the solution-metal interface is considered to connect the standard electrode potential to the statistics of localized electronic states in solution. We argue that a correct derivation of the Nernst equation for the electrode potential requires a careful separation of the relevant time scales. An equation for the standard metal potential is derived linking it to the thermodynamics of solvation. The Anderson-Newns model for electronic delocalization between the solution and the electrode is combined with a bilinear model of solute-solvent coupling introducing nonlinear solvation into the theory of heterogeneous electron transfer. We therefore are capable of addressing the question of how nonlinear solvation affects electrochemical observables. The transfer coefficient of electrode kinetics is shown to be equal to the derivative of the free energy, or generalized force, required to shift the unoccupied electronic level in the bulk. The transfer coefficient thus directly quantifies the extent of nonlinear solvation of the redox couple. The current model allows the transfer coefficient to deviate from the value of 0.5 of the linear solvation models at zero electrode overpotential. The electrode current curves become asymmetric in respect to the change in the sign of the electrode overpotential.

  8. Theoretical analysis and experimental study of oxygen transfer under regular and non-breaking waves

    Institute of Scientific and Technical Information of China (English)

    尹则高; 梁丙臣; 王乐

    2013-01-01

    The dissolved oxygen concentration is an important index of water quality, and the atmosphere is one of the important sources of the dissolved oxygen. In this paper, the mass conservation law and the dimensional analysis method are employed to study the oxygen transfer under regular and non-breaking waves, and a unified oxygen transfer coefficient equation is obtained with consi-deration of the effect of kinetic energy and wave period. An oxygen transfer experiment for the intermediate depth water wave is per-formed to measure the wave parameters and the dissolved oxygen concentration. The experimental data and the least squares method are used to determine the constant in the oxygen transfer coefficient equation. The experimental data and the previous reported data are also used to further validate the oxygen transfer coefficient, and the agreement is satisfactory. The unified equation shows that the oxygen transfer coefficient increases with the increase of a parameter coupled with the wave height and the wave length, but it de-creases with the increase of the wave period, which has a much greater influence on the oxygen transfer coefficient than the coupled parameter.

  9. Theory of light transfer in food and biological materials

    Science.gov (United States)

    In this chapter, we first define the basic radiometric quantities that are needed for describing light propagation in food and biological materials. Radiative transfer theory is then derived, according to the principle of the conservation of energy. Because the radiative transfer theory equation is ...

  10. Equations for transient flow-boiling in a duct

    International Nuclear Information System (INIS)

    Mathers, W.G.; Ferch, R.L.; Hancox, W.T.; McDonald, B.H.

    1981-01-01

    In this paper we derive a separated phase model for weakly coupled flows which extends a model presented elsewhere (BANERJEE, FERCH, MATHERS and McDONALD, 1978). A hyperbolic system of seven partial differential equations results with ensemble-averaged phase velocities, enthalpies and pressures, and void fraction as dependent variables (UVUTUP model). The required constitutive equations for mass, momentum and energy transfer between phases and between the phases and the boundaries are discussed. The relationship of the UVUTUP model to other existing models is also presented

  11. Experimental measurement of zero power reactor transfer function

    International Nuclear Information System (INIS)

    Liang Shuhong

    2011-01-01

    In order to study the zero power reactor (ZPR) transfer function, the ZPR transfer function expression was deduced with the point reactor kinetics equation, which was disturbed by reactivity input response. Based on the Fourier analysis for the input of triangular wave, the relation between the transfer function and reactivity was got. Validating research experiment was made on the DF-VI fast ZPR. After the disturbed reactivity was measured, the experimental value of the transfer function was got. According to the experimental value and the calculated value, the expression of the ZPR transfer function is proved, whereas the disturbed reactivity is got from the transfer function. (authors)

  12. Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation

    Directory of Open Access Journals (Sweden)

    Jinping Tang

    2017-01-01

    Full Text Available Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE. It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.

  13. Numerical simulations of a coupled radiative?conductive heat transfer model using a modified Monte Carlo method

    KAUST Repository

    Kovtanyuk, Andrey E.

    2012-01-01

    Radiative-conductive heat transfer in a medium bounded by two reflecting and radiating plane surfaces is considered. This process is described by a nonlinear system of two differential equations: an equation of the radiative heat transfer and an equation of the conductive heat exchange. The problem is characterized by anisotropic scattering of the medium and by specularly and diffusely reflecting boundaries. For the computation of solutions of this problem, two approaches based on iterative techniques are considered. First, a recursive algorithm based on some modification of the Monte Carlo method is proposed. Second, the diffusion approximation of the radiative transfer equation is utilized. Numerical comparisons of the approaches proposed are given in the case of isotropic scattering. © 2011 Elsevier Ltd. All rights reserved.

  14. Laminar forced convective/conductive heat transfer by finite element method

    International Nuclear Information System (INIS)

    Kushwaha, H.S.; Kakodkar, A.

    1982-01-01

    The present study is directed at developing a finite element computer program for solution of decoupled convective/conductive heat transfer problems. Penalty function formulation has been used to solve momentum equations and subsequently transient energy equation is solved using modified Crank-Nicolson method. The optimal upwinding scheme has been employed in energy equation to remove oscillations at high Peclet number. (author)

  15. Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

    Directory of Open Access Journals (Sweden)

    Hożejowska Sylwia

    2015-01-01

    Full Text Available The paper presents mathematical modelling of flow boiling heat transfer in a rectangular minichannel asymmetrically heated by a thin and one-sided enhanced foil. Both surfaces are available for observations due to the openings covered with glass sheets. Thus, changes in the colour of the plain foil surface can be registered and then processed. Plain side of the heating foil is covered with a base coat and liquid crystal paint. Observation of the opposite, enhanced surface of the minichannel allows for identification of the gas-liquid two-phase flow patterns and vapour quality. A two-dimensional mathematical model of heat transfer in three subsequent layers (sheet glass, heating foil, liquid was proposed. Heat transfer in all these layers was described with the respective equations: Laplace equation, Poisson equation and energy equation, subject to boundary conditions corresponding to the observed physical process. The solutions (temperature distributions in all three layers were obtained by Trefftz method. Additionally, the temperature of the boiling liquid was obtained by homotopy perturbation method (HPM combined with Trefftz method. The heat transfer coefficient, derived from Robin boundary condition, was estimated in both approaches. In comparison, the results by both methods show very good agreement especially when restricted to the thermal sublayer.

  16. Boundary value problemfor multidimensional fractional advection-dispersion equation

    Directory of Open Access Journals (Sweden)

    Khasambiev Mokhammad Vakhaevich

    2015-05-01

    Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

  17. Nonlinear behavior of micro bubbles under ultrasound due to heat transfer

    International Nuclear Information System (INIS)

    Lim, Chan Soo; Kwak, Ho Young; Kim, Jeong Eun; Lee, Jae Young

    2009-01-01

    We investigated the nonlinear behavior of a microbubble under ultrasound, taking into account the heat transfer inside the bubble and through the bubble wall. The polytropic relation, which has been used for the process of pressure change depending on the volume variation of ideal gases, cannot properly treat heat transfer involving the oscillating bubble under ultrasound. In this study, a set of solutions of the Navier-Stokes equations for the gas inside the bubble along with an analytical treatment of the Navier-Stokes equations for the liquid adjacent to the bubble wall was used to treat properly the heat transfer process for the oscillating bubble under ultrasound. Entropy generation due to finite heat transfer, which induces the lost work during bubble evolution, reduces the collapsing process and considerably affects the nonlinear behavior of the bubble

  18. Real-time tumor ablation simulation based on the dynamic mode decomposition method

    KAUST Repository

    Bourantas, George C.

    2014-05-01

    Purpose: The dynamic mode decomposition (DMD) method is used to provide a reliable forecasting of tumor ablation treatment simulation in real time, which is quite needed in medical practice. To achieve this, an extended Pennes bioheat model must be employed, taking into account both the water evaporation phenomenon and the tissue damage during tumor ablation. Methods: A meshless point collocation solver is used for the numerical solution of the governing equations. The results obtained are used by the DMD method for forecasting the numerical solution faster than the meshless solver. The procedure is first validated against analytical and numerical predictions for simple problems. The DMD method is then applied to three-dimensional simulations that involve modeling of tumor ablation and account for metabolic heat generation, blood perfusion, and heat ablation using realistic values for the various parameters. Results: The present method offers very fast numerical solution to bioheat transfer, which is of clinical significance in medical practice. It also sidesteps the mathematical treatment of boundaries between tumor and healthy tissue, which is usually a tedious procedure with some inevitable degree of approximation. The DMD method provides excellent predictions of the temperature profile in tumors and in the healthy parts of the tissue, for linear and nonlinear thermal properties of the tissue. Conclusions: The low computational cost renders the use of DMD suitable forin situ real time tumor ablation simulations without sacrificing accuracy. In such a way, the tumor ablation treatment planning is feasible using just a personal computer thanks to the simplicity of the numerical procedure used. The geometrical data can be provided directly by medical image modalities used in everyday practice. © 2014 American Association of Physicists in Medicine.

  19. A multilevel method for conductive-radiative heat transfer

    Energy Technology Data Exchange (ETDEWEB)

    Banoczi, J.M.; Kelley, C.T. [North Carolina State Univ., Raleigh, NC (United States)

    1996-12-31

    We present a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. The equations can be formulated as a compact fixed point problem with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We use fast transport solvers developed by the second author, to construct an efficient evaluation of the fixed point map and then apply the Atkinson-Brakhage, method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system.

  20. Double diffusive conjugate heat transfer: Part I

    Science.gov (United States)

    Azeem, Soudagar, Manzoor Elahi M.

    2018-05-01

    The present work is undertaken to investigate the effect of solid wall being placed at left of square cavity filled with porous medium. The presence of a solid wall in the porous medium turns the situation into a conjugate heat transfer problem. The boundary conditions are such that the left vertical surface is maintained at highest temperature and concentration whereas right vertical surface at lowest temperature and concentration in the medium. The top and bottom surfaces are adiabatic. The additional conduction equation along with the regular momentum and energy equations of porous medium are solved in an iterative manner with the help of finite element method. It is seen that the heat and mass transfer rate is lesser due to smaller thermal and concentration gradients.

  1. Models for fluid flows with heat transfer in mixed convection

    International Nuclear Information System (INIS)

    Mompean Munhoz da Cruz, G.

    1989-06-01

    Second order models were studied in order to predict turbulent flows with heat transfer. The equations used correspond to the characteristic scale of turbulent flows. The order of magnitude of the terms of the equation is analyzed by using Reynolds and Peclet numbers. The two-equation model (K-ε) is applied in the hydrodynamic study. Two models are developed for the heat transfer analysis: the Prt + teta 2 and the complete model. In the first model, the turbulent thermal diffusivity is calculated by using the Prandtl number for turbulent flow and an equation for the variance of the temperature fluctuation. The second model consists of three equations concerning: the turbulent heat flow, the variance of the temperature fluctuation and its dissipation ratio. The equations were validated by four experiments, which were characterized by the analysis of: the air flow after passing through a grid of constant average temperature and with temperature gradient, an axysymmetric air jet submitted to high and low heating temperature, the mixing (cold-hot) of two coaxial jets of sodium at high Peclet number. The complete model is shown to be the most suitable for the investigations presented [fr

  2. Analytical Evalution of Heat Transfer Conductivity with Variable Properties

    DEFF Research Database (Denmark)

    Rahimi, Masoume; Hosseini, Mohammad Javad; Barari, Amin

    2011-01-01

    The homotopy analysis method (HAM) as a new technique which is powerful and easy-to-use, is applied to solve heat transfer problems. In this paper, we use HAM for heat transfer conductivity equation with variable properties which may contain highly nonlinear terms. The obtained results are also...

  3. The influence of physical properties of materials used for slide rings on the process of heat transfer in the non-contacting face seals

    Directory of Open Access Journals (Sweden)

    Blasiak Slawomir

    2017-01-01

    Full Text Available The paper presents the results of analytical solution of the model of heat transfer for non-contacting face seals. Comparative analyses were performed for various physical properties of materials used for slide rings. A mathematical model includes a series of differential equations of partial derivatives with generally used boundary conditions, i.e. the Reynold’s equation, energy equation and heat transfer equations, which describe the heat transfer in sealing rings with surrounding medium. Heat transfer equation is written in the Cartesian coordinate system and solved using the Green’s functions method. Theoretical studies made it possible to draw a number of practical conclusions on the phenomena of heat transfer in the node seal. The presented model will allow more accurate identification of the heat transfer mechanism in the node seal. The results will help to select appropriate materials for sealing rings, depending on operating conditions of non-contacting face seals.

  4. Radiation heat transfer within an open-cycle MHD generator channel

    Science.gov (United States)

    Delil, A. A. M.

    1983-05-01

    Radiation heat transfer in an MHD generator was modeled using the Sparrow and Cess model for radiation in an emitting, absorbing and scattering medium. The resulting general equations can be considerably reduced by introducing simplifying approximations for the channel and MHD gas properties. The simplifications lead to an engineering model, which is very useful for one-dimensional channel flow approximation. The model can estimate thermo-optical MHD gas properties, which can be substituted in the energy equation. The model considers the contribution of solid particles in the MHD gas to radiation heat transfer, considerable in coal-fired closed cycle MHD generators. The modeling is applicable also for other types of flow at elevated temperatures, where radiation heat transfer is an important quantity.

  5. Heat transfer analysis of parabolic trough solar receiver

    International Nuclear Information System (INIS)

    Padilla, Ricardo Vasquez; Demirkaya, Gokmen; Goswami, D. Yogi; Stefanakos, Elias; Rahman, Muhammad M.

    2011-01-01

    Highlights: → In this paper a detailed one dimensional numerical heat transfer analysis of a PTC is performed. → The receiver and envelope were divided into several segments and mass and energy balance were applied in each segment. → Improvements either in the heat transfer correlations or radiative heat transfer analysis are presented. → The proposed heat transfer model was validated with experimental data obtained from Sandia National Laboratory. → Our results showed a better agreement with experimental data compared to other models. -- Abstract: Solar Parabolic Trough Collectors (PTCs) are currently used for the production of electricity and applications with relatively higher temperatures. A heat transfer fluid circulates through a metal tube (receiver) with an external selective surface that absorbs solar radiation reflected from the mirror surfaces of the PTC. In order to reduce the heat losses, the receiver is covered by an envelope and the enclosure is usually kept under vacuum pressure. The heat transfer and optical analysis of the PTC is essential to optimize and understand its performance under different operating conditions. In this paper a detailed one dimensional numerical heat transfer analysis of a PTC is performed. The receiver and envelope were divided into several segments and mass and energy balance were applied in each segment. Improvements either in the heat transfer correlations or radiative heat transfer analysis are presented as well. The partial differential equations were discretized and the nonlinear algebraic equations were solved simultaneously. Finally, to validate the numerical results, the model was compared with experimental data obtained from Sandia National Laboratory (SNL) and other one dimensional heat transfer models. Our results showed a better agreement with experimental data compared to other models.

  6. Integrable boundary conditions and modified Lax equations

    International Nuclear Information System (INIS)

    Avan, Jean; Doikou, Anastasia

    2008-01-01

    We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding 'transfer' matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix

  7. Comparison of the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering.

    Science.gov (United States)

    da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques

    2003-12-01

    Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.

  8. Semi-analog Monte Carlo (SMC) method for time-dependent non-linear three-dimensional heterogeneous radiative transfer problems

    International Nuclear Information System (INIS)

    Yun, Sung Hwan

    2004-02-01

    Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with

  9. Ventilation equations for improved exothermic process control.

    Science.gov (United States)

    McKernan, John L; Ellenbecker, Michael J

    2007-04-01

    Exothermic or heated processes create potentially unsafe work environments for an estimated 5-10 million American workers each year. Excessive heat and process contaminants have the potential to cause acute health effects such as heat stroke, and chronic effects such as manganism in welders. Although millions of workers are exposed to exothermic processes, insufficient attention has been given to continuously improving engineering technologies for these processes to provide effective and efficient control. Currently there is no specific occupational standard established by OSHA regarding exposure to heat from exothermic processes, therefore it is important to investigate techniques that can mitigate known and potential adverse occupational health effects. The current understanding of engineering controls for exothermic processes is primarily based on a book chapter written by W. C. L. Hemeon in 1955. Improvements in heat transfer and meteorological theory necessary to design improved process controls have occurred since this time. The research presented involved a review of the physical properties, heat transfer and meteorological theories governing buoyant air flow created by exothermic processes. These properties and theories were used to identify parameters and develop equations required for the determination of buoyant volumetric flow to assist in improving ventilation controls. Goals of this research were to develop and describe a new (i.e. proposed) flow equation, and compare it to currently accepted ones by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH). Numerical assessments were conducted to compare solutions from the proposed equations for plume area, mean velocity and flow to those from the ACGIH and Hemeon. Parameters were varied for the dependent variables and solutions from the proposed, ACGIH, and Hemeon equations for plume area, mean velocity and flow were analyzed using a randomized complete block statistical

  10. A Forward GPS Multipath Simulator Based on the Vegetation Radiative Transfer Equation Model.

    Science.gov (United States)

    Wu, Xuerui; Jin, Shuanggen; Xia, Junming

    2017-06-05

    Global Navigation Satellite Systems (GNSS) have been widely used in navigation, positioning and timing. Nowadays, the multipath errors may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), i.e., GPS-Multipath Reflectometry (GPS-MR). However, bistatic scattering properties and the relation between GPS observables and geophysical parameters are not clear, e.g., vegetation. In this paper, a new element on bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that the wheat will decrease the amplitudes of GPS multipath observables (SNR, phase and code), if we increase the vegetation moisture contents or the scatters sizes (stem or leaf). Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with previous results for environmental parameter detections by GPS-MR.

  11. Theory of periodic conjugate heat transfer

    CERN Document Server

    Zudin, Yuri B

    2016-01-01

    This book presents the theory of periodic conjugate heat transfer in detail. It offers a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body.

  12. Transfer equations for cesium-137 for coniferous forest understorey plant species

    International Nuclear Information System (INIS)

    Wirth, E.; Hiersche, L.; Kammerer, L.; Krajewska, G.; Krestel, R.; Mahler, S.; Roemmelt, R.

    1994-01-01

    The transfer of cesium-137 from organic soil horizons to understorey vegetation has been studied on two coniferous tree sites. In total, 14 different plants preferably taking up their nutrients from organic soil layers were taken into account. A relatively good correlation was found to exist between the transfer factor (Bq/kg plant dry wt./Bq/kg O-horizons dry wt.) for dicotyledons (r=0.51) and berry plants (r=0.63), but there was no correlation for monocotyledons (r= 0 .15). The correlations could not be improved by additionally taking potassium in plant and soil into account. These results are discussed in respect to different parameters influencing the amount of cesium-137 uptake, including plants supported by mycorrhizal fungi

  13. Mass transfer from smooth alabaster surfaces in turbulent flows

    Science.gov (United States)

    Opdyke, Bradley N.; Gust, Giselher; Ledwell, James R.

    1987-11-01

    The mass transfer velocity for alabaster plates in smooth-wall turbulent flow is found to vary with the friction velocity according to an analytic solution of the advective diffusion equation. Deployment of alabaster plates on the sea floor can perhaps be used to estimate the viscous stress, and transfer velocities for other species.

  14. Photon-momentum transfer in molecular photoionization

    Science.gov (United States)

    Chelkowski, Szczepan; Bandrauk, André D.

    2018-05-01

    In most models and theoretical calculations describing multiphoton ionization by infrared light, the dipole approximation is used. This is equivalent to setting the very small photon momentum to zero. Using numerical solutions of the (nondipole) three-dimensional time-dependent Schrödinger equation for one electron in a H2+ molecular ion we investigate the effect the photon-momentum transfer to the photoelectron in an H2+ ion in various regimes. We find that the photon-momentum transfer in a molecule is very different from the transfer in atoms due to two-center interference effects. The photon-momentum transfer is very sensitive to the symmetry of the initial electronic state and is strongly dependent on the internuclear distance and on the ellipticity of the laser.

  15. Development of platform to compare different wall heat transfer packages for system analysis codes

    International Nuclear Information System (INIS)

    Kim, Min-Gil; Lee, Won Woong; Lee, Jeong Ik; Shin, Sung Gil

    2016-01-01

    System thermal hydraulic (STH) analysis code is used for analyzing and evaluating the safety of a designed nuclear system. The system thermal hydraulic analysis code typically solves mass, momentum and energy conservation equations for multiple phases with sets of selected empirical constitutive equations to close the problem. Several STH codes are utilized in academia, industry and regulators, such as MARS-KS, SPACE, RELAP5, COBRA-TF, TRACE, and so on. Each system thermal hydraulic code consists of different sets of governing equations and correlations. However, the packages and sets of correlations of each code are not compared quantitatively yet. Wall heat transfer mode transition maps of SPACE and MARS-KS have a little difference for the transition from wall nucleate heat transfer mode to wall film heat transfer mode. Both codes have the same heat transfer packages and correlations in most region except for wall film heat transfer mode. Most of heat transfer coefficients calculated for the range of selected variables of SPACE are the same with those of MARS-KS. For the intervals between 500K and 540K of wall temperature, MARS-KS selects the wall film heat transfer mode and Bromley correlation but SPACE select the wall nucleate heat transfer mode and Chen correlation. This is because the transition from nucleate boiling to film boiling of MARS-KS is earlier than SPACE. More detailed analysis of the heat transfer package and flow regime package will be followed in the near future

  16. Transient heat transfer in longitudinal fins of various profiles with ...

    Indian Academy of Sciences (India)

    Transient heat transfer through a longitudinal fin of various profiles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are ...

  17. Mathematical Model for Fluid Flow and Heat Transfer Processes in Plate Exchanger

    Directory of Open Access Journals (Sweden)

    Cvete B. Dimitrieska

    2015-11-01

    Full Text Available Within the analytical solution of the system of equations which solve fluid flow and heat transfer processes, the elliptical and parabolic differential equations based on initial and boundary conditions is usually unfamiliar in a closed form. Numerical solution of equation system is necessarily obtained by discretization of equations. When system of equations relate to estimation of two dimensional stationary problems, the applicable method for estimation in basic two – dimensional form is recommended.

  18. Classical collisions of protons with hydrogen atoms. [Equations of motion, cross sections, C code, FORTRAN, moments of inertia

    Energy Technology Data Exchange (ETDEWEB)

    Banks, D; Hughes, P E; Percival, I C [Queen Mary Coll., London (UK); Barnes, K S [National Health Service Operational Research Group, Royal Institute of Public Administration, Reading, Berkshire, UK; Richards, D [Open Univ., Milton Keynes (UK); Valentine, N A [Digital Equipment Corporation, Bilton House, Uxbridge Road, Ealing, London, UK; Wilson, Mc B [Glasgow Univ. (UK). Dept. of Natural Philosophy

    1977-01-01

    The program solves the equations of motion for the interaction of 3 charged particles, obtaining final states in terms of initial states, and energy transfers, angles of ejection, and final cartesian co-ordinates of relative motion. Using a Monte Carlo method on many orbits total ionization and charge transfer cross sections, integral energy transfer cross sections and moments of energy transfers are estimated. Facilities are provided for obtaining angular distributions, momentum transfer cross sections and for comparison with various approximate classical theories. The equations of motion are solved using stepwise fourth-order Runge-Kutta integration with automatic steplength change. Selection of initial conditions is determined by the user, usually as a statistical distribution determined by a pseudorandom number subroutine. Classical representation theory and transformation methods are extensively used.

  19. A mathematical model of endovascular heat transfer for human brain cooling

    Science.gov (United States)

    Salsac, Anne-Virginie; Lasheras, Juan Carlos; Yon, Steven; Magers, Mike; Dobak, John

    2000-11-01

    Selective cooling of the brain has been shown to exhibit protective effects in cerebral ischemia, trauma, and spinal injury/ischemia. A multi-compartment, unsteady thermal model of the response of the human brain to endovascular cooling is discussed and its results compared to recent experimental data conducted with sheep and other mammals. The model formulation is based on the extension of the bioheat equation, originally proposed by Pennes(1) and later modified by Wissler(2), Stolwijk(3) and Werner and Webb(4). The temporal response of the brain temperature and that of the various body compartments to the cooling of the blood flowing through the common carotid artery is calculated under various scenarios. The effect of the boundary conditions as well as the closure assumptions used in the model, i.e. perfusion rate, metabolism heat production, etc. on the cooling rate of the brain are systematically investigated. (1) Pennes H. H., “Analysis of tissue and arterial blood temperature in the resting forearm.” J. Appl. Physiol. 1: 93-122, 1948. (2) Wissler E. H., “Steady-state temperature distribution in man”, J. Appl. Physiol., 16: 764-740, 1961. (3) Stolwick J. A. J., “Mathematical model of thermoregulation” in “Physiological and behavioral temperature regulation”, edited by J. D. Hardy, A. P. Gagge and A. J. Stolwijk, Charles C. Thomas Publisher, Springfiels, Ill., 703-721, 1971. (4) Werner J., Webb P., “A six-cylinder model of human thermoregulation for general use on personal computers”, Ann. Physiol. Anthrop., 12(3): 123-134, 1993.

  20. A boundary element model for investigating the effects of eye tumor on the temperature distribution inside the human eye.

    Science.gov (United States)

    Ooi, E H; Ang, W T; Ng, E Y K

    2009-08-01

    A three-dimensional boundary element model of the human eye is developed to investigate the thermal effects of eye tumor on the ocular temperature distribution. The human eye is modeled as comprising several regions which have different thermal properties. The tumor is one of these regions. The thermal effects of the tumor are simulated by taking it to have a very high metabolic heat generation and blood perfusion rate. Inside the tumor, the steady state temperature is governed by the Pennes bioheat equation. Elsewhere, in normal tissues of the eye, the temperature satisfies the Laplace's equation. To compute the temperature on the corneal surface, the surface boundary of each region is divided into triangular elements.

  1. An optimal control problem by controlling heat source of the surface of tissue

    OpenAIRE

    Dhar, 1Rikhiya; Dhar, Ranajit; Dhar, Piyanka

    2013-01-01

    A distributed optimal control problem for a system described by bio-heat equation for a homogeneous plane tissue is analytically investigated such that a desired temperature of the tissue at a particular point of location of tumour in hyperthermia can be attained at the end of a total time of operation of the process due to induced microwave on the surface of the tissue which is taken as control. Here the temperature of the tissue along the length of the tissue at different times of operation...

  2. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  3. Numerical investigation into the highly nonlinear heat transfer equation with bremsstrahlung emission in the inertial confinement fusion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Habibi, M.; Oloumi, M.; Hosseinkhani, H.; Magidi, S. [Plasma and Fusion Research School, Nuclear Science and Technology Research Institute, Tehran (Iran, Islamic Republic of)

    2015-10-15

    A highly nonlinear parabolic partial differential equation that models the electron heat transfer process in laser inertial fusion has been solved numerically. The strong temperature dependence of the electron thermal conductivity and heat loss term (Bremsstrahlung emission) makes this a highly nonlinear process. In this case, an efficient numerical method is developed for the energy transport mechanism from the region of energy deposition into the ablation surface by a combination of the Crank-Nicolson scheme and the Newton-Raphson method. The quantitative behavior of the electron temperature and the comparison between analytic and numerical solutions are also investigated. For more clarification, the accuracy and conservation of energy in the computations are tested. The numerical results can be used to evaluate the nonlinear electron heat conduction, considering the released energy of the laser pulse at the Deuterium-Tritium (DT) targets and preheating by heat conduction ahead of a compression shock in the inertial confinement fusion (ICF) approach. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  4. A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer

    International Nuclear Information System (INIS)

    Kim, Hyun Keol; Charette, Andre

    2007-01-01

    The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved

  5. Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

    International Nuclear Information System (INIS)

    Tanaka, Midori; Tanimura, Yoshitaka

    2010-01-01

    Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.

  6. Simple Ion Transfer at Liquid|Liquid Interfaces

    Directory of Open Access Journals (Sweden)

    L. J. Sanchez Vallejo

    2012-01-01

    Full Text Available The main aspects related to the charge transfer reactions occurring at the interface between two immiscible electrolyte solutions (ITIES are described. The particular topics to be discussed involve simple ion transfer. Focus is given on theoretical approaches, numerical simulations, and experimental methodologies. Concerning the theoretical procedures, different computational simulations related to simple ion transfer are reviewed. The main conclusions drawn from the most accepted models are described and analyzed in regard to their relevance for explaining different aspects of ion transfer. We describe numerical simulations implementing different approaches for solving the differential equations associated with the mass transport and charge transfer. These numerical simulations are correlated with selected experimental results; their usefulness in designing new experiments is summarized. Finally, many practical applications can be envisaged regarding the determination of physicochemical properties, electroanalysis, drug lipophilicity, and phase-transfer catalysis.

  7. Numerical instability of time-discretized one-point kinetic equations

    International Nuclear Information System (INIS)

    Hashimoto, Kengo; Ikeda, Hideaki; Takeda, Toshikazu

    2000-01-01

    The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank-Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank-Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula

  8. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu

    2017-01-01

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  9. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed

    2017-07-06

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  10. Verification of radiation heat transfer analysis in KSTAR PFC and vacuum vessel during baking

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, S.Y. [Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 34167 (Korea, Republic of); Kim, Y.J., E-mail: k43689@nfri.re.kr [National Fusion Research Institute, 169-148 Gwahang-ro, Yuseong-gu, Daejeon 34133 (Korea, Republic of); Kim, S.T.; Jung, N.Y.; Im, D.S.; Gong, J.D.; Lee, J.M.; Park, K.R.; Oh, Y.K. [National Fusion Research Institute, 169-148 Gwahang-ro, Yuseong-gu, Daejeon 34133 (Korea, Republic of)

    2016-11-01

    Highlights: • Thermal network is used to analyze heat transfer from PFC to VV. • Three heat transfer rate equations are derived based on the thermal network. • The equations is verified using Experimental data and design documents. • Most of the heat lost in tokamak is transferred to experimental room air. • The heat loss to the air is 101 kW of the total heat loss of 154 kW in tokamak. - Abstract: KSTAR PFC (Plasma Facing Component) and VV (Vacuum Vessel) were not arrived at the target temperatures in bake-out phase, which are 300 °C and 110 °C, respectively. The purpose of this study is to find out the reason why they have not been reached the target temperature. A thermal network analysis is used to investigate the radiation heat transfer from PFC to VV, and the thermal network is drawn up based on the actual KSTAR tokamak. The analysis model consists of three equations, and is solved using the EES (Engineering Equation Solver). The heat transfer rates obtained with the analysis model is verified using the experimental data at the KSTAR bake-out phase. The analyzed radiation heat transfer rates from PFC to VV agree quite well with those of experiment throughout the bake-out phase. Heat loss from PFC to experimental room air via flange of VV is also calculated and compared, which is found be the main reason of temperature gap between the target temperature and actually attained temperature of KSTAR PFC.

  11. Verification of radiation heat transfer analysis in KSTAR PFC and vacuum vessel during baking

    International Nuclear Information System (INIS)

    Yoo, S.Y.; Kim, Y.J.; Kim, S.T.; Jung, N.Y.; Im, D.S.; Gong, J.D.; Lee, J.M.; Park, K.R.; Oh, Y.K.

    2016-01-01

    Highlights: • Thermal network is used to analyze heat transfer from PFC to VV. • Three heat transfer rate equations are derived based on the thermal network. • The equations is verified using Experimental data and design documents. • Most of the heat lost in tokamak is transferred to experimental room air. • The heat loss to the air is 101 kW of the total heat loss of 154 kW in tokamak. - Abstract: KSTAR PFC (Plasma Facing Component) and VV (Vacuum Vessel) were not arrived at the target temperatures in bake-out phase, which are 300 °C and 110 °C, respectively. The purpose of this study is to find out the reason why they have not been reached the target temperature. A thermal network analysis is used to investigate the radiation heat transfer from PFC to VV, and the thermal network is drawn up based on the actual KSTAR tokamak. The analysis model consists of three equations, and is solved using the EES (Engineering Equation Solver). The heat transfer rates obtained with the analysis model is verified using the experimental data at the KSTAR bake-out phase. The analyzed radiation heat transfer rates from PFC to VV agree quite well with those of experiment throughout the bake-out phase. Heat loss from PFC to experimental room air via flange of VV is also calculated and compared, which is found be the main reason of temperature gap between the target temperature and actually attained temperature of KSTAR PFC.

  12. Numerical solutions of ordinary and partial differential equations in the frequency domain

    International Nuclear Information System (INIS)

    Hazi, G.; Por, G.

    1997-01-01

    Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

  13. Comparative analysis of solution methods of the punctual kinetic equations

    International Nuclear Information System (INIS)

    Hernandez S, A.

    2003-01-01

    The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)

  14. From quantum to semiclassical kinetic equations: Nuclear matter estimates

    International Nuclear Information System (INIS)

    Galetti, D.; Mizrahi, S.S.; Nemes, M.C.; Toledo Piza, A.F.R. de

    1985-01-01

    Starting from the exact microscopic time evolution of the quantum one body density associated with a many fermion system semiclassical approximations are derived to it. In the limit where small momentum transfer two body collisions are dominant we get a Fokker-Planck equation and work out friction and diffusion tensors explicitly for nuclear matter. If arbitrary momentum transfers are considered a Boltzmann equation is derived and used to calculate the viscosity coefficient of nuclear matter. A derivation is given of the collision term used by Landau to describe the damping of zero sound waves at low temperature in Plasmas. Memory effects are essential for this. The damping of zero sound waves in nuclear matter is also calculated and the value so obtained associated with the bulk value of the damping of giant resonances in finite nuclei. The bulk value is estimated to be quite small indicating the importance of the nuclear surface for the damping. (Author) [pt

  15. Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

    International Nuclear Information System (INIS)

    Mishra, Subhash C.; Roy, Hillol K.

    2007-01-01

    The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable

  16. Linear fractional diffusion-wave equation for scientists and engineers

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  17. Heat transfer with freezing and thawing

    CERN Document Server

    Lunardini, VJ

    1991-01-01

    This volume provides a comprehensive overview on the vast amount of literature on solidification heat transfer. Chapter one develops important basic equations and discusses the validity of considering only conductive heat transfer, while ignoring convection, in the large class of materials which make up the porous media. Chapters 2 to 4 deal with problems that can be expressed in plane (Cartesian) coordinates. These problems are further divided into boundary conditions of temperature, prescribed heat flux, and surface convection. Chapter 5 examines some plane geometries involving three-dime

  18. Sine-Gordon equation and its application to tectonic stress transfer

    Science.gov (United States)

    Bykov, Victor G.

    2014-07-01

    An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

  19. A literature survey on numerical heat transfer

    Science.gov (United States)

    Shih, T. M.

    1982-12-01

    Technical papers in the area of numerical heat transfer published from 1977 through 1981 are reviewed. The journals surveyed include: (1) ASME Journal of Heat Transfer, (2) International Journal of Heat and Mass Transfer, (3) AIAA Journal, (4) Numerical Heat Transfer, (5) Computers and Fluids, (6) International Journal for Numerical Methods in Engineering, (7) SIAM Journal of Numerical Analysis, and (8) Journal of Computational Physics. This survey excludes experimental work in heat transfer and numerical schemes that are not applied to equations governing heat transfer phenomena. The research work is categorized into the following areas: (A) conduction, (B) boundary-layer flows, (C) momentum and heat transfer in cavities, (D) turbulent flows, (E) convection around cylinders and spheres or within annuli, (F) numerical convective instability, (G) radiation, (H) combustion, (I) plumes, jets, and wakes, (J) heat transfer in porous media, (K) boiling, condensation, and two-phase flows, (L) developing and fully developed channel flows, (M) combined heat and mass transfer, (N) applications, (O) comparison and properties of numerical schemes, and (P) body-fitted coordinates and nonuniform grids.

  20. Large eddy simulations of turbulent flows with heat transfer

    International Nuclear Information System (INIS)

    Chatelain, Alexandre

    2004-01-01

    LES of turbulent flows with heat transfer was used within the framework of conjugate heat transfer problems. The objective of this work lies not only in identifying the various elements likely to impair temperature fluctuations estimations at the fluid/solid interface but also to introduce adequate wall modeling. The choice of a proper convection scheme for the transport of passive scalars led to the adoption of a high order upwind scheme with slope limiter. The use of classical wall models having shown some weaknesses as for the estimation of parietal temperature fluctuations, two new approaches are proposed and tested. The first one relies on a complete resolution of the Navier-Stokes equations on a refined grid close to the wall making it possible to rebuild the temperature fluctuations near the wall. The second one relies on the simultaneous and one dimensional resolution of a turbulent boundary layer equation and a variance transport equation near the wall. (author) [fr

  1. Heat and Mass Transfer on Squeezing Unsteady MHD Nano fluid Flow between Parallel Plates with Slip Velocity Effect

    International Nuclear Information System (INIS)

    Singh, K.; Rawat, S. K.; Kumar, M.

    2016-01-01

    Heat and mass transfer behavior of unsteady flow of squeezing between two parallel plates in the sight of uniform magnetic field with slip velocity effect is investigated. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained have been solved numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity, temperature, and concentration for various values of relevant parameters are illustrated graphically. The skin-friction coefficient and heat and mass transfer rate are also tabulated for various governing parameters. The results indicate that, for nano fluid flow, the rates of heat and mass transfer are inversely proportional to nanoparticle volume fraction and magnetic parameter. The rate of mass transfer increases with increasing values of Schmidt number and squeeze number.

  2. Obtention of an empirical equation for annular channels

    International Nuclear Information System (INIS)

    Diaz H, C.; Salinas R, G.A.

    1996-01-01

    Using a trial circuit, the experimental heat transfer coefficient is determined, in forced convection at one phase only within an annular channel in which water flows ascendantly and for this reason an empirical equation is determined. This work tries to contribute to the understanding of the forced convection phenomena in non tubular geometries like the annular channels. (Author)

  3. Two-state approximation of the Fadeev-Hahn equations

    International Nuclear Information System (INIS)

    Brener, S.E.

    1993-01-01

    The equations have been chosen which allow both to solve the scattering problems and to calculate the parameters of bound states of three particles with Coulomb interaction when the system energy is below the decay to three separate particles. The method of constructing of equations which are most suitable for concrete problems is considered. Different numerical schemes to calculate the low energy scattering cross sections with two-particle clusterization in 'in' and 'out' collision's channels have been developed. The bounds of applied approaches were determined and the peculiarities connected with differently defined reaction amplitudes under these approaches have been considered. The interpretation of obtained results at different definitions of reaction amplitudes was demonstrated, and the elastic, inelastic cross sections and muon transfer rates in hydrogen isotope mesic atom collisions have been calculated using Fadeev-Hahn equations. (author)

  4. A relativistic radiation transfer benchmark

    International Nuclear Information System (INIS)

    Munier, A.

    1988-01-01

    We use the integral form of the radiation transfer equation in an one dimensional slab to determine the time-dependent propagation of the radiation energy, flux and pressure in a collisionless homogeneous medium. First order v/c relativistic terms are included and the solution is given in the fluid frame and the laboratory frame

  5. Theoretical aspects of electron transfer reactions of complex molecules

    DEFF Research Database (Denmark)

    Kuznetsov, A. M.; Ulstrup, Jens

    2001-01-01

    Features of electron transfer involving complex molecules are discussed. This notion presently refers to molecular reactants where charge transfer is accompanied by large molecular reorganization, and commonly used displaced harmonic oscillator models do not apply. It is shown that comprehensive...... theory of charge transfer in polar media offers convenient tools for the treatment of experimental data for such systems, with due account of large-amplitude strongly anharmonic intramolecular reorganization. Equations for the activation barrier and free energy relationships are provided, incorporating...

  6. Theoretical and Numerical Study of Heat Transfer Deterioration in High Performance Light Water Reactor

    Directory of Open Access Journals (Sweden)

    David Palko

    2008-01-01

    Full Text Available A numerical investigation of the heat transfer deterioration (HTD phenomena is performed using the low-Re k-ω turbulence model. Steady-state Reynolds-averaged Navier-Stokes equations are solved together with equations for the transport of enthalpy and turbulence. Equations are solved for the supercritical water flow at different pressures, using water properties from the standard IAPWS (International Association for the Properties of Water and Steam tables. All cases are extensively validated against experimental data. The influence of buoyancy on the HTD is demonstrated for different mass flow rates in the heated pipes. Numerical results prove that the RANS low-Re turbulence modeling approach is fully capable of simulating the heat transfer in pipes with the water flow at supercritical pressures. A study of buoyancy influence shows that for the low-mass flow rates of coolant, the influence of buoyancy forces on the heat transfer in heated pipes is significant. For the high flow rates, buoyancy influence could be neglected and there are clearly other mechanisms causing the decrease in heat transfer at high coolant flow rates.

  7. Evaluation of radiation heat transfer in porous medial: Application for a pebble bed modular reactor cooled by CO2 gas

    Directory of Open Access Journals (Sweden)

    Sidi-Ali Kamel

    2013-01-01

    Full Text Available This work analyses the contribution of radiation heat transfer in the cooling of a pebble bed modular reactor. The mathematical model, developed for a porous medium, is based on a set of equations applied to an annular geometry. Previous major works dealing with the subject have considered the forced convection mode and often did not take into account the radiation heat transfer. In this work, only free convection and radiation heat transfer are considered. This can occur during the removal of residual heat after shutdown or during an emergency situation. In order to derive the governing equations of radiation heat transfer, a steady-state in an isotropic and emissive porous medium (CO2 is considered. The obtained system of equations is written in a dimensionless form and then solved. In order to evaluate the effect of radiation heat transfer on the total heat removed, an analytical method for solving the system of equations is used. The results allow quantifying both radiation and free convection heat transfer. For the studied situation, they show that, in a pebble bed modular reactor, more than 70% of heat is removed by radiation heat transfer when CO2 is used as the coolant gas.

  8. Second Law Analysis in Convective Heat and Mass Transfer

    Directory of Open Access Journals (Sweden)

    A. Ben Brahim

    2006-02-01

    Full Text Available This paper reports the numerical determination of the entropy generation due to heat transfer, mass transfer and fluid friction in steady state for laminar double diffusive convection, in an inclined enclosure with heat and mass diffusive walls, by solving numerically the mass, momentum, species conservation and energy balance equations, using a Control Volume Finite-Element Method. The influences of the inclination angle, the thermal Grashof number and the buoyancy ratio on total entropy generation were investigated. The irreversibilities localization due to heat transfer, mass transfer and fluid friction is discussed for three inclination angles at a fixed thermal Grashof number.

  9. Heat transfer enhancement in nanofluids. A numerical approach

    International Nuclear Information System (INIS)

    Fariñas Alvariño, P; Sáiz Jabardo, J M; Arce, A; Llamas Galdo, M I

    2012-01-01

    The aim of the reported investigation is to asses the effect of brownian and thermophoretic diffusion in nanofluids convective heat transfer. In order to capture these effects, a new equation for particles distribution had to be consider. Momentum and energy equations have been reformulated in order to include brownian and thermophretic diffusion. These modes of diffusion have been suggested extensively in the literature but their effect on momentum and energy transport has not yet been numerically analyzed. In order to obtain a solution for the modified set of governing equations, a new CFD solver had to be devised. The new solver has been applied to a case study involving hydrodynamic and thermally developing laminar flow regime in a pipe. Pure base fluid solutions have been used to asses the accuracy of the model. Numerical nanofluid solutions compare reasonably well with both experimental results obtained elsewhere and the Churchill and Ozoe correlation. The observed heat transfer enhancement by the nanofluid has been attributed to its transport properties rather than to another transport mechanism.

  10. Ingestion Pathway Transfer Factors for Plutonium and Americium

    International Nuclear Information System (INIS)

    Blanchard, A.

    1999-01-01

    Overall transfer factors for major ingestion pathways are derived for plutonium and americium. These transfer factors relate the radionuclide concentration in a given foodstuff to deposition on the soil. Equations describing basic relationships consistent with Regulatory Guide 1.109 are followed. Updated values and coefficients from IAEA Technical Reports Series No. 364 are used when a available. Preference is given to using factors specific to the Savannah River Site

  11. Mathematical modeling of heat transfer in production premises heated by gas infrared emitters

    Directory of Open Access Journals (Sweden)

    Maksimov Vyacheslav I.

    2017-01-01

    Full Text Available The results of numerical modeling of the process of free convective heat transfer in the regime of turbulent convection in a closed rectangular region heated by an infrared radiator are presented. The system of Navier-Stokes equations in the Boussinesq approximation is solved, the energy equation for the gas and the heat conduction equations for the enclosing vertical and horizontal walls. A comparative analysis of the heat transfer regimes in the considered region for different Grashof numbers is carried out. The features of the formation of heated air flows relative to the infrared emitter located at some distance from the upper horizontal boundary of the region are singled out.

  12. Computational evaluation of amplitude modulation for enhanced magnetic nanoparticle hyperthermia.

    Science.gov (United States)

    Soetaert, Frederik; Dupré, Luc; Ivkov, Robert; Crevecoeur, Guillaume

    2015-10-01

    Magnetic nanoparticles (MNPs) can interact with alternating magnetic fields (AMFs) to deposit localized energy for hyperthermia treatment of cancer. Hyperthermia is useful in the context of multimodality treatments with radiation or chemotherapy to enhance disease control without increased toxicity. The unique attributes of heat deposition and transfer with MNPs have generated considerable attention and have been the focus of extensive investigations to elucidate mechanisms and optimize performance. Three-dimensional (3D) simulations are often conducted with the finite element method (FEM) using the Pennes' bioheat equation. In the current study, the Pennes' equation was modified to include a thermal damage-dependent perfusion profile to improve model predictions with respect to known physiological responses to tissue heating. A normal distribution of MNPs in a model liver tumor was combined with empirical nanoparticle heating data to calculate tumor temperature distributions and resulting survival fraction of cancer cells. In addition, calculated spatiotemporal temperature changes were compared among magnetic field amplitude modulations of a base 150-kHz sinusoidal waveform, specifically, no modulation, sinusoidal, rectangular, and triangular modulation. Complex relationships were observed between nanoparticle heating and cancer tissue damage when amplitude modulation and damage-related perfusion profiles were varied. These results are tantalizing and motivate further exploration of amplitude modulation as a means to enhance efficiency of and overcome technical challenges associated with magnetic nanoparticle hyperthermia (MNH).

  13. The role of energy conservation in the BFKL equation

    International Nuclear Information System (INIS)

    Forshaw, J.R.; Harriman, P.N.; Sutton, P.J.

    1993-01-01

    We study a modification to the BFKL equation at zero momentum transfer due to the imposition of energy conservation. The significance of our modification, which enters in the form of an ultraviolet cutoff, is illustrated directly and is discussed within the context of the gluon diffusion in k T . (Author)

  14. Mixed convection flow and heat transfer in a vertical wavy channel ...

    African Journals Online (AJOL)

    Mixed convection flow and heat transfer in a vertical wavy channel filled with porous and fluid layers is studied analytically. The flow in the porous medium is modeled using Darcy-Brinkman equation. The coupled non-linear partial differential equations describing the conservation of mass, momentum and energy are solved ...

  15. Non-Markovian reduced dynamics of ultrafast charge transfer at an oligothiophene–fullerene heterojunction

    Energy Technology Data Exchange (ETDEWEB)

    Hughes, Keith H., E-mail: keith.hughes@bangor.ac.uk [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Cahier, Benjamin [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Martinazzo, Rocco [Dipartimento di Chimica Università degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Tamura, Hiroyuki [WPI-Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt/Main (Germany)

    2014-10-17

    Highlights: • Quantum dynamical study of exciton dissociation at a heterojunction interface. • The non-Markovian quantum dynamics involves a highly structured spectral density. • Spectral density is reconstructed from an effective mode transformation of the Hamiltonian. • The dynamics is studied using the hierarchical equations of motion approach. • It was found that the temperature has little effect on the charge transfer. - Abstract: We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene–fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway.

  16. Condensation heat transfer of a feed-water heater and improvement of its performance

    International Nuclear Information System (INIS)

    Takamori, Kazuhide; Murase, Michio; Baba, Yoshikazu; Aihara, Tsuyoshi

    1995-01-01

    In this study, a condensation heat transfer model, coupled with a three-dimensional two-phase flow analysis, was developed. In the heat transfer model, the liquid film flow rate on the heat transfer tubes was calculated by a mass balance equation and the liquid film thickness was calculated from the liquid film flow rate using Nusselt's laminar flow model and Fujii's equation for the steam velocity effect. The model was verified by condensation heat transfer experiments. In the experiments, 112 horizontal, staggered tubes with an outer diameter of 16mm and length of 0.55m were used. The calculated over-all heat transfer coefficients agreed with the data within ±5% under the inlet quality conditions of 13-100%. Based on a three-dimensional two-phase flow analysis, an improved feed-water heater with support plates, which have flow holes between the upper and lower tube bundles, was designed. The total heat exchange capacity of the improved feed-water heater increased about 6%. (author)

  17. Experiment on transient heat transfer in closed narrow channel

    International Nuclear Information System (INIS)

    Ochiai, Masaaki

    1985-01-01

    Heat transfer coefficients and transient pressures in closed narrow channels were obtained experimentally, in order to assess the gap heat transfer models in the computer code WTRLGD which were devised to analyze the internal pressure behavior of waterlogged fuel rods. Gap widths of channels are 0.1--0.5mm to simulate the gap region of waterlogged fuel rods, and test fluids are water (7--89.2 0 C) and Freon-113 (9.2 0 C). The results show that the heater temperature and the pressure measured in the experiments without the DNB occurrence are simulated fairly well by the calculational model of WTRLGD where the heat transfer in a closed narrow channel is evaluated with one-dimensional transient thermal conduction equation and Jens and Lottes' correlation for nucleate boiling. Consequently, it is also suggested that the above equations are available for evaluation of heat flux from fuel to internal water of waterlogged fuel rods. The film boiling heat transfer coefficient was in the same order of that evaluated by Bromley's correlation and the DNB heat flux was smaller than that obtained in quasi-steady experiments with ordinary systems, although the experimental data for them were not enough. (author)

  18. Effects of heat and mass transfer on unsteady boundary layer flow of a chemical reacting Casson fluid

    Science.gov (United States)

    Khan, Kashif Ali; Butt, Asma Rashid; Raza, Nauman

    2018-03-01

    In this study, an endeavor is to observe the unsteady two-dimensional boundary layer flow with heat and mass transfer behavior of Casson fluid past a stretching sheet in presence of wall mass transfer by ignoring the effects of viscous dissipation. Chemical reaction of linear order is also invoked here. Similarity transformation have been applied to reduce the governing equations of momentum, energy and mass into non-linear ordinary differential equations; then Homotopy analysis method (HAM) is applied to solve these equations. Numerical work is done carefully with a well-known software MATHEMATICA for the examination of non-dimensional velocity, temperature, and concentration profiles, and then results are presented graphically. The skin friction (viscous drag), local Nusselt number (rate of heat transfer) and Sherwood number (rate of mass transfer) are discussed and presented in tabular form for several factors which are monitoring the flow model.

  19. Turbulent mixed buoyancy driven flow and heat transfer in lid driven enclosure

    International Nuclear Information System (INIS)

    Mishra, Ajay Kumar; Sharma, Anil Kumar

    2015-01-01

    Turbulent mixed buoyancy driven flow and heat transfer of air in lid driven rectangular enclosure has been investigated for Grashof number in the range of 10 8 to 10 11 and for Richardson number 0.1, 1 and 10. Steady two dimensional Reynolds-Averaged-Navier-Stokes equations and conservation equations of mass and energy, coupled with the Boussinesq approximation, are solved. The spatial derivatives in the equations are discretized using the finite-element method. The SIMPLE algorithm is used to resolve pressure-velocity coupling. Turbulence is modeled with the k-ω closure model with physical boundary conditions along with the Boussinesq approximation, for the flow and heat transfer. The predicted results are validated against benchmark solutions reported in literature. The results include stream lines and temperature fields are presented to understand flow and heat transfer characteristics. There is a marked reduction in mean Nusselt number (about 58%) as the Richardson number increases from 0.1 to 10 for the case of Ra=10 10 signifying the effect of reduction of top lid velocity resulting in reduction of turbulent mixing. (author)

  20. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  1. Numerical analysis of mass transfer with graphite oxidation in a laminar flow of multi-component gas mixture through a circular tube

    International Nuclear Information System (INIS)

    Ogawa, Masuro

    1992-10-01

    In the present paper, mass transfer has been numerically studied in a laminar flow through a circular graphite tube to evaluate graphite corrosion rate and generation rate of carbon monoxide during a pipe rupture accident in a high temperature gas cooled reactor. In the analysis, heterogeneous (graphite oxidation and graphite/carbon dioxide reaction) and homogeneous (carbon monoxide combustion) chemical reactions were dealt in the multi-component gas mixture; helium, oxygen, carbon monoxide and carbon dioxide. Multi-component diffusion coefficients were used in a diffusion term. Mass conservation equations of each gas component, mass conservation equation and momentum conservation equations of the gas mixture were solved by using SIMPLE algorism. Chemical reactions between graphite and oxygen, graphite and carbon dioxide, and carbon monoxide combustion were taken into account in the present numerical analysis. An energy equation for the gas mixture was not solved and temperature was held to be constant in order to understand basic mass transfer characteristics without heat transfer. But, an energy conservation equation for single component gas was added to know heat transfer characteristics without mass transfer. The effects of these chemical reactions on the mass transfer coefficients were quantitatively and qualitatively clarified in the range of 50 to 1000 of inlet Reynolds numbers, 0 to 0.5 of inlet oxygen mass fraction and 800 to 1600degC of temperature. (author)

  2. High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mozolevski, I.E.

    2001-01-01

    We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

  3. The generalized approximation method and nonlinear heat transfer equations

    Directory of Open Access Journals (Sweden)

    Rahmat Khan

    2009-01-01

    Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.

  4. Implementing Parquet equations using HPX

    Science.gov (United States)

    Kellar, Samuel; Wagle, Bibek; Yang, Shuxiang; Tam, Ka-Ming; Kaiser, Hartmut; Moreno, Juana; Jarrell, Mark

    A new C++ runtime system (HPX) enables simulations of complex systems to run more efficiently on parallel and heterogeneous systems. This increased efficiency allows for solutions to larger simulations of the parquet approximation for a system with impurities. The relevancy of the parquet equations depends upon the ability to solve systems which require long runs and large amounts of memory. These limitations, in addition to numerical complications arising from stability of the solutions, necessitate running on large distributed systems. As the computational resources trend towards the exascale and the limitations arising from computational resources vanish efficiency of large scale simulations becomes a focus. HPX facilitates efficient simulations through intelligent overlapping of computation and communication. Simulations such as the parquet equations which require the transfer of large amounts of data should benefit from HPX implementations. Supported by the the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.

  5. Line radiative transfer and statistical equilibrium*

    Directory of Open Access Journals (Sweden)

    Kamp Inga

    2015-01-01

    Full Text Available Atomic and molecular line emission from protoplanetary disks contains key information of their detailed physical and chemical structures. To unravel those structures, we need to understand line radiative transfer in dusty media and the statistical equilibrium, especially of molecules. I describe here the basic principles of statistical equilibrium and illustrate them through the two-level atom. In a second part, the fundamentals of line radiative transfer are introduced along with the various broadening mechanisms. I explain general solution methods with their drawbacks and also specific difficulties encountered in solving the line radiative transfer equation in disks (e.g. velocity gradients. I am closing with a few special cases of line emission from disks: Radiative pumping, masers and resonance scattering.

  6. Exact solutions for MHD flow of couple stress fluid with heat transfer

    Directory of Open Access Journals (Sweden)

    Najeeb Alam Khan

    2016-01-01

    Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.

  7. Relativistic point dynamics general equations, constant proper masses, interactions between electric charges, variable proper masses, collisions

    CERN Document Server

    Arzeliès, Henri

    1972-01-01

    Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int

  8. Frumkin-Butler-Volmer theory and mass transfer

    NARCIS (Netherlands)

    Soestbergen, van M.

    2012-01-01

    An accurate mathematical description of the charge transfer rate at electrodes due to an electro chemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin-Butler-Volmer (gFBV) equation to describe electrochemical reactions, an

  9. Radiation transfer and stellar atmospheres

    Science.gov (United States)

    Swihart, T. L.

    This is a revised and expanded version of the author's Basic Physics of Stellar Atmospheres, published in 1971. The equation of transfer is considered, taking into account the intensity and derived quantities, the absorption coefficient, the emission coefficient, the source function, and special integrals for plane media. The gray atmosphere is discussed along with the nongray atmosphere, and aspects of line formation. Topics related to polarization are explored, giving attention to pure polarized radiation, general polarized radiation, transfer in a magnetic plasma, and Rayleigh scattering and the sunlit sky. Physical and astronomical constants, and a number of problems related to the subjects of the book are presented in an appendix.

  10. Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

    Science.gov (United States)

    Pikichyan, H. V.

    2017-07-01

    In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

  11. Analysis of a wavelength selectable cascaded DFB laser based on the transfer matrix method

    International Nuclear Information System (INIS)

    Xie Hongyun; Chen Liang; Shen Pei; Sun Botao; Wang Renqing; Xiao Ying; You Yunxia; Zhang Wanrong

    2010-01-01

    A novel cascaded DFB laser, which consists of two serial gratings to provide selectable wavelengths, is presented and analyzed by the transfer matrix method. In this method, efficient facet reflectivity is derived from the transfer matrix built for each serial section and is then used to simulate the performance of the novel cascaded DFB laser through self-consistently solving the gain equation, the coupled wave equation and the current continuity equations. The simulations prove the feasibility of this kind of wavelength selectable laser and a corresponding designed device with two selectable wavelengths of 1.51 μm and 1.53 μm is realized by experiments on InP-based multiple quantum well structure. (semiconductor devices)

  12. MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate

    International Nuclear Information System (INIS)

    Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.

    2011-01-01

    An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate. (fundamental areas of phenomenology(including applications))

  13. Trefftz method in solving Fourier-Kirchhoff equation for two-phase flow boiling in a vertical rectangular minichannel

    Directory of Open Access Journals (Sweden)

    Hożejowska Sylwia

    2017-01-01

    Full Text Available This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.

  14. Bethe ansatz equations for open spin chains from giant gravitons

    International Nuclear Information System (INIS)

    Nepomechie, Rafael I.

    2009-01-01

    We investigate the open spin chain describing the scalar sector of the Y = 0 giant graviton brane at weak coupling. We provide a direct proof of integrability in the SU(2) and SU(3) sectors by constructing the transfer matrices. We determine the eigenvalues of these transfer matrices in terms of roots of the corresponding Bethe ansatz equations (BAEs). Based on these results, we propose BAEs for the full SO(6) sector. We find that, in the weak-coupling limit, the recently-proposed all-loop BAEs essentially agree with those proposed in the present work.

  15. Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

    International Nuclear Information System (INIS)

    Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang; Kraft, Markus

    2015-01-01

    Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

  16. Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Kok Foong [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA (United Kingdom); Patterson, Robert I.A.; Wagner, Wolfgang [Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin (Germany); Kraft, Markus, E-mail: mk306@cam.ac.uk [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA (United Kingdom); School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore, 637459 (Singapore)

    2015-12-15

    Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

  17. Method of calculating heat transfer in furnaces of small power

    Directory of Open Access Journals (Sweden)

    Khavanov Pavel

    2016-01-01

    Full Text Available This publication presents the experiences and results of generalization criterion equation of importance in the analysis of the processes of heat transfer and thermal calculations of low-power heat generators cooled combustion chambers. With generalizing depending estimated contribution of radiation and convective heat transfer component in the complex for the combustion chambers of small capacity boilers. Determined qualitative and quantitative dependence of the integrated radiative-convective heat transfer from the main factors working combustion chambers of small volume.

  18. The role of the velocity gradient in laminar convective heat transfer through a tube with a uniform wall heat flux

    International Nuclear Information System (INIS)

    Wang Liangbi; Zhang Qiang; Li Xiaoxia

    2009-01-01

    This paper aims to contribute to a better understanding of convective heat transfer. For this purpose, the reason why thermal diffusivity should be placed before the Laplacian operator of the heat flux, and the role of the velocity gradient in convective heat transfer are analysed. The background to these analyses is that, when the energy conservation equation of convective heat transfer is used to explain convective heat transfer there are two points that are difficult for teachers to explain and for undergraduates to understand: thermal diffusivity is placed before the Laplacian operator of temperature; on the wall surface (the fluid side) the velocity is zero, a diffusion equation of temperature is gained from energy conservation equation, however, temperature cannot be transported. Consequently, the real physical meaning of thermal diffusivity is not clearly reflected in the energy conservation equation, and whether heat transfer occurs through a diffusion process or a convection process on the wall surface is not clear. Through a simple convective heat transfer case: laminar convective heat transfer in a tube with a uniform wall heat flux on the tube wall, this paper explains these points more clearly. The results declare that it is easier for teachers to explain and for undergraduates to understand these points when a description of heat transfer in terms of the heat flux is used. In this description, thermal diffusivity is placed before the Laplacian operator of the heat flux; the role of the velocity gradient in convective heat transfer appears, on the wall surface, the fact whether heat transfer occurs through a diffusion process or a convection process can be explained and understood easily. The results are not only essential for teachers to improve the efficiency of university-level physics education regarding heat transfer, but they also enrich the theories for understanding heat transfer

  19. Numerical Investigation of Jet Impingement Heat Transfer on a Flat plate

    Directory of Open Access Journals (Sweden)

    Asem Nabadavis

    2016-12-01

    Full Text Available The numerical investigation emphasizes on studying the heat transfer characteristics when a high velocity air jet impinges upon a flat plate having constant heat flux. Numerical analysis has been conducted by solving conservation equations of momentum, mass and energy with two equations based k- ε turbulence model to determine the wall temperature and Nu of the plate considering the flow to be incompressible. It was found from the investigation that the heat transfer rate increases with the increase of Reynolds number of the jet (Rej. It was also found that there is an optimum value for jet distance to nozzle diameter ratio (H/d for maximum heat transfer when all the other parameters were kept fixed. Similar results as above were found when two jets of air were used instead of one jet keeping the mass flow rate constant. For a two jets case it was also found that heat transfer rate over the surface increases when the jets are inclined outward compared to vertical and inward jets and also there exists an optimum angle of jet for maximum heat transfer. Further investigation was carried out for different jetto-jet separation distance for a twin jet impingement model where it was noted that heat transfer is more distributed in case of larger values of L and the rate of heat transfer increases as the separation between the jet increases till a certain point after which the rate of heat transfer decreases.

  20. Reaction of electron-transfer flavoprotein with electron-transfer flavoprotein-ubiquinone oxidoreductase

    International Nuclear Information System (INIS)

    Beckmann, J.D.; Frerman, F.E.

    1985-01-01

    The oxidative half-reaction of electron-transfer flavoprotein (ETF), electron transfer from ETF to electron-transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO), is dependent on complementary surface charges on the two proteins. ETF is the positively charged member of the redox pair. The evidence is based on the pH and ionic strength dependencies of the comproportionation of oxidized ETF and ETF hydroquinone catalyzed by ETF-QO and on the effects of chemical modification of ETF on the comproportionation reaction. Acetylation of one and five epsilon-amino groups of lysyl residues results in 3- and 13-fold increases, respectively, in the K/sub m/ of ETF-QO for ETF but no change in V/sub max/. Amidination, which maintains positive charge at modified loci, has no effect on steady-state kinetic constants. These chemical modifications have no effect on the equilibrium constant for equilibration of ETF redox states. The K/sub m/ of ETF-QO for ETF is pH dependent above pH 8.5, suggesting titration of lysyl residues. The ionic strength dependence of TN/KmETF for the reaction follows the limiting Bronsted equation. The ETF-QO-catalyzed comproportionation reaction exhibits a primary deuterium isotope effect in D 2 O, perhaps indicating the participation of solvent water in the electron-transfer reaction

  1. Nonlinear integral equations for thermodynamics of the sl(r + 1) Uimin-Sutherland model

    International Nuclear Information System (INIS)

    Tsuboi, Zengo

    2003-01-01

    We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the those from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIEs). In particular, a subset of these NLIEs forms a system of NLIEs which contains only a finite number of unknown functions. For r=1, this subset of NLIEs reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIEs is clarified. Based on our new NLIEs, we also calculate the high-temperature expansion of the free energy

  2. Analysis of combined heat and mass transfer of water- Vapor in a ...

    African Journals Online (AJOL)

    In this paper, the combined heat and mass transfer of water-vapor into a cylindrical zeolite adsorber has been numerically simulated The twodimensional heat and mass transfer equations are numerically solved using gPROMS program - a general Process Modeling System {lJ program, inserting the proper initial and ...

  3. Analysis of combined heat and mass transfer of water-vapor in a ...

    African Journals Online (AJOL)

    Jn this paper, the combined heat and mass transfer of water-vapor into a cylindrical zeolite adsorber has been numerically simulated The twodimensional heat and mass transfer equations are numerically solved using gPROMS program - a general Process Modeling System [J] program, inserting the proper initial and ...

  4. Post-CHF heat transfer: a non-equilibrium, relaxation model

    International Nuclear Information System (INIS)

    Jones, O.C. Jr.; Zuber, N.

    1977-01-01

    Existing phenomenological models of heat transfer in the non-equilibrium, liquid-deficient, dispersed flow regime can sometimes predict the thermal behavior fairly well but are quite complex, requiring coupled simultaneous differential equations to describe the axial gradients of mass and energy along with those of droplet acceleration and size. In addition, empirical relations are required to express the droplet breakup and increased effective heat transfer due to holdup. This report describes the development of a different approach to the problem. It is shown that the non-equilibrium component of the total energy can be expressed as a first order, inhomogeneous relaxation equation in terms of one variable coefficient termed the Superheat Relaxation number. A demonstration is provided to show that this relaxation number can be correlated using local variables in such a manner to allow the single non-equilibrium equation to accurately calculate the effects of mass velocity and heat flux along with tube length, diameter, and critical quality for equilibrium qualities from 0.13 to over 3.0

  5. About local fractional three-dimensional compressible Navier-Stokes equations in Cantor-type cylindrical co-ordinate system

    Directory of Open Access Journals (Sweden)

    Gao Guo-Ping

    2016-01-01

    Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.

  6. Application of Monte Carlo method to solving boundary value problem of differential equations

    International Nuclear Information System (INIS)

    Zuo Yinghong; Wang Jianguo

    2012-01-01

    This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

  7. The solution of heat transfer problems using HEATRAN

    International Nuclear Information System (INIS)

    Collier, W.D.

    1976-07-01

    HEATRAN solves the heat diffusion equation over a two dimensional area of any shape or material distribution. Transfer by radiation across voids is allowed and special provsion is made for narrow gaps. A wide range of boundary conditions is available. (author)

  8. Reduced equations of motion for quantum systems driven by diffusive Markov processes.

    Science.gov (United States)

    Sarovar, Mohan; Grace, Matthew D

    2012-09-28

    The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

  9. Multidimensional Wave Field Signal Theory: Transfer Function Relationships

    Directory of Open Access Journals (Sweden)

    Natalie Baddour

    2012-01-01

    Full Text Available The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber or pseudo-Helmholtz (complex wavenumber equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.

  10. Solution of the kinetic equation in the P3-approximation in a plane geometry

    International Nuclear Information System (INIS)

    Vlasov, Yu.A.

    1975-01-01

    A method and a program are described for solving single-velocity kinetic equations of neutron transfer for the plane geometry in the finite-difference approximation. A difference high-accuracy scheme and a matrix factorization method are used for the differential-difference equation systems. The program is written in the ALGOL-60 language and is adapted for M-20, M-220, M-222 and BESM-4 computers

  11. In vivo characterization of tissue thermal properties of the kidney during local hyperthermia induced by MR-guided high-intensity focused ultrasound.

    Science.gov (United States)

    Cornelis, François; Grenier, Nicolas; Moonen, Chrit T; Quesson, Bruno

    2011-08-01

    The purpose of this study was to evaluate quantitatively in vivo the tissue thermal properties during high-intensity focused ultrasound (HIFU) heating. For this purpose, a total of 52 localized sonications were performed in the kidneys of six pigs with HIFU monitored in real time by volumetric MR thermometry. The kidney perfusion was modified by modulation of the flow in the aorta by insertion of an inflatable angioplasty balloon. The resulting temperature data were analyzed using the bio-heat transfer model in order to validate the model under in vivo conditions and to estimate quantitatively the absorption (α), thermal diffusivity (D) and perfusion (w(b)) of renal tissue. An excellent correspondence was observed between the bio-heat transfer model and the experimental data. The absorption and thermal diffusivity were independent of the flow, with mean values (± standard deviation) of 20.7 ± 5.1 mm(3) K J(-1) and 0.23 ± 0.11 mm(2) s(-1), respectively, whereas the perfusion decreased significantly by 84% (p < 0.01) with arterial flow (mean values of w(b) of 0.06 ± 0.02 and 0.008 ± 0.007 mL(-1) mL s(-1)), as predicted by the model. The quantitative analysis of the volumetric temperature distribution during nondestructive HIFU sonication allows the determination of the thermal parameters, and may therefore improve the quality of the planning of noninvasive therapy with MR-guided HIFU. Copyright © 2010 John Wiley & Sons, Ltd.

  12. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Directory of Open Access Journals (Sweden)

    Linares OA

    2015-07-01

    Full Text Available Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic Medicine Lab, Plymouth Pharmacokinetic Modeling Study Group, Plymouth, MI, 2Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA, 3University of Connecticut School of Pharmacy, Storrs, CT, 4Western New England College of Pharmacy, Springfield, MA, 5Albany College of Pharmacy and Health Sciences, Albany, NY, 6Stratton VA Medical Center, Albany, NY, 7Grace Hospice of Ann Arbor, Ann Arbor, MI, USA Background: There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim: To build a one-dimensional (1-D, hollow-fiber geometry, ordinary differential equation (ODE and partial differential equation (PDE countercurrent hemodialyzer model (ODE/PDE model. Methodology: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results: The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δ km=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11. This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11. The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value

  13. Effective methods of solving of model equations of certain class of thermal systems

    International Nuclear Information System (INIS)

    Lach, J.

    1985-01-01

    A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)

  14. Mathematical models of the theory of the radiative transfer

    International Nuclear Information System (INIS)

    Lin, Ch.

    2007-06-01

    We are interested in various different models arising in radiative transfer, which describe the interactions between the medium and the photons. The radiation is described in terms of energy and energy flux in the macroscopic view, the material being described by the Euler equations (radiative hydrodynamic model). In another way, the radiation can be seen as a collection of photons, in the microscopic view point; the photons can be absorbed or emitted by the material. The absorption and the emission of photons depend on the internal excitation and ionization state of the material. We begin with the local existence (in time) of smooth solutions to a system coupling the Euler equations and the transfer equation. This system describes the exchange of energy and moment between the radiation and the material. Next, we give an asymptotic discussion for this model in the NON-LTE regime and get a simple system: coupling the Euler equations with an elliptic equation. We show the existence of (smooth) shock profiles to this system and the regularity of the shock profile as a function of the strength of the shock. Then we study the asymptotic stability of the shock profile. Finally, we study a system describing the radiation and the internal state of the material, in the microscopic view point. We prove the existence of the solution to this system and study the convergence towards the statistical equilibrium. The theoretical results are illustrated by numerical simulations. (author)

  15. Temperature distribution in spouted bed and heat transfer

    International Nuclear Information System (INIS)

    Takeda, Hiroshi; Yamamoto, Yutaka

    1976-01-01

    Temperature distribution in spouted bed was measured by using brass and graphite spouted beds so as to investigate heat transfer characteristic of spouted bed applied to an apparatus of PyC coating. These spouted beds are batch type and are spouted by air or nitrogen gas of room temperature, and the outer wall of beds are heated by nichrome or graphite heater. Particles used for experiments are alumina spherical particles and the diameter is 0.80 -- 1.12 mm. Temperature condition is in the range of 400 -- 1,400 0 C. In the neighborhood of 400 0 C, the spouting condition is stable, while the spouting condition becomes unstable in the case of above 1,000 0 C. This is caused by abrupt temperature increase of spouting gas. It was found that heat transfer coefficient h sub(w) of our low temperature experiments was closer to the calculated from Malek et al.'s equation, h sub(p) of our experiments was several times greater than the calculated from Uemaki et al.'s equation. On the other hand, h sub(p) of high temperature experiments was compared with an experimental relation for convective heat transfer of fluidized bed, it was found that Nu sub(p) of our experiments was nearly equal to or greater than the calculated from the relation, this would be caused by radiant heat transfer. (auth.)

  16. Detection of tumor-like inclusions embedded within human liver tissue using a short-pulsed near-infrared laser beam: Parallel simulations with radiative transfer equation

    International Nuclear Information System (INIS)

    Asllanaj, Fatmir; Addoum, Ahmad; Contassot-Vivier, Sylvain

    2015-01-01

    An efficient solution to detect tumor-like inclusions embedded within a human liver tissue model is presented, using illumination by a short-pulsed laser beam. Light propagation was accurately solved using the time-dependent radiative transfer equation, with multithreaded parallel computing. A modified finite volume method based on unstructured grids and the fourth-order Runge–Kutta approach was employed to solve the equation in the (2-D/3-D) spatial and time domains. The normalization technique applied to the Henyey–Greenstein phase function was adopted to ensure numerical stability for values of the anisotropy factor that were close to unity. The presence of one or two circular/spherical inclusions was analyzed from the time and spatially resolved reflectance on the medium bounding surface. The results allowed a minimal size and a maximum distance for the detection of the inclusion to be highlighted. - Highlights: • We detect tumor-like inclusions embedded within a (2D/3D) human liver tissue model. • The technique is based on a short-pulsed near-infrared laser beam. • We solve the (2D/3D) time-dependent RTE, with multithreaded parallel computing. • The presence of one or two circular/spherical inclusions is analyzed. • The results allows a minimal size and a maximum distance for the detection

  17. Theory of Periodic Conjugate Heat Transfer

    CERN Document Server

    Zudin, Yuri B

    2012-01-01

    This book presents the theory of periodic conjugate heat transfer in a detailed way. The effects of thermophysical properties and geometry of a solid body on the commonly used and experimentally determined heat transfer coefficient are analytically presented from a general point of view. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body. At the body surface, the true heat transfer coefficient is composed of two parts: the true mean value resulting from the solution of the steady state heat transfer problem and a periodically variable part, the periodic time and length to describe the oscillatory hydrodynamic effects. The second edition is extended by (i) the analysis of stability boundaries in helium flow at supercritical conditions in a heated channel with respect to the interaction between a solid body and a fluid; (ii) a periodic model and a method of heat transfer sim...

  18. Effect of radiant heat transfer on the performance of high temperature heat exchanger

    International Nuclear Information System (INIS)

    Mori, Yasuo; Hijikata, Kunio; Yamada, Yukio

    1975-01-01

    The development of high temperature gas-cooled reactors is motivated by the consideration of the application of nuclear heat for industrial uses or direct steelmaking and chemical processes. For these purposes, reliable and efficient heat exchangers should be developed. This report analyzes the effect of radiant heat transfer on the performance of high temperature heat exchangers. The heat transfer model is as follows: the channel composed with two parallel adiabatic walls is divided with one parallel plate between the walls. Non-radiative fluid flows in the two separated channels in opposite direction. Heat transfer equations for this system were obtained, and these equations were solved by some approximate method and numerical analysis. The effect of radiation on heat transfer became larger as the radiant heat transfer between two walls was larger. In the heat exchangers of counter flow type, the thermal efficiency is controlled with three parameters, namely radiation-convection parameter, Stanton number and temperature difference. The thermal efficiency was larger with the increase of these parameters. (Iwase, T.)

  19. Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Larsen, Edward W.

    2004-01-01

    The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions

  20. Numerical simulation of gas-liquid two-phase flow behavior with condensation heat transfer

    International Nuclear Information System (INIS)

    Takamori, Kazuhide; Murase, Michio; Baba, Yoshikazu; Aihara, Tsuyoshi.

    1995-01-01

    In this study, condensation heat transfer experiments were performed in order to verify a condensation heat transfer model coupled with a three-dimensional two-phase flow analysis. In the heat transfer model, the liquid film flow rate on the heat transfer tubes was calculated by a mass balance equation and the liquid film thickness was calculated from the liquid film flow rate using Nusselt's laminar flow model and Fujii's equation for steam velocity effect. In the experiments, 112 horizontal staggered tubes with an outer diameter of 16 mm and length of 0.55 m were used. Steam and spray water were supplied to the test section, and inlet quality was controlled by the spray water flow rate. The temperature was 100degC and the pressure was 0.1 MPa. The overall heat transfer coefficients were measured for inlet quality of 13-100%. From parameter calculations for the falling liquid film ratio from the upper tubes to the lower tubes, the calculated overall heat transfer coefficients agreed with the data to within ±5% at the falling liquid film ratio of 0.7. (author)

  1. The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

    Science.gov (United States)

    Sorokin, Sergey V

    2011-03-01

    Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

  2. Heat transfer and thermoregulation in the largemouth blackbass, Micropterus salmoides

    Energy Technology Data Exchange (ETDEWEB)

    Erskine, D. J.

    1976-01-01

    An energy budget equation, based on energy budget theory for terrestrial organisms, was developed to describe the heat energy exchange between a largemouth bass (Micropterus salmoides) and its aquatic environment. The energy budget equation indicated that convection and a combined conduction-convection process were major avenues of heat exchange for a fish. Solid aluminum castings were used to experimentally determine heat transfer coefficients for the largemouth bass at water velocities covering the free and forced convection ranges. Heat energy budget theory was applied to the casting data and the derived coefficients were used to characterize heat exchange between the bass and its aquatic habitat. The results indicate that direct transfer of heat from the body surface is the major mechanism of heat exchange for a fish.

  3. Theoretical thermal dosimetry produced by an annular phased array system in CT-based patient models

    International Nuclear Information System (INIS)

    Paulsen, K.D.; Strohbehn, J.W.; Lynch, D.R.

    1984-01-01

    Theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions produced by an annular phased array (APA) type system are made. The finite element numerical method is used in the formulation of both the electromagnetic (EM) and the thermal boundary value problems. A number of detailed patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to stimulate a variety of tumor locations and surrounding normal tissues. The SAR values from the EM solution are input into the bioheat transfer equation, and steady-rate temperature distributions are calculated for a wide variety of blood flow rates. Based on theoretical modeling, the APA shows no preferential heating of superficial over deep-seated tumors. However, in most cases satisfactory thermal profiles (therapeutic volume near 60%) are obtained in all three regions of the human trunk only for tumors with little or no blood flow. Unsatisfactory temperature patterns (therapeutic volume <50%) are found for tumors with moderate to high perfusion rates. These theoretical calculations should aid the clinician in the evaluation of the effectiveness of APA type devices in heating tumors located in the trunk region

  4. Comparison between coupled KZK-BHTE numerical simulations and scanned HIFU exposures in excised bovine liver

    Science.gov (United States)

    Andrew, Marilee A.; Brayman, Andrew A.; Kaczkowski, Peter J.; Kargl, Steven G.

    2004-05-01

    The use of moving high intensity focused ultrasound (HIFU) treatment protocols is of interest in achieving efficient formation of large-volume lesions in tissue. However, potentially unwanted thermal effects, such as prefocal heating, should be considered. A KZK acoustic model coupled with the BioHeat Transfer Equation has been extended to simulate multiple, moving scans in tissue. Simulation results are compared with experimental data collected over a range of exposure regimes for linear and concentric circular scans with a 3.5-MHz single-element transducer in ex vivo bovine liver. Of particular interest are investigating prefocal thermal buildup and ablating the central core of a circular pattern through conductive heating, that is without direct HIFU exposure. Qualitative agreement is observed between experimental and simulated data; limits of the predictive capability of the model in cavitation regimes will be discussed. [Support provided by the U.S. Army Medical Research Acquisition Activity through The University of Mississippi under terms of Agreement No. DAMD17-02-2-0014. The opinions expressed herein are those of the author(s) and do not necessarily reflect the views of U.S. Army Medical Research Acquisition Activity or The University of Mississippi.

  5. Zakharov equations for viscous flow and their use in the blood clot ...

    Indian Academy of Sciences (India)

    Ai-Ping Zhou

    2017-11-14

    Nov 14, 2017 ... Blood plasma; Zakharov equations; viscosity; modulation instability. PACS Nos 52.27. .... For fluid, the proton thermal velocity vT p is much less than the phase ..... The heavy ion can transfer greater momentum, then in general ...

  6. Excited TBA equations I: Massive tricritical Ising model

    International Nuclear Information System (INIS)

    Pearce, Paul A.; Chim, Leung; Ahn, Changrim

    2001-01-01

    We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II

  7. Scaling analysis of the coupled heat transfer process in the high-temperature gas-cooled reactor core

    International Nuclear Information System (INIS)

    Conklin, J.C.

    1986-08-01

    The differential equations representing the coupled heat transfer from the solid nuclear core components to the helium in the coolant channels are scaled in terms of representative quantities. This scaling process identifies the relative importance of the various terms of the coupled differential equations. The relative importance of these terms is then used to simplify the numerical solution of the coupled heat transfer for two bounding cases of full-power operation and depressurization from full-system operating pressure for the Fort St. Vrain High-Temperature Gas-Cooled Reactor. This analysis rigorously justifies the simplified system of equations used in the nuclear safety analysis effort at Oak Ridge National Laboratory

  8. An inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin

    International Nuclear Information System (INIS)

    Nepomechie, Rafael I

    2013-01-01

    An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues of the transfer matrix of this model. We also propose a generating function for the inhomogeneous T-Q equations of arbitrary spin. (fast track communication)

  9. Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine

    Science.gov (United States)

    Lee, Chi M.; Schock, Harold J.

    1988-01-01

    Currently, the heat transfer equation used in the rotary combustion engine (RCE) simulation model is taken from piston engine studies. These relations have been empirically developed by the experimental input coming from piston engines whose geometry differs considerably from that of the RCE. The objective of this work was to derive equations to estimate heat transfer coefficients in the combustion chamber of an RCE. This was accomplished by making detailed temperature and pressure measurements in a direct injection stratified charge (DISC) RCE under a range of conditions. For each specific measurement point, the local gas velocity was assumed equal to the local rotor tip speed. Local physical properties of the fluids were then calculated. Two types of correlation equations were derived and are described in this paper. The first correlation expresses the Nusselt number as a function of the Prandtl number, Reynolds number, and characteristic temperature ratio; the second correlation expresses the forced convection heat transfer coefficient as a function of fluid temperature, pressure and velocity.

  10. Heat transfer enhancement by additive in vertical falling film absorption of H2O/LiBr

    International Nuclear Information System (INIS)

    Cheng Wenlong; Houda, Kouichi; Chen Zeshao; Akisawa, Atsushi; Hu Peng; Kashiwagi, Takao

    2004-01-01

    The enhancement effects of additive on vertical falling film of water into aqueous lithium bromide (LiBr) were studied by an experimental method. Based on the Navier-Stokes equations of falling film absorption, a new dimensionless parameter, surface renewal number Rn, was introduced, and a semi-empirical equation of enhancement factor of additive was obtained. It was shown that the absorption Marangoni number Ma, the surface Marangoni number M aA , and the surface renewal number Rn enhance the heat transfer of absorption, however the adsorption number Π and the Reynolds number Re weaken the heat transfer of absorption. It was proved that the semi-empirical equation agreed well with the experimental results by introduction of the parameters related to surface tension characters presented by the authors into the equation

  11. Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

    International Nuclear Information System (INIS)

    Yi Hongliang; Tan Heping; Lu Yiping

    2005-01-01

    Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative-conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative-convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index

  12. Role of phase breaking processes on resonant spin transfer torque nano-oscillators

    Science.gov (United States)

    Sharma, Abhishek; Tulapurkar, Ashwin A.; Muralidharan, Bhaskaran

    2018-05-01

    Spin transfer torque nano-oscillators (STNOs) based on magnetoresistance and spin transfer torque effects find potential applications in miniaturized wireless communication devices. Using the non-coherent non-equilibrium Green's function spin transport formalism self-consistently coupled with the stochastic Landau-Lifshitz-Gilbert-Slonczewski's equation and the Poisson's equation, we elucidate the role of elastic phase breaking on the proposed STNO design featuring double barrier resonant tunneling. Demonstrating the immunity of our proposed design, we predict that despite the presence of elastic dephasing, the resonant tunneling magnetic tunnel junction structures facilitate oscillator designs featuring a large enhancement in microwave power up to 8μW delivered to a 50Ω load.

  13. Consideration of heat transfer performance of helium-gas/water coolers in HENDEL

    International Nuclear Information System (INIS)

    Inagaki, Yoshiyuki; Miyamoto, Yoshiaki

    1986-10-01

    The helium engineering loop (HENDEL) has four helium-gas/water coolers, where the cooling water flows in the tubes and the helium gas flows on the shell side. Their cooling performance depends on mainly the heat transfer of helium gas on the shell side. This report describes the operational data of the coolers and the consideration of the heat transfer performance which is important for the design of coolers. It becomes clear that Donohue's equation is close to the operational data and conservative for the segmental baffle type cooler and preduction by Fishenden-Saunders or Zukauskas' equation is conservation for the step-up baffle type cooler. (author)

  14. The determination of an unknown source for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer; Laleg-Kirati, Taous-Meriem; Liu, Dayan

    2014-01-01

    source in groundwater transport. We propose to use the socalled modulating functions method which has been introduced for parameters estimation. This method allows to transfer the estimation problem into solving a system of algebraic equations. Numerical

  15. Fourier-Based Fast Multipole Method for the Helmholtz Equation

    KAUST Repository

    Cecka, Cris

    2013-01-01

    The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.

  16. Heat transfer coefficient for flow boiling in an annular mini gap

    Directory of Open Access Journals (Sweden)

    Hożejowska Sylwia

    2016-01-01

    Full Text Available The aim of this paper was to present the concept of mathematical models of heat transfer in flow boiling in an annular mini gap between the metal pipe with enhanced exterior surface and the external glass pipe. The one- and two-dimensional mathematical models were proposed to describe stationary heat transfer in the gap. A set of experimental data governed both the form of energy equations in cylindrical coordinates and the boundary conditions. The models were formulated to minimize the number of experimentally determined constants. Known temperature distributions in the enhanced surface and in the fluid helped to determine, from the Robin condition, the local heat transfer coefficients at the enhanced surface – fluid contact. The Trefftz method was used to find two-dimensional temperature distributions for the thermal conductive filler layer, enhanced surface and flowing fluid. The method of temperature calculation depended on whether the area of single-phase convection ended with boiling incipience in the gap or the two-phase flow region prevailed, with either fully developed bubbly flow or bubbly-slug flow. In the two–phase flow, the fluid temperature was calculated by Trefftz method. Trefftz functions for the Laplace equation and for the energy equation were used in the calculations.

  17. Dominant factors affecting temperature rise in simulations of human thermoregulation during RF exposure

    International Nuclear Information System (INIS)

    Laakso, Ilkka; Hirata, Akimasa

    2011-01-01

    Numerical models of the human thermoregulatory system can be used together with realistic voxel models of the human anatomy to simulate the body temperature increases caused by the power absorption from radio-frequency electromagnetic fields. In this paper, the Pennes bioheat equation with a thermoregulatory model is used for calculating local peak temperatures as well as the body-core-temperature elevation in a realistic human body model for grounded plane-wave exposures at frequencies 39, 800 and 2400 MHz. The electromagnetic power loss is solved by the finite-difference time-domain (FDTD) method, and the discretized bioheat equation is solved by the geometric multigrid method. Human thermoregulatory models contain numerous thermophysiological and computational parameters—some of which may be subject to considerable uncertainty—that affect the simulated core and local temperature elevations. The goal of this paper is to find how greatly the computed temperature is influenced by changes in various modelling parameters, such as the skin blood flow rate, models for vasodilation and sweating, and clothing and air movement. The results show that the peak temperature rises are most strongly affected by the modelling of tissue blood flow and its temperature dependence, and mostly unaffected by the central control mechanism for vasodilation and sweating. Almost the opposite is true for the body-core-temperature rise, which is however typically greatly lower than the peak temperature rise. It also seems that ignoring the thermoregulation and the blood temperature increase is a good approximation when the local 10 g averaged specific absorption rate is smaller than 10 W kg −1 .

  18. Finite difference approximation of control via the potential in a 1-D Schrodinger equation

    Directory of Open Access Journals (Sweden)

    K. Kime

    2000-04-01

    Full Text Available We consider the problem of steering given initial data to given terminal data via a time-dependent potential, the control, in a 1-D Schrodinger equation. We determine a condition for existence of a transferring potential within our approximation. Using Maple, we give equations for the control and also examples in which the potential is restricted to be centralized and to be a step potential.

  19. A study on gap heat transfer of LWR fuel rods under reactivity initiated accident conditions

    International Nuclear Information System (INIS)

    Fujishiro, Toshio

    1984-03-01

    Gap heat transfer between fuel pellet and cladding have a large influence on the LWR fuel behaviors under reactivity initiated accident (RIA) conditions. The objective of the present study is to investigate the effects of gap heat transfer on RIA fuel behaviors based on the results of the gap-gas parameter tests in NSRR and on their analysis with NSR-77 code. Through this study, transient variations of gap heat transfer, the effects of the gap heat transfer on fuel thermal behaviors and on fuel failure, effects of pellet-cladding sticking by eutectic formation, and the effects of cladding collapse under high external pressure have been clearified. The studies have also been performed on the applicability and its limit of modified Ross and Stoute equation which is extensively utilized to evaluate the gap heat transfer coefficient in the present fuel behavior codes. The method to evaluate the gap conductance to the conditions beyond the applicability limit of the Ross and Stoute equation has also been proposed. (author)

  20. A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations

    Directory of Open Access Journals (Sweden)

    Wenhua Zhang

    2013-01-01

    Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.

  1. Annual review of numerical fluid mechanics and heat transfer. Volume 1

    International Nuclear Information System (INIS)

    Chawla, T.C.

    1987-01-01

    Numerical techniqes for the analysis of problems in fluid mechanics and heat transfer are discussed, reviewing the results of recent investigations. Topics addressed include thermal radiation in particulate media with dependent and independent scattering, pressure-velocity coupling in incompressiblefluid flow, new explicit methods for diffusion problems, and one-dimensional reaction-diffusion equations in combustion theory. Consideration is given to buckling flows, multidimensional radiative-transfer analysis in participating media, freezing and melting problems, and complex heat-transfer processes in heat-generating horizontal fluid layers

  2. A mathematical model for localized corrosion in steam generator crevices under heat transfer conditions

    International Nuclear Information System (INIS)

    Engelhardt, G.; Urquidi-Macdonald, M.; Sikora, J.; Macdonald, D.D.

    1995-01-01

    A predictive and self-consistent mathematical model has been developed to describe the localized corrosion in steam generators. The model recognizes that the internal and external environment are coupled by the need to conserve charge in the system. Thus, solution of Laplace's equation for the external environment (outside the crevice) provides the boundary condition for the electric potential at the crevice mouth, which is needed for solving the system of mass transfer equations for the internal environment (inside the crevice). Mass transfer by diffusion, ion migration, and convection was considered. Heat and momentum transfer equations are solved simultaneously, with the mass balance equation for each species and the condition of electroneutrality inside the cavity being considered. The model takes into account the porosity and tortuosity in the corrosion product deposit in the crevice. The homogeneous chemical reactions (hydrolysis of the products of the anodic reaction and the autoprotolysis of water) are included in the model. The model, in this preliminary form predicts the solution chemistry, potential drop, and temperature distribution inside the crevice. An order of magnitude estimate of the crevice corrosion rate also obtained. At this point, the model predicts only the steady state solution, but it is recognized that a steady state may not exist under normal conditions

  3. Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation

    Directory of Open Access Journals (Sweden)

    Qinglin Cheng

    2018-04-01

    Full Text Available With the increasing demand of oil products in China, the energy consumption of pipeline operation will continue to rise greatly, as well as the cost of oil transportation. In the field of practical engineering, saving energy, reducing energy consumption and adapting to the international oil situation are the development trends and represent difficult problems. Based on the basic principle of non-equilibrium thermodynamics, this paper derives the field equilibrium equations of non-equilibrium thermodynamic process for pipeline transportation. To seek the bilinear form of “force” and “flow” in the non-equilibrium thermodynamics of entropy generation rate, the oil pipeline exergy balance equation and the exergy transfer pipeline dynamic equation of the irreversibility were established. The exergy balance equation was applied to energy balance evaluation system, which makes the system more perfect. The exergy flow transfer law of the waxy oil pipeline were explored deeply from the directions of dynamic exergy, pressure exergy, thermal exergy and diffusion exergy. Taking an oil pipeline as an example, the influence factors of exergy transfer coefficient and exergy flow density were analyzed separately.

  4. Efficient quantum state transfer in an engineered chain of quantum bits

    Science.gov (United States)

    Sandberg, Martin; Knill, Emanuel; Kapit, Eliot; Vissers, Michael R.; Pappas, David P.

    2016-03-01

    We present a method of performing quantum state transfer in a chain of superconducting quantum bits. Our protocol is based on engineering the energy levels of the qubits in the chain and tuning them all simultaneously with an external flux bias. The system is designed to allow sequential adiabatic state transfers, resulting in on-demand quantum state transfer from one end of the chain to the other. Numerical simulations of the master equation using realistic parameters for capacitive nearest-neighbor coupling, energy relaxation, and dephasing show that fast, high-fidelity state transfer should be feasible using this method.

  5. Deviations from mass transfer equilibrium and mathematical modeling of mixer-settler contactors

    International Nuclear Information System (INIS)

    Beyerlein, A.L.; Geldard, J.F.; Chung, H.F.; Bennett, J.E.

    1980-01-01

    This paper presents the mathematical basis for the computer model PUBG of mixer-settler contactors which accounts for deviations from mass transfer equilibrium. This is accomplished by formulating the mass balance equations for the mixers such that the mass transfer rate of nuclear materials between the aqueous and organic phases is accounted for. 19 refs

  6. New Correlation Methods of Evaporation Heat Transfer in Horizontal Microfine Tubes

    Science.gov (United States)

    Makishi, Osamu; Honda, Hiroshi

    A stratified flow model and an annular flow model of evaporation heat transfer in horizontal microfin tubes have been proposed. In the stratified flow model, the contributions of thin film evaporation and nucleate boiling in the groove above a stratified liquid were predicted by a previously reported numerical analysis and a newly developed correlation, respectively. The contributions of nucleate boiling and forced convection in the stratified liquid region were predicted by the new correlation and the Carnavos equation, respectively. In the annular flow model, the contributions of nucleate boiling and forced convection were predicted by the new correlation and the Carnavos equation in which the equivalent Reynolds number was introduced, respectively. A flow pattern transition criterion proposed by Kattan et al. was incorporated to predict the circumferential average heat transfer coefficient in the intermediate region by use of the two models. The predictions of the heat transfer coefficient compared well with available experimental data for ten tubes and four refrigerants.

  7. Maternal transfer of contaminants in birds: Mercury and selenium concentrations in parents and their eggs

    International Nuclear Information System (INIS)

    Ackerman, Joshua T.; Eagles-Smith, Collin A.; Herzog, Mark P.; Hartman, C. Alex

    2016-01-01

    We conducted a detailed assessment of the maternal transfer of mercury and selenium to eggs in three bird species (n = 107 parents and n = 339 eggs), and developed predictive equations linking contaminant concentrations in eggs to those in six tissues of the mother (blood, muscle, liver, kidney, breast feathers, and head feathers). Mercury concentrations in eggs were positively correlated with mercury concentrations in each of the mother's internal tissues (R"2 ≥ 0.95), but generally not with feathers. For each species, the proportion of mercury transferred to eggs decreased as mercury concentrations in the mother increased. At the same maternal mercury concentration, the proportion of mercury transferred to eggs differed among species, such that Forster's tern (Sterna forsteri) and black-necked stilt (Himantopus mexicanus) females transferred more methylmercury to their eggs than American avocet (Recurvirostra americana) females. Selenium concentrations in eggs also were correlated with selenium concentrations in the mother's liver (R"2 = 0.87). Furthermore, mercury and selenium concentrations in tern eggs were positively correlated with those in the father (R"2 = 0.84). Incubating male terns had 21% higher mercury concentrations in blood compared to incubating females at the same egg mercury concentration. We provide equations to predict contaminant concentrations in eggs from each of the commonly sampled bird tissues. - Highlights: • We developed predictive equations linking contaminant concentrations in eggs to those in the mother. • Mercury concentrations in eggs were positively correlated with those in the mother. • The proportion of mercury transferred to eggs decreased as mercury in the mother increased. • The proportion of mercury transferred to eggs differed among species. • Selenium concentrations in eggs also were correlated with those in the mother's liver. - We examined the maternal transfer of mercury and selenium to eggs in

  8. Arcmancer: Geodesics and polarized radiative transfer library

    Science.gov (United States)

    Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.

    2018-05-01

    Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.

  9. Dunajski–Tod equation and reductions of the generalized dispersionless 2DTL hierarchy

    Energy Technology Data Exchange (ETDEWEB)

    Bogdanov, L.V., E-mail: leonid@landau.ac.ru [L.D. Landau ITP RAS, Moscow (Russian Federation)

    2012-10-01

    We transfer the scheme for constructing differential reductions recently developed for the Manakov–Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. We demonstrate that the equation arising as a result of the simplest reduction is equivalent (up to a Legendre type transformation) to the Dunajski–Tod equation, locally describing general ASD vacuum metric with conformal symmetry. We consider higher reductions and corresponding reduced hierarchies also. -- Highlights: ► We introduce a differential reduction for the two-component d2DTL equation. ► We demonstrate that it is connected with ASD vacuum metric with conformal symmetry. ► We construct higher reductions and the reduced hierarchies.

  10. Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

    Energy Technology Data Exchange (ETDEWEB)

    Hatami, M., E-mail: m.hatami@tue.nl [Esfarayen University of Technology, Mechanical Engineering Department, Esfarayen, North Khorasan (Iran, Islamic Republic of); Jing, Dengwei; Song, Dongxing [International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi' an 710049 (China); Sheikholeslami, M.; Ganji, D.D. [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of)

    2015-12-15

    In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number.

  11. Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

    International Nuclear Information System (INIS)

    Hatami, M.; Jing, Dengwei; Song, Dongxing; Sheikholeslami, M.; Ganji, D.D.

    2015-01-01

    In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number

  12. Theory of coherent resonance energy transfer

    International Nuclear Information System (INIS)

    Jang, Seogjoo; Cheng, Y.-C.; Reichman, David R.; Eaves, Joel D.

    2008-01-01

    A theory of coherent resonance energy transfer is developed combining the polaron transformation and a time-local quantum master equation formulation, which is valid for arbitrary spectral densities including common modes. The theory contains inhomogeneous terms accounting for nonequilibrium initial preparation effects and elucidates how quantum coherence and nonequilibrium effects manifest themselves in the coherent energy transfer dynamics beyond the weak resonance coupling limit of the Foerster and Dexter (FD) theory. Numerical tests show that quantum coherence can cause significant changes in steady state donor/acceptor populations from those predicted by the FD theory and illustrate delicate cooperation of nonequilibrium and quantum coherence effects on the transient population dynamics.

  13. A perturbational h4 exponential finite difference scheme for the convective diffusion equation

    International Nuclear Information System (INIS)

    Chen, G.Q.; Gao, Z.; Yang, Z.F.

    1993-01-01

    A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic

  14. Numerical study of the heat transfer in wound woven wire matrix of a Stirling regenerator

    International Nuclear Information System (INIS)

    Costa, S.C.; Barrutia, Harritz; Esnaola, Jon Ander; Tutar, Mustafa

    2014-01-01

    Highlights: • A correlation equation to characterize regenerator heat transfer is proposed. • Proposed correlation can be used as a effective tool to optimize the heat transfer. • Thermal efficiency can be maximized by optimizing Stirling regenerator heat transfer. • The wound woven wire matrix provides lower Nusselt numbers compared to stacked. • The developed correlation can be used for Reynolds number range from 4 to 400. - Abstract: Nusselt number correlation equations are numerically derived by characterizing the heat transfer phenomena through porous medium of both stacked and wound woven wire matrices of a Stirling engine regenerator over a specified range of Reynolds number, diameter and porosity. A finite volume method (FVM) based numerical approach is proposed and validated against well known experimentally obtained empirical correlations for a random stacking woven wire matrix, the most widely used due to fabrication issues, for Reynolds number up to 400. The results show that the numerically derived correlation equation corresponds well with the experimentally obtained correlations with less than 6% deviation with the exception of low Reynolds numbers. Once the numerical approach is validated, the study is further extended to characterize the heat transfer in a wound woven wire matrix model for a diameter range from 0.08 to 0.11 mm and a porosity range from 0.60 to 0.68 within the same Reynolds number range. Thus, the new correlation equations are numerically derived for different flow configurations of the Stirling engine regenerator. It is believed that the developed correlations can be applied with confidence as a cost effective solution to characterize and hence to optimize stacked and wound woven wire Stirling regenerator in the above specified ranges

  15. Discrete diffusion Monte Carlo for frequency-dependent radiative transfer

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.

    2011-01-01

    Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique. (author)

  16. The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

    Directory of Open Access Journals (Sweden)

    D. R. V. S. R. K. Sastry

    2013-01-01

    Full Text Available The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

  17. Major controlling factors and predictions for cadmium transfer from the soil into spinach plants.

    Science.gov (United States)

    Liang, Zhenfei; Ding, Qiong; Wei, Dongpu; Li, Jumei; Chen, Shibao; Ma, Yibing

    2013-07-01

    Predicting the mobility, bioavailability and transfer of cadmium (Cd) in the soil-plant system is of great importance with regards to food safety and environmental management. In this study, the transfer characteristics of Cd (exogenous salts) from a wide range of Chinese soils to spinach (Spinacia oleracea L.) were investigated. The major controlling factors and prediction equations for Cd transfer in the soil-plant system were also investigated. The results showed that plant Cd concentration was positively correlated with soil Cd concentration. The maximum transfer factor (ratio of the Cd concentration in the plant to that in the soil) was found in acid soils. The extended Freundlich-type function was able to describe the Cd transfer from soil to spinach plants. Combining soil total Cd, pH and organic carbon (OC) content in the prediction equation greatly improved the correlation performance compared with predictions based on total Cd only. A slight protection effect of OC on Cd uptake was observed at low soil Cd concentrations. The results are a useful tool that can be used to predict Cd transfer from soil to plant. Copyright © 2013 Elsevier Inc. All rights reserved.

  18. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Directory of Open Access Journals (Sweden)

    Yu Bai

    2017-12-01

    Full Text Available This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  19. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Science.gov (United States)

    Bai, Yu; Jiang, Yuehua; Liu, Fawang; Zhang, Yan

    2017-12-01

    This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  20. New model reduction technique for a class of parabolic partial differential equations

    NARCIS (Netherlands)

    Vajta, Miklos

    1991-01-01

    A model reduction (or lumping) technique for a class of parabolic-type partial differential equations is given, and its application is discussed. The frequency response of the temperature distribution in any multilayer solid is developed and given by a matrix expression. The distributed transfer

  1. Microporous hollow fibre membrane modules as gas-liquid contactors. Part 2. Mass transfer with chemical reaction

    NARCIS (Netherlands)

    Kreulen, H.; Versteeg, G.F.; Swaaij, W.P.M. van

    1993-01-01

    Absorption determined by mass transfer in the liquid is described well with the Graetz-Lévèque equation adapted from heat transfer. The influence of a chemical reaction on the mass transfer was simulated with a numerical model and tested on the absorption of CO2 in a hydroxide solution. Absorption

  2. Study of mixed radiative thermal mass transfer in the case of spherical liquide particle evaporation in a high temperature thermal air plasma

    International Nuclear Information System (INIS)

    Garandeau, S.

    1984-01-01

    Radiative transfer in a semi-transparent non-isothermal medium with spherical configuration has been studied. Limit conditions have been detailed, among which the semi-transparent inner sphere case is a new case. Enthalpy and matter transfer equations related to these different cases have been established. An adimensional study of local conservation laws allowed to reveal a parameter set characteristic of radiation coupled phenomena thermal conduction, convection, diffusion. Transfer equations in the case of evaporation of a liquid spherical particle in an air thermal plasma have been simplified. An analytical solution for matter transfer is proposed. Numerical solution of radiative problems and matter transfer has been realized [fr

  3. Numerical simulation on coolant flow and heat transfer in core

    International Nuclear Information System (INIS)

    Yao Zhaohui; Wang Xuefang; Shen Mengyu

    1997-01-01

    To simulate the coolant flow and the heat transfer characteristics of a core, a computer code, THAPMA (Thermal Hydraulic Analysis Porous Medium Analysis) has been developed. In THAPMA code, conservation equations are based on a porous-medium formulation, which uses four parameters, i.e, volume porosity, directional surface porosity, distributed resistance, and distributed heat source (sink), to model the effects of fuel rods and other internal solid structures on flow and heat transfer. Because the scheme and the solution are very important in accuracy and speed of calculation, a new difference scheme (WSUC) has been used in the energy equation, and a modified PISO solution method have been employed to simulate the steady/transient states. The code has been proved reliable and can effectively solve the transient state problem by several numerical tests. According to the design of Qinshan NPP-II, the flow and heat transfer phenomena in reactor core have been numerically simulated. The distributions of the velocity and the temperature can provide a theoretical basis for core design and safety analysis

  4. Film boiling heat transfer in liquid helium

    International Nuclear Information System (INIS)

    Inai, Nobuhiko

    1979-01-01

    The experimental data on the film boiling heat transfer in liquid helium are required for investigating the stability of superconducting wires. On the other hand, liquid helium has the extremely different physical properties as compared with the liquids at normal temperature such as water. In this study, the experiments on pool boiling were carried out, using the horizontal top surface of a 20 mm diameter copper cylinder in liquid helium. For observing individual bubbles, the experiments on film boiling from a horizontal platinum wire were performed separately in liquid nitrogen and liquid helium, and photographs of floating-away bubbles were taken. The author pointed out the considerable upward shift of the boiling curve near the least heat flux point in film boiling from the one given by the Berenson's equation which has been said to agree comparatively well with the data on the film boiling of the liquids at normal temperature, and the reason was investigated. Consequently, a model for film boiling heat transfer was presented. Also one equation expressing the film boiling at low heat flux for low temperature liquids was proposed. It represents well the tendency to shift from Berenson's equation of the experimental data on film boiling at the least heat flux point for liquid helium, liquid nitrogen and water having extremely different physical properties. Some discussions are added at the end of the paper. (Wakatsuki, Y.)

  5. Bivariational calculations for radiation transfer in an inhomogeneous participating media

    International Nuclear Information System (INIS)

    El Wakil, S.A.; Machali, H.M.; Haggag, M.H.; Attia, M.T.

    1986-07-01

    Equations for radiation transfer are obtained for dispersive media with space dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared. (author)

  6. Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux

    International Nuclear Information System (INIS)

    Kawamura, Hiroshi

    1978-01-01

    Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)

  7. About the possible options for models of convective heat transfer in closed volumes with local heating source

    Directory of Open Access Journals (Sweden)

    Maksimov Vyacheslav I.

    2015-01-01

    Full Text Available Results of mathematical modeling of convective heat transfer in air area surrounded on all sides enclosing structures, in the presence of heat source at the lower boundary of the media are presented. Solved the system of differential equations of unsteady Navier-Stokes equations with the appropriate initial and boundary conditions. The process of convective heat transfer is calculated using the models of turbulence Prandtl and Prandtl-Reichard. Takes into account the processes of heat exchange region considered with the environment. Is carried out the analysis of the dimensionless heat transfer coefficient at interfaces “air – enclosures”. The distributions average along the gas temperature range are obtained.

  8. Natural Convective Heat Transfer from Narrow Plates

    CERN Document Server

    Oosthuizen, Patrick H

    2013-01-01

    Natural Convective Heat Transfer from Narrow Plates deals with a heat transfer situation that is of significant practical importance but which is not adequately dealt with in any existing textbooks or in any widely available review papers. The aim of the book is to introduce the reader to recent studies of natural convection from narrow plates including the effects of plate edge conditions, plate inclination, thermal conditions at the plate surface and interaction of the flows over adjacent plates. Both numerical and experimental studies are discussed and correlation equations based on the results of these studies are reviewed.

  9. Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity

    International Nuclear Information System (INIS)

    Sadri, Somayyeh; Raveshi, Mohammad Reza; Amiri, Shayan

    2012-01-01

    In this study, one type of applicable analytical method, differential transformation method (DTM), is used to evaluate the efficiency and behavior of a straight fin with variable thermal conductivity and heat transfer coefficient. Fins are widely used to enhance heat transfer between primary surface and the environment in many industrial applications. The performance of such a surface is significantly affected by variable thermal conductivity and heat transfer coefficient, particularly for large temperature differences. General heat transfer equation related to the fin is derived and dimensionalized. The concept of differential transformation is briefly introduced, and then this method is employed to derive solutions of nonlinear equations. Results are evaluated for several cases such as: laminar film boiling or condensation, forced convection, laminar natural convection, turbulent natural convection, nucleate boiling, and radiation. The obtained results from DTM are compared with the numerical solution to verify the accuracy of the proposed method. The effects of design parameters on temperature and efficiency are evaluated by some figures. The major aim of the present study, which is exclusive for this article, is to find the effect of the modes of heat transfer on fin efficiency. It has been shown that for radiation heat transfer, thermal efficiency reaches its maximum value

  10. Finite life time effects in the coherent exciton transfer

    International Nuclear Information System (INIS)

    Barvik, I.; Herman, P.

    1992-04-01

    The paper addresses a specific problem in the exciton transfer in molecular aggregates, namely the influence of the finite life time effects, on the memory functions entering the Generalized Master Equation (GME) which connect different sites of the system. 7 refs, 2 figs

  11. Convective heat transfer from a heated elliptic cylinder at uniform wall temperature

    Energy Technology Data Exchange (ETDEWEB)

    Kaprawi, S.; Santoso, Dyos [Mechanical Department of Sriwijaya University, Jl. Raya Palembang-Prabumulih Km. 32 Inderalaya 50062 Ogan Ilir (Indonesia)

    2013-07-01

    This study is carried out to analyse the convective heat transfer from a circular and an elliptic cylinders to air. Both circular and elliptic cylinders have the same cross section. The aspect ratio of cylinders range 0-1 are studied. The implicit scheme of the finite difference is applied to obtain the discretized equations of hydrodynamic and thermal problem. The Choleski method is used to solve the discretized hydrodynamic equation and the iteration method is applied to solve the discretized thermal equation. The circular cylinder has the aspect ratio equal to unity while the elliptical cylinder has the aspect ratio less than unity by reducing the minor axis and increasing the major axis to obtain the same cross section as circular cylinder. The results of the calculations show that the skin friction change significantly, but in contrast with the elliptical cylinders have greater convection heat transfer than that of circular cylinder. Some results of calculations are compared to the analytical solutions given by the previous authors.

  12. General post-Minkowskian expansion of time transfer functions

    Energy Technology Data Exchange (ETDEWEB)

    Teyssandier, Pierre; Poncin-Lafitte, Christophe Le [Departement Systemes de Reference Temps et Espace, CNRS/UMR 8630, Observatoire de Paris, 61 avenue de l' Observatoire, F-75014 Paris (France)

    2008-07-21

    Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

  13. General post-Minkowskian expansion of time transfer functions

    International Nuclear Information System (INIS)

    Teyssandier, Pierre; Poncin-Lafitte, Christophe Le

    2008-01-01

    Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation

  14. Solving fractal steady heat-transfer problems with the local fractional Sumudu transform

    Directory of Open Access Journals (Sweden)

    Wang Yi

    2015-01-01

    Full Text Available In this paper the linear oscillator problem in fractal steady heat-transfer is studied within the local fractional theory. In particular, the local fractional Sumudu transform (LFST will be used to solve both the homogeneous and the non-homogeneous local fractional oscillator equations (LFOEs under fractal steady heat-transfer. It will be shown that the obtained non-differentiable solutions characterize the fractal phenomena with and without the driving force in fractal steady heat transfer at low excess temperatures.

  15. GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS

    Directory of Open Access Journals (Sweden)

    Túlio Jardim Raad

    2006-06-01

    Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.

  16. Heat transfer in vapour-liquid flow of carbon dioxide

    International Nuclear Information System (INIS)

    Yagov, V.V.

    2009-01-01

    During the last decade a number of studies of boiling heat transfer in carbon dioxide notably increase. As a field of CO 2 practical using corresponds to high reduced pressures, and a majority of available experimental data on CO 2 flow boiling even in submillimetric channels relate to turbulent liquid flow regimes, a possibility arises to develop sufficiently general method for HTC predicting. Under the above conditions nucleate boiling occurs up to rather high flow quality, even in annular flow regime due to extremely small size of an equilibrium vapour bubble. This conclusion is in agreement with the available experimental data. The predicting equation for nucleate boiling heat transfer developed by the present author in 1988 is valid for any nonmetallic liquid. A contribution of forced convection in heat transfer is calculated according to the Petukhov et al. equation with correction factor, which accounted for an effect of velocity increase due to evaporation. This effect can be essential at relatively small heat fluxes and rather high mass flow rates. The Reynolds analogy and homogeneous model are used in order to account for the convective heat transfer augmentation in two-phase flow. Due to low ratio of liquid and vapour densities at high reduced pressures the homogeneous approximation of two-phase flow seems to be warranted. A total heat transfer coefficient is calculated as an interpolated value of boiling and convective HTCs. The experimental data on CO 2 flow boiling related to regimes before heated wall dryout incipience are in rather good agreement with the calculations. (author)

  17. Experimental Waterflow Determination of the Dynamic Hydraulic Transfer Function for the J-2X Oxidizer Turbopump. Part Two; Results and Interpretation

    Science.gov (United States)

    Zoladz, Tom; Patel, Sandeep; Lee, Erik; Karon, Dave

    2011-01-01

    Experimental results describing the hydraulic dynamic pump transfer matrix (Yp) for a cavitating J-2X oxidizer turbopump inducer+impeller tested in subscale waterflow are presented. The transfer function is required for integrated vehicle pogo stability analysis as well as optimization of local inducer pumping stability. Dynamic transfer functions across widely varying pump hydrodynamic inlet conditions are extracted from measured data in conjunction with 1D-model based corrections. Derived Dynamic transfer functions are initially interpreted relative to traditional Pogo pump equations. Water-to-liquid oxygen scaling of measured cavitation characteristics are discussed. Comparison of key dynamic transfer matrix terms derived from waterflow testing are made with those implemented in preliminary Ares Upper Stage Pogo stability modeling. Alternate cavitating pump hydraulic dynamic equations are suggested which better reflect frequency dependencies of measured transfer matrices.

  18. Influence of heat transfer on the dynamic response of a spherical gas/vapour bubble

    International Nuclear Information System (INIS)

    Hegedus, Ferenc; Hos, Csaba; Kullmann, Laszlo

    2010-01-01

    The standard approach to analyse the bubble motion is the well known Rayleigh-Plesset equation. When applying the toolbox of nonlinear dynamical systems to this problem several aspects of physical modelling are usually sacrificed. Particularly in vapour bubbles the heat transfer in the liquid domain has a significant effect on the bubble motion; therefore the nonlinear energy equation coupled with the Rayleigh-Plesset equation must be solved. The main aim of this paper is to find an efficient numerical method to transform the energy equation into an ODE system, which, after coupling with the Rayleigh-Plesset equation can be analysed with the help of bifurcation theory. Due to the strong nonlinearity and violent bubble motions the computational effort can be high, thus it is essential to reduce the size of the problem as much as possible. In the first part of the paper finite difference, Galerkin and spectral collocation methods are examined and compared in terms of efficiency. In the second part free and forced oscillations are analysed with an emphasis on the influence of heat transfer. In the case of forced oscillations the unstable branches of the amplification diagrams are also computed.

  19. Variational principles in terms of entransy for heat transfer

    International Nuclear Information System (INIS)

    Xu, Mingtian

    2012-01-01

    A variational principle for heat conduction is formulated which results in the steady state heat conduction equation established from the Fourier law. Furthermore based on the thermodynamics in terms of entransy a more general functional is defined for incompressible fluids. We show that extremizing this functional gives rise to the state described by the Navier-Stokes-Fourier equations with vanishing substantive derivatives of the temperature and velocity field. In this sense one may conclude that this variational principle is consistent with the Navier-Stokes-Fourier equations. Therefore the variational principle developed in the present work demonstrates a great advantage over the minimum entropy production principle. -- Highlights: ► A variational principle for heat transfer of incompressible fluid is established in terms of entransy. ► For pure heat conduction the variational principle leads to the classical steady state heat conduction equation. ► For heat convection the variational principle is consistent with the Navier-Stokes-Fourier equations.

  20. Mass and heat transfer mechanism in wood during radio frequency/vacuum drying and numerical analysis

    Institute of Scientific and Technical Information of China (English)

    Xiaoran Jia; Jingyao Zhao; Yingchun Cai

    2017-01-01

    The mass and heat transfer mechanisms during radio frequency/vacuum (RF/V) drying of square-edged timber were analyzed and discussed in detail,and a new one-dimensional mathematical model to describe the transport phenomena of mass and heat during continuous RF/V drying was derived from conservation equations based on the mass and heat transfer theory of porous materials.The new model provided a relatively fast and efficient way to simulate vacuum drying behavior assisted by dielectric heating.Its advantages compared with the conventional models include:(1) Each independent variable has a separate control equation and is solved independently by converting the partial differential equation into a difference equation with the finite volume method;(2) The calculated data from different parts of the specimen can be displayed in the evolution curves,and the change law of the parameters can be better described.After analyzing the calculated results,most of the important phenomena observed during RF/V drying were adequately described by this model.

  1. Handbook of heat and mass transfer. Volume 2

    International Nuclear Information System (INIS)

    Cheremisinoff, N.P.

    1986-01-01

    This two-volume series, the work of more than 100 contributors, presents advanced topics in industrial heat and mass transfer operations and reactor design technology. Volume 2 emphasizes mass transfer and reactor design. Some of the contents discussed are: MASS TRANSFER PRINCIPLES - Effect of turbulence promoters on mass transfer. Mass transfer principles with homogeneous and heterogeneous reactions. Convective diffusion with reactions in a tube. Transient mass transfer onto small particles and drops. Modeling heat and mass transport in falling liquid films. Heat and mass transfer in film absorption. Multicomponent mass transfer: theory and applications. Diffusion limitation for reaction in porous catalysts. Kinetics and mechanisms of catalytic deactivation. DISTILLATION AND EXTRACTION - Generalized equations of state for process design. Mixture boiling. Estimating vapor pressure from normal boiling points of hydrocarbons. Estimating liquid and vapor molar fractions in distillation columns. Principles of multicomponent distillation. Generalized design methods for multicomponent distillation. Interfacial films in inorganic substances extraction. Liquid-liquid extraction in suspended slugs. MULTIPHASE REACTOR SYSTEMS - Reaction and mass transport in two-phase reactors. Mass transfer and kinetics in three-phase reactors. Estimating liquid film mass transfer coefficients in randomly packed columns. Designing packed tower wet scrubbers - emphasis on nitrogen oxides. Gas absorption in aerated mixers. Axial dispersion and heat transfer in gas-liquid bubble columns. Operation and design of trickle-bed reactors

  2. Analysis of Influence of the Thermal Dependence of Air Thermophysical Properties on the Accuracy of Simulation of Heat Transfer in a Turbulent Flow in Case of Applying Different Methods of Averaging Navier-Stokes Equations

    Directory of Open Access Journals (Sweden)

    A. D. Kliukvin

    2014-01-01

    Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and

  3. Solution of the porous media equation by Adomian's decomposition method

    International Nuclear Information System (INIS)

    Pamuk, Serdal

    2005-01-01

    The particular exact solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer, and in biological systems are obtained using Adomian's decomposition method. Also, numerical comparison of particular solutions in the decomposition method indicate that there is a very good agreement between the numerical solutions and particular exact solutions in terms of efficiency and accuracy

  4. Numerical assessment and comparison of heat transfer characteristics of supercritical water in bare tubes and tubes with heat transfer enhancing appendages

    International Nuclear Information System (INIS)

    Farah, Amjad; Harvel, Glenn; Pioro, Igor

    2015-01-01

    Computational Fluid Dynamics (CFD) is a numerical approach to model fluids in multidimensional space using the Navier-Stokes equations and databases of fluid properties to arrive at a full simulation of a fluid dynamics and heat transfer system. A numerical study on heat transfer to supercritical water (SCW) flowing in a vertical tube is carried out using the ANSYS FLUENT code and employing the SST k-ω turbulence model. The 3D mesh consists of a 1/8 section (45deg radially) of a bare tube. The numerical results on wall temperature distributions under normal and deteriorated heat transfer conditions are compared to experimental results. The same geometry is then simulated with an orifice to study the effect of geometrical perturbation on the flow and heat transfer characteristics of SCW. The orifice is placed areas to test the effect on normal, deteriorated and enhanced heat transfer regimes. The flow effects and heat transfer characteristics will be studied around the appendages to arrive at a fundamental understanding of the phenomena related to supercritical water turbulence. (author)

  5. Heat transfer in porous media

    Directory of Open Access Journals (Sweden)

    N. Amanifard

    2007-06-01

    Full Text Available In this work, the effects of electrical double layer (EDL near the solid/ liquid interface, on three dimensional heat transfer characteristic and pressure drop of water flow through a rectangular microchannel numerically are investigated. An additional body force originating from the existence of EDL is considered to modify the conventional Navier-stokes and energy equations. These modified equations are solved numerically for steady laminar flow on the basis of control volume approaches. Fluid velocity distribution and temperature with presence and absence of EDL effects are presented for various geometric cases and different boundary conditions. The results illustrate that, the liquid flow in rectangular microchannels is influenced significantly by the EDL, particularly in the high electric potentials, and hence deviates from flow characteristics described by classical fluid mechanics.

  6. Excited-state lifetime measurements: Linearization of the Foerster equation by the phase-plane method

    International Nuclear Information System (INIS)

    Love, J.C.; Demas, J.N.

    1983-01-01

    The Foerster equation describes excited-state decay curves involving resonance intermolecular energy transfer. A linearized solution based on the phase-plane method has been developed. The new method is quick, insensitive to the fitting region, accurate, and precise

  7. Influence of vapor-mass flux on simultaneous heat and moisture transfer in unsaturated porous media

    International Nuclear Information System (INIS)

    Hartley, J.G.; Boo, J.H.

    1987-01-01

    This paper evaluates the validity of neglecting vapor transport by moisture content gradients (VMG) and liquid transport by temperature gradients (LTG) in coupled heat and moisture transfer in moist porous media. A review of previous work reveals discrepancies between model predictions and experimental data. The results presented here show that these discrepancies result from neglecting VMG. The governing equations which describe the coupled heat and moisture transfer are solved numerically for an infinite slab of an unsaturated porous medium, and existing experimental and empirical data for a moist sandy silt soil are used. Predicted moisture content distributions during dry-out and drying rates are found to be significantly affected by VMG. Accurate results can be obtained when VMG is neglected in the energy equation provided that it is retained in the mass conservation equation

  8. Influence of concentration and hydrodynamic factors in sorption of iodine by anion-exchangers of the mass-transfer rate

    International Nuclear Information System (INIS)

    Sokolov, V.V.; Smirnov, N.N.

    1982-01-01

    An investigation of the joint influence of hydrodynamic and concentration factors in sorption of iodine by AV-17-8 and anion exchange resins on the mass-transfer coefficient is the subject of this report. The method of central composite rotatable experimental design was used for quantitative assessment and derivation of the appropriate equations. The investigation yielded the necessary regression equations satisfactorily describing the influence of all the factors in the mass-transfer coefficient. the optimal mass-transfer conditions were determined. On the basis of the values obtained, recommendations are made on the optimal hydrodynamic conditions of operation of equipment with pneumatic circulation of the ion-exchanger

  9. Laplace transform analysis of a multiplicative asset transfer model

    Science.gov (United States)

    Sokolov, Andrey; Melatos, Andrew; Kieu, Tien

    2010-07-01

    We analyze a simple asset transfer model in which the transfer amount is a fixed fraction f of the giver’s wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of f∈(0,1). The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

  10. Heat-and-mass transfer during a laminar dissociating gas flow in eccentric annular channels

    International Nuclear Information System (INIS)

    Besedina, T.V.; Udot, A.V.; Yakushev, A.P.

    1987-01-01

    An algorithm to calculate heat-and-mass transfer processes during dissociating gas laminar flow in an eccentric annular channels is considered. Analytical solutions of the heat transfer equations for a rod clodding and gap with boundary conditions of conjugation of temperatures and heat fluxes have been used to determine temperature field. This has made it possible to proceed from slution of the conjugate problem to solution of the equation of energy only for the coolant. The results of calculation of temperature distribution along the cladding for different values of its eccentricity and thermal conductivity coefficient both for the case of frozen flow and in the presence of chemical reactions in the flow are given. When calculating temperatures with conjugation boundary conditions temperature gradients in azimuthal direction are far less and heat transfer in concentration diffusion is carried out mainly in radial direction

  11. Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation.

    Science.gov (United States)

    Roux, L; Mareschal, P; Vukadinovic, N; Thibaud, J B; Greffet, J J

    2001-02-01

    This study is devoted to the examination of scattering of waves by a slab containing randomly located cylinders. For the first time to our knowledge, the complete transmission problem has been solved numerically. We have compared the radiative transfer theory with a numerical solution of the wave equation. We discuss the coherent effects, such as forward-scattering dip and backscattering enhancement. It is seen that the radiative transfer equation can be used with great accuracy even for optically thin systems whose geometric thickness is comparable with the wavelength. We have also shown the presence of dependent scattering.

  12. 3D modelling of coupled mass and heat transfer of a convection-oven roasting process

    DEFF Research Database (Denmark)

    Feyissa, Aberham Hailu; Adler-Nissen, Jens; Gernaey, Krist

    2013-01-01

    A 3D mathematical model of coupled heat and mass transfer describing oven roasting of meat has been developed from first principles. The proposed mechanism for the mass transfer of water is modified and based on a critical literature review of the effect of heat on meat. The model equations...... are based on a conservation of mass and energy, coupled through Darcy's equations of porous media - the water flow is mainly pressure-driven. The developed model together with theoretical and experimental assessments were used to explain the heat and water transport and the effect of the change...

  13. Validation of a numerical algorithm based on transformed equations

    International Nuclear Information System (INIS)

    Xu, H.; Barron, R.M.; Zhang, C.

    2003-01-01

    Generally, a typical equation governing a physical process, such as fluid flow or heat transfer, has three types of terms that involve partial derivatives, namely, the transient term, the convective terms and the diffusion terms. The major difficulty in obtaining numerical solutions of these partial differential equations is the discretization of the convective terms. The transient term is usually discretized using the first-order forward or backward differencing scheme. The diffusion terms are usually discretized using the central differencing scheme and no difficulty arises since these terms involve second-order spatial derivatives of the flow variables. The convective terms are non-linear and contain first-order spatial derivatives. The main difference between various numerical algorithms is the discretization of the convective terms. In the present study, an alternative approach to discretizing the governing equations is presented. In this algorithm, the governing equations are first transformed by introducing an exponential function to eliminate the convective terms in the equations. The proposed algorithm is applied to simulate some fluid flows with exact solutions to validate the proposed algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. The comparisons with the power-law scheme indicate that the proposed scheme exhibits better performance. (author)

  14. Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser

    Science.gov (United States)

    Cui, H.; Wang, H.; Chen, S.

    2015-04-01

    In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.

  15. Disentangling the triadic interactions in Navier-Stokes equations.

    Science.gov (United States)

    Sahoo, Ganapati; Biferale, Luca

    2015-10-01

    We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, |k| ~ k(m). Changing k(m) to be above or below the forcing scale, k(f), we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.

  16. Multigrid solution of the convection-diffusion equation with high-Reynolds number

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Jun [George Washington Univ., Washington, DC (United States)

    1996-12-31

    A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.

  17. Numerical simulation of heat transfer in power law fluid flow through a stenosed artery

    Science.gov (United States)

    Talib, Amira Husni; Abdullah, Ilyani

    2017-11-01

    A numerical study of heat transfer in a power law fluid is investigated in this paper. The blood flow is treated as power law fluid with a presence of cosine shaped stenosis. This study reveals the effect of stenosis on the heat transfer and velocity of blood flowing in the constricted artery. The governing and energy equations are formulated in a cylindrical coordinate system. Hence, the set of equations and boundary conditions are solved numerically by Marker and Cell (MAC) method. The graphical result shows the profile of blood temperature is increased while the blood velocity is decreased at the critical height of stenosis.

  18. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  19. Equating error in observed-score equating

    NARCIS (Netherlands)

    van der Linden, Willem J.

    2006-01-01

    Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

  20. Thermosolutal MHD flow and radiative heat transfer with viscous ...

    African Journals Online (AJOL)

    This paper investigates double diffusive convection MHD flow past a vertical porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic ...

  1. From convolutionless generalized master to Pauli master equations

    International Nuclear Information System (INIS)

    Capek, V.

    1995-01-01

    The paper is a continuation of previous work within which it has been proved that time integrals of memory function (i.e. Markovian transfer rates from Pauli Master Equations, PME) in Time-Convolution Generalized Master Equations (TC-GME) for probabilities of finding a state of an asymmetric system interacting with a bath with a continuous spectrum are exactly zero, provided that no approximation is involved, irrespective of the usual finite-perturbation-order correspondence with the Golden Rule transition rates. In this paper, attention is paid to an alternative way of deriving the rigorous PME from the TCL-GME. Arguments are given in favor of the proposition that the long-time limit of coefficients in TCL-GME for the above probabilities, under the same assumption and presuming that this limit exists, is equal to zero. 11 refs

  2. On the physical solutions to the heat equation subjected to nonlinear boundary conditions

    International Nuclear Information System (INIS)

    Gama, R.M.S. da.

    1990-01-01

    This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)

  3. Measurement of Membrane Characteristics Using the Phenomenological Equation and the Overall Mass Transport Equation in Ion-Exchange Membrane Electrodialysis of Saline Water

    Directory of Open Access Journals (Sweden)

    Yoshinobu Tanaka

    2012-01-01

    Full Text Available The overall membrane pair characteristics included in the overall mass transport equation are understandable using the phenomenological equations expressed in the irreversible thermodynamics. In this investigation, the overall membrane pair characteristics (overall transport number , overall solute permeability , overall electro-osmotic permeability and overall hydraulic permeability were measured by seawater electrodialysis changing current density, temperature and salt concentration, and it was found that occasionally takes minus value. For understanding the above phenomenon, new concept of the overall concentration reflection coefficient ∗ is introduced from the phenomenological equation. This is the aim of this investigation. ∗ is defined for describing the permselectivity between solutes and water molecules in the electrodialysis system just after an electric current interruption. ∗ is expressed by the function of and . ∗ is generally larger than 1 and is positive, but occasionally ∗ becomes less than 1 and becomes negative. Negative means that ions are transferred with water molecules (solvent from desalting cells toward concentrating cells just after an electric current interruption, indicating up-hill transport or coupled transport between water molecules and solutes.

  4. An immersed-boundary method for conjugate heat transfer analysis

    Energy Technology Data Exchange (ETDEWEB)

    Song, Jeong Chul; Lee, Joon Sik [Seoul National University, Seoul (Korea, Republic of); Ahn, Joon [Kookmin University, Seoul (Korea, Republic of)

    2017-05-15

    An immersed-boundary method is proposed for the analysis of conjugate problems of convective heat transfer in conducting solids. In- side the solid body, momentum forcing is applied to set the velocity to zero. A thermal conductivity ratio and a heat capacity ratio, between the solid body and the fluid, are introduced so that the energy equation is reduced to the heat diffusion equation. At the solid fluid interface, an effective conductivity is introduced to satisfy the heat flux continuity. The effective thermal conductivity is obtained by considering the heat balance at the interface or by using a harmonic mean formulation. The method is first validated against the analytic solution to the heat transfer problem in a fully developed laminar channel flow with conducting solid walls. Then it is applied to a laminar channel flow with a heated, block-shaped obstacle to show its validity for geometry with sharp edges. Finally the validation for a curvilinear solid body is accomplished with a laminar flow through arrayed cylinders.

  5. A methodology for constraining power in finite element modeling of radiofrequency ablation.

    Science.gov (United States)

    Jiang, Yansheng; Possebon, Ricardo; Mulier, Stefaan; Wang, Chong; Chen, Feng; Feng, Yuanbo; Xia, Qian; Liu, Yewei; Yin, Ting; Oyen, Raymond; Ni, Yicheng

    2017-07-01

    Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power. Copyright © 2016 John Wiley & Sons, Ltd.

  6. Flow and Convective Heat Transfer of Cylinder Misaligned from Aerodynamic Axis of Cyclone Flow

    Directory of Open Access Journals (Sweden)

    I. L. Leukhin

    2008-01-01

    Full Text Available The paper provides and analyzes results of experimental investigations on physical specific features of hydrodynamics and convective heat transfer of a cyclone flow with a group of round cylinders located symmetrically relative to its aerodynamic axis, calculative equations for average and local heat transfer factors at characteristic sections of cylinder surface.

  7. Sumudu transform series expansion method for solving the local fractional Laplace equation in fractal thermal problems

    Directory of Open Access Journals (Sweden)

    Guo Zheng-Hong

    2016-01-01

    Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.

  8. Application of artificial neural network for heat transfer in porous cone

    Science.gov (United States)

    Athani, Abdulgaphur; Ahamad, N. Ameer; Badruddin, Irfan Anjum

    2018-05-01

    Heat transfer in porous medium is one of the classical areas of research that has been active for many decades. The heat transfer in porous medium is generally studied by using numerical methods such as finite element method; finite difference method etc. that solves coupled partial differential equations by converting them into simpler forms. The current work utilizes an alternate method known as artificial neural network that mimics the learning characteristics of neurons. The heat transfer in porous medium fixed in a cone is predicted using backpropagation neural network. The artificial neural network is able to predict this behavior quite accurately.

  9. Conjugate Image Theory Applied on Capacitive Wireless Power Transfer

    Directory of Open Access Journals (Sweden)

    Ben Minnaert

    2017-01-01

    Full Text Available Wireless power transfer using a magnetic field through inductive coupling is steadily entering the market in a broad range of applications. However, for certain applications, capacitive wireless power transfer using electric coupling might be preferable. In order to obtain a maximum power transfer efficiency, an optimal compensation network must be designed at the input and output ports of the capacitive wireless link. In this work, the conjugate image theory is applied to determine this optimal network as a function of the characteristics of the capacitive wireless link, as well for the series as for the parallel topology. The results are compared with the inductive power transfer system. Introduction of a new concept, the coupling function, enables the description of the compensation network of both an inductive and a capacitive system in two elegant equations, valid for the series and the parallel topology. This approach allows better understanding of the fundamentals of the wireless power transfer link, necessary for the design of an efficient system.

  10. Numerical simulation of the thermal behavior of heat transfer equipment operated at low temperature

    International Nuclear Information System (INIS)

    Pearsica, C.; Zamfirache, M.; Bornea, A.; Gherghinescu, S.

    2003-01-01

    The paper presents a method for calculating the non-steady heat transfer in a shell and tube heat exchanger. The characteristic equations were solved with a Finite Element Method. As the geometry is cylindrical and axial symmetry was assumed, the equations were solved in a two dimensional geometry. The interpolation functions are linear and the Galerkin method was applied. The process occurred without phase change. For the solving of the algebraic equations associated with the differential equations, we used the method of steepest descendent (gradient method). As results, we present the temperature profile for the tube and shell gas. (author)

  11. Modeling of the coupled radiative and conductive heat transfer within fibrous media at high temperature

    International Nuclear Information System (INIS)

    Dauvois, Yann

    2016-01-01

    In the present work, the effective heat transfer properties of fibrous medium are determined by taking into account a coupling of heat conduction and radiation. A virtual, statistically homogeneous, two-phase fibrous sample has been built by stacking finite absorbing cylinders in vacuum. These cylinders are dispersed according to prescribed distribution functions defining the cylinder positions and orientations. Cylinder overlappings are allowed. Extinction, absorption and scattering are characterised by radiative statistical functions which allow the Beerian behaviour of a medium to be assessed (or not). They are accurately determined with a Monte Carlo method. Whereas the gaseous phase exhibits a Beerian behaviour, the fibre phase is strongly non Beerian. The radiative power field deposited within the fibrous material is calculated by resolving a model which couples a Generalized Radiative Transfer Equation (GRTE) and a classic Radiative Transfer Equation (RTE). The model of conduction transfer is based on a random walk method without meshing. The simulation of Brownian motion of walkers in fibres allows the energy equation to be solved. The idea of the method is to characterize the temperature in an elementary volume by the density of walkers, which roam the medium. The problem is governed by boundary conditions; A constant concentration of walkers (or a constant flux) is associated with a fixed temperature (or flux). (author) [fr

  12. DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER

    Directory of Open Access Journals (Sweden)

    Chun-Hui He

    2011-01-01

    Full Text Available According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.

  13. Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

    Science.gov (United States)

    Abd Elazem, Nader Y.; Ebaid, Abdelhalim

    2017-12-01

    In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

  14. Moisture transfer in concrete elements under thermal gradients

    International Nuclear Information System (INIS)

    Lien, H.P.; Wittmann, F.H.

    1995-01-01

    A realistic simulation of the coupled heat- and mass transfer in concrete elements requires detailed knowledge of the dominant transfer mechanisms. Depending on the the local temperatures and moisture content, a description in terms of diffusion or Darcy flow respectively is appropriate. However, a simultaneous application of these fundamental physical transfer mechanisms necessary when subjecting concrete elements to wide-ranging temperature distributions. With rising temperatures, continuing hydration also influences the moisture distribution in a increasingly important manner in addition to the transport phenomena. The description of the relevant transport process can be handled by thermodynamic concepts and, in general, the resulting time-space evolution of the state variables in described in terms of coupled nonlinear partial differential equations. A numerical model of the coupled heat-and mass transfer as influenced by continuing hydration with a temperature-dependent reaction rate is presented, and the simulation of the hygral transfer is compared with experimentally determined moisture distributions obtained on a prestressed concrete vessel under thermal gradients. (author). 14 refs., 10 figs

  15. Exciton transfer under dichotomic noise: GME treatment

    International Nuclear Information System (INIS)

    Barvik, I.; Warns, C.; Reineker, P.

    1995-08-01

    The exciton energy transfer between molecules in a dimer is investigated using a model, in which the influence of the phonons is described by a dichotomic stochastic process with colored noise giving rise to modulations of the molecular excitation energies. The solution of equations of motion for the density matrix of the system (obtained algebraically on a computer) is used to determine (also algebraically) the form of the memory functions which enter the Generalized Master Equation. The behaviour of the roots and their weights in the memory function is discussed thoroughly. Connection of the so called coherence time to stochastic parameters is treated analytically. Different limiting cases are investigated. (author). 14 refs, 9 figs

  16. Study of the temperature rise induced by a focusing transducer with a wide aperture angle on biological tissue containing ribs

    International Nuclear Information System (INIS)

    Wang Xin; Lin Jiexing; Liu Xiaozhou; Liu Jiehui; Gong Xiufen

    2016-01-01

    We used the spheroidal beam equation to calculate the sound field created by focusing a transducer with a wide aperture angle to obtain the heat deposition, and then we used the Pennes bioheat equation to calculate the temperature field in biological tissue with ribs and to ascertain the effects of rib parameters on the temperature field. The results show that the location and the gap width between the ribs have a great influence on the axial and radial temperature rise of multilayer biological tissue. With a decreasing gap width, the location of the maximum temperature rise moves forward; as the ribs are closer to the transducer surface, the sound energy that passes through the gap between the ribs at the focus decreases, the maximum temperature rise decreases, and the location of the maximum temperature rise moves forward with the ribs. (paper)

  17. Lesions in Porcine Liver Tissues Created by Continuous High Intensity Ultrasound Exposures in Vitro

    International Nuclear Information System (INIS)

    Zhang Zhe; Chen Tao; Zhang Dong

    2013-01-01

    Lesions in porcine liver tissues created by continuous high intensity focused ultrasound (HIFU) exposures in vitro are theoretically and experimentally investigated, with the transmitter moving along a linear path at a fixed speed. Numerical simulations of the lesion formation are performed based on the Khokhlov—Zabolotskaya—Kuznetov equation and the bio-heat equation. In order to verify the theoretical predictions, experiments are performed in the one-dimensional scanning mode to measure the cross-sectional area of lesions created in the in vitro porcine liver exposed to 1.01-MHz HIFU pulses with the acoustic power of 70 W. The results indicate that, compared to the traditional discrete treatment protocol, the application of a continuous scanning model can create more uniform lesions in tissues and significantly reduces the total treatment time from 47s to 30s

  18. Wireless Power Transfer for Space Applications

    Science.gov (United States)

    Ramos, Gabriel Vazquez; Yuan, Jiann-Shiun

    2011-01-01

    This paper introduces an implementation for magnetic resonance wireless power transfer for space applications. The analysis includes an equivalent impedance study, loop material characterization, source/load resonance coupling technique, and system response behavior due to loads variability. System characterization is accomplished by executing circuit design from analytical equations and simulations using Matlab and SPICE. The theory was validated by a combination of different experiments that includes loop material consideration, resonance coupling circuits considerations, electric loads considerations and a small scale proof-of-concept prototype. Experiment results shows successful wireless power transfer for all the cases studied. The prototype provided about 4.5 W of power to the load at a separation of -5 cm from the source using a power amplifier rated for 7 W.

  19. Mass and heat transfer between evaporation and condensation surfaces: Atomistic simulation and solution of Boltzmann kinetic equation.

    Science.gov (United States)

    Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I

    2018-04-16

    Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.

  20. Relations between transfer matrices and numerical stability analysis to avoid the $\\Omega d$ problem

    OpenAIRE

    Pérez-Álvarez, R.; Pernas-Salomón, R.; Velasco, V. R.

    2015-01-01

    The transfer matrix method is usually employed to study problems described by $N$ equations of matrix Sturm-Liouville (MSL) kind. In some cases a numerical degradation (the so called $\\Omega d$ problem) appears thus impairing the performance of the method. We present here a procedure that can overcome this problem in the case of multilayer systems having piecewise constant coefficients. This is performed by studying the relations between the associated transfer matrix and other transfer matri...

  1. The solution of radiative transfer problems in molecular bands without the LTE assumption by accelerated lambda iteration methods

    Science.gov (United States)

    Kutepov, A. A.; Kunze, D.; Hummer, D. G.; Rybicki, G. B.

    1991-01-01

    An iterative method based on the use of approximate transfer operators, which was designed initially to solve multilevel NLTE line formation problems in stellar atmospheres, is adapted and applied to the solution of the NLTE molecular band radiative transfer in planetary atmospheres. The matrices to be constructed and inverted are much smaller than those used in the traditional Curtis matrix technique, which makes possible the treatment of more realistic problems using relatively small computers. This technique converges much more rapidly than straightforward iteration between the transfer equation and the equations of statistical equilibrium. A test application of this new technique to the solution of NLTE radiative transfer problems for optically thick and thin bands (the 4.3 micron CO2 band in the Venusian atmosphere and the 4.7 and 2.3 micron CO bands in the earth's atmosphere) is described.

  2. Numerical investigation of heat transfer in high-temperature gas-cooled reactors

    Energy Technology Data Exchange (ETDEWEB)

    Chen, g.; Anghaie, S. [Univ. of Florida, Gainesville, FL (United States)

    1995-09-01

    This paper proposes a computational model for analysis of flow and heat transfer in high-temperature gas-cooled reactors. The formulation of the problem is based on using the axisymmetric, thin layer Navier-Stokes equations. A hybrid implicit-explicit method based on finite volume approach is used to numerically solve the governing equations. A fast converging scheme is developed to accelerate the Gauss-Siedel iterative method for problems involving the wall heat flux boundary condition. Several cases are simulated and results of temperature and pressure distribution in the core are presented. Results of a parametric analysis for the assessment of the impact of power density on the convective heat transfer rate and wall temperature are discussed. A comparative analysis is conducted to identify the Nusselt number correlation that best fits the physical conditions of the high-temperature gas-cooled reactors.

  3. Transport Visualization for Studying Mass Transfer and Solute Transport in Permeable Media

    International Nuclear Information System (INIS)

    Roy Haggerty

    2004-01-01

    Understanding and predicting mass transfer coupled with solute transport in permeable media is central to several energy-related programs at the US Department of Energy (e.g., CO 2 sequestration, nuclear waste disposal, hydrocarbon extraction, and groundwater remediation). Mass transfer is the set of processes that control movement of a chemical between mobile (advection-dominated) domains and immobile (diffusion- or sorption-dominated) domains within a permeable medium. Consequences of mass transfer on solute transport are numerous and may include (1) increased sequestration time within geologic formations; (2) reduction in average solute transport velocity by as much as several orders of magnitude; (3) long ''tails'' in concentration histories during removal of a solute from a permeable medium; (4) poor predictions of solute behavior over long time scales; and (5) changes in reaction rates due to mass transfer influences on pore-scale mixing of solutes. Our work produced four principle contributions: (1) the first comprehensive visualization of solute transport and mass transfer in heterogeneous porous media; (2) the beginnings of a theoretical framework that encompasses both macrodispersion and mass transfer within a single set of equations; (3) experimental and analytical tools necessary for understanding mixing and aqueous reaction in heterogeneous, granular porous media; (4) a clear experimental demonstration that reactive transport is often not accurately described by a simple coupling of the convection-dispersion equation with chemical reaction equations. The work shows that solute transport in heterogeneous media can be divided into 3 regimes--macrodispersion, advective mass transfer, and diffusive mass transfer--and that these regimes can be predicted quantitatively in binary media. We successfully predicted mass transfer in each of these regimes and verified the prediction by completing quantitative visualization experiments in each of the regimes, the

  4. Description of deeply inelastic collisions in terms of a transport equation

    International Nuclear Information System (INIS)

    Weidenmueller, H.A.

    1977-01-01

    A transport equation for deeply inelastic collisions is derived from a random-matrix model for the form factors for inelastic scattering and transfer reactions. The parametrization of these form factors is discussed. Results in one dimension indicate the importance of quantum fluctuations, and limitations of other approaches to the same problem. Results of three dimensions are compared with the data

  5. Transfer parameters for routine release of HTO. Consideration of OBT

    International Nuclear Information System (INIS)

    Galeriu, D.; Paunescu, N.; Cotarlea

    1997-01-01

    Knowledge of the transfer parameters for tritium is a key requirement to assess the public dose or to establish Derived Release Limit (DRL) proper for a heavy water reactor. This report revised the transfer parameters used to assess tritium doses via the ingestion pathway. First, the procedure used in Canadian standard CSA-N288.1 to assess the DRL for tritium is revisited, clearing up some misunderstandings about the derivation of transfer parameters from air to forage and animal products. Secondly, we derive the transfer parameters applying conditions of full equilibrium to dynamic equations that describe the transfer of tritiated water in food. The new transfer parameters for tritiated water in food are more plant- and site-specific then the generic transfer parameters. The most important improvement is the introduction of organically bound tritium (OBT) production in plants or animal products. Bulk transfer parameters are introduced, which include OBT as well as HTO. Based on a standard Canadian diet, the dose increase considering OBT is almost 50 %. Recent experimental data obtained under equilibrium condition are discussed, and the revised transfer parameters for assessment purposes is demonstrated. (authors)

  6. Transfer parameters for routine release of HTO - consideration of OBT

    International Nuclear Information System (INIS)

    Galeriu, D.

    1994-06-01

    Knowledge of the transfer parameters for tritium is a key requirement to assess the public dose or to establish Derived Release Limits (DRL) appropriate for a heavy-water reactor. This report revises the transfer parameters used to assess tritium doses via the ingestion pathway. First, the procedure used in Canadian standard CSA-N288.1 to assess the DRL for tritium is revised, clearing up some misunderstandings about the derivation of transfer parameters for air to forage and animal products. Second, we rederive the transfer parameters, applying conditions of full equilibrium to dynamic equations that describe the transfer of tritiated water in food. The new transfer parameters for tritiated water in food are more plant- and site-specific than the generic transfer parameters. The most important improvement is the introduction of organically bound tritium (OBT) production in plants or animal products. Bulk transfer parameters are introduced, which include OBT as well as HTO. Based on a standard Canadian diet, the dose increase considering OBT is almost 50%. Recent experimental data obtained under equilibrium conditions are discussed, and the appropriateness of the revised transfer parameters for assessment purposes is demonstrated. (author). 26 refs., 7 tabs

  7. Dynamic modeling of fixed-bed adsorption of flue gas using a variable mass transfer model

    International Nuclear Information System (INIS)

    Park, Jehun; Lee, Jae W.

    2016-01-01

    This study introduces a dynamic mass transfer model for the fixed-bed adsorption of a flue gas. The derivation of the variable mass transfer coefficient is based on pore diffusion theory and it is a function of effective porosity, temperature, and pressure as well as the adsorbate composition. Adsorption experiments were done at four different pressures (1.8, 5, 10 and 20 bars) and three different temperatures (30, 50 and 70 .deg. C) with zeolite 13X as the adsorbent. To explain the equilibrium adsorption capacity, the Langmuir-Freundlich isotherm model was adopted, and the parameters of the isotherm equation were fitted to the experimental data for a wide range of pressures and temperatures. Then, dynamic simulations were performed using the system equations for material and energy balance with the equilibrium adsorption isotherm data. The optimal mass transfer and heat transfer coefficients were determined after iterative calculations. As a result, the dynamic variable mass transfer model can estimate the adsorption rate for a wide range of concentrations and precisely simulate the fixed-bed adsorption process of a flue gas mixture of carbon dioxide and nitrogen.

  8. To the generalization of experimental data on heat and mass transfer in evaporation and condensation

    International Nuclear Information System (INIS)

    Berman, L.D.

    1980-01-01

    Similarity equations for heat-and-mass transfer in binary gas or steam-gas layers in the processes of liquid evaporation, condensation and desublimation of vapours, desorption and absorption and porous body cooling are considered. It is accepted that steam-gas components obey to the equation of ideal gas state and that evaporation and condensation condititons permit to neglect the influence of compressability of gas (steam-gas) mixture, non-isothermality of boundary layer and interphase kinetic resistance to mass transfer onto the interfaces. It is concluded that the results of considered experimental and theoretical investigations of the above processes are in a satisfactory agreement and show insignificance of the effect of hydrodynamic conditions determining the regime of main steam-gas mixture flow on relative heat-and-mass transfer coefficients. According to the theoretical calculation results with increase of the factor of M steam-gas mixture non-uniformity mass transfer intensity in evaporation decreases, while in condensation it grows, but M effect on the mass transfer coefficient is rather small and sowhat increases in the case of a turbulent boundary layer evaporation. In condensation it is less than in evaporation

  9. Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method

    DEFF Research Database (Denmark)

    Zhang, Xuping; Sørensen, Rasmus; RahbekIversen, Mathias

    2018-01-01

    , and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size...... manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies....

  10. Lie group analysis of flow and heat transfer of non-Newtonian ...

    Indian Academy of Sciences (India)

    2017-01-09

    Jan 9, 2017 ... of its industrial and engineering applications. In view of all these ... fluids). Applying nanotechnology to heat transfer, the new concept of ..... The set of nonlinear ordinary differential equations of. (28) and (32) subject to the ...

  11. On an integral equation arising in the transport of radiation through a slab involving internal reflection

    International Nuclear Information System (INIS)

    Williams, M.M.R.

    2005-01-01

    The integral equation derived by Nieuwenhuizen and Luck for transmission of radiation through an optically thick diffusive medium is reconsidered in the light of radiative transfer theory and extended to slabs of arbitrary thickness. (author)

  12. A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

    Science.gov (United States)

    Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

    2016-10-01

    Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

  13. Analysis of thermal effects in endoscopic nanocarriers-based photodynamic therapy applied to esophageal diseases

    Science.gov (United States)

    Salas-García, I.; Fanjul-Vélez, F.; Ortega-Quijano, N.; Wilfert, O.; Hudcova, L.; Poliak, J.; Barcik, P.; Arce-Diego, J. L.

    2014-02-01

    In this work we propose a predictive model that allows the study of thermal effects produced when the optical radiation interacts with an esophageal or stomach disease with gold nanoparticles embedded. The model takes into account light distribution in the tumor tissue by means of a Monte Carlo method. Mie theory is used to obtain the gold nanoparticles optical properties and the thermal model employed is based on the bio-heat equation. The complete model was applied to two types of tumoral tissue (squamous cell carcinoma located in the esophagus and adenocarcinoma in the stomach) in order to study the thermal effects induced by the inclusion of gold nanoparticles.

  14. Heat Transfer to a Thin Solid Combustible in Flame Spreading at Microgravity

    Science.gov (United States)

    Bhattacharjee, S.; Altenkirch, R. A.; Olson, S. L.; Sotos, R. G.

    1991-01-01

    The heat transfer rate to a thin solid combustible from an attached diffusion flame, spreading across the surface of the combustible in a quiescent, microgravity environment, was determined from measurements made in the drop tower facility at NASA-Lewis Research Center. With first-order Arrhenius pyrolysis kinetics, the solid-phase mass and energy equations along with the measured spread rate and surface temperature profiles were used to calculate the net heat flux to the surface. Results of the measurements are compared to the numerical solution of the complete set of coupled differential equations that describes the temperature, species, and velocity fields in the gas and solid phases. The theory and experiment agree on the major qualitative features of the heat transfer. Some fundamental differences are attributed to the neglect of radiation in the theoretical model.

  15. Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

    Science.gov (United States)

    Sutjahjo, Edhi; Chamis, Christos C.

    1993-01-01

    Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

  16. Introduction to computational mass transfer with applications to chemical engineering

    CERN Document Server

    Yu, Kuo-Tsung

    2017-01-01

    This book offers an easy-to-understand introduction to the computational mass transfer (CMT) method. On the basis of the contents of the first edition, this new edition is characterized by the following additional materials. It describes the successful application of this method to the simulation of the mass transfer process in a fluidized bed, as well as recent investigations and computing methods for predictions for the multi-component mass transfer process. It also demonstrates the general issues concerning computational methods for simulating the mass transfer of the rising bubble process. This new edition has been reorganized by moving the preparatory materials for Computational Fluid Dynamics (CFD) and Computational Heat Transfer into appendices, additions of new chapters, and including three new appendices on, respectively, generalized representation of the two-equation model for the CMT, derivation of the equilibrium distribution function in the lattice-Boltzmann method, and derivation of the Navier-S...

  17. An anisotropic diffusion approximation to thermal radiative transfer

    International Nuclear Information System (INIS)

    Johnson, Seth R.; Larsen, Edward W.

    2011-01-01

    This paper describes an anisotropic diffusion (AD) method that uses transport-calculated AD coefficients to efficiently and accurately solve the thermal radiative transfer (TRT) equations. By assuming weak gradients and angular moments in the radiation intensity, we derive an expression for the radiation energy density that depends on a non-local function of the opacity. This nonlocal function is the solution of a transport equation that can be solved with a single steady-state transport sweep once per time step, and the function's second angular moment is the anisotropic diffusion tensor. To demonstrate the AD method's efficacy, we model radiation flow down a channel in 'flatland' geometry. (author)

  18. Dynamical interaction of He atoms with metal surfaces: Charge transfer processes

    International Nuclear Information System (INIS)

    Flores, F.; Garcia Vidal, F.J.; Monreal, R.

    1993-01-01

    A self-consistent Kohn-Sham LCAO method is presented to calculate the charge transfer processes between a He * -atom and metal surfaces. Intra-atomic correlation effects are taken into account by considering independently each single He-orbital and by combining the different charge transfer processes into a set of dynamical rate equations for the different ion charge fractions. Our discussion reproduces qualitatively the experimental evidence and gives strong support to the method presented here. (author). 24 refs, 4 figs

  19. Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet

    International Nuclear Information System (INIS)

    Bachok, Norfifah; Ishak, Anuar; Pop, Ioan

    2010-01-01

    An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching/shrinking sheet. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, before being solved numerically using the Runge-Kutta-Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, stretching/shrinking parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.

  20. Iterative discrete ordinates solution of the equation for surface-reflected radiance

    Science.gov (United States)

    Radkevich, Alexander

    2017-11-01

    This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

  1. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  2. Investigation of thermo-fluid behavior of mixed convection heat transfer of different dimples-protrusions wall patterns to heat transfer enhancement

    Science.gov (United States)

    Sobhani, M.; Behzadmehr, A.

    2018-05-01

    This study is a numerical investigation of the effect of improving heat transfer namely, modified rough (dimples and protrusions) surfaces on the mixed convective heat transfer of a turbulent flow in a horizontal tube. The effects of different dimples-protrusions arrangements on the improving the thermal performance of a rough tube are investigated at various Richardson numbers. Three dimensional governing equations are discretized by the finite-volume technique. Based on the obtained results the dimples-protrusions arrangements are modified to find a suitable configuration for which heat transfer coefficient and pressure drop to be balanced. Modified dimples-protrusions arrangements that shows higher performance is presented. Its average thermal performance 18% and 11% is higher than the other arrangements. In addition, the results show that roughening a smooth tube is more effective at the higher Richardson number.

  3. On the economical solution method for a system of linear algebraic equations

    Directory of Open Access Journals (Sweden)

    Jan Awrejcewicz

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  4. Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents.

    Science.gov (United States)

    Urtenov, Mahamet A-Kh; Kirillova, Evgeniya V; Seidova, Natalia M; Nikonenko, Victor V

    2007-12-27

    This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current

  5. Carbon dioxide stripping in aquaculture -- part II: development of gas transfer models

    Science.gov (United States)

    Colt, John; Watten, Barnaby; Pfeiffer, Tim

    2012-01-01

    The basic mass transfer equation for gases such as oxygen and carbon dioxide can be derived from integration of the driving force equation. Because of the physical characteristics of the gas transfer processes, slightly different models are used for aerators tested under the non steady-state procedures, than for packed columns, or weirs. It is suggested that the standard condition for carbon dioxide should be 20 °C, 1 atm, CCO2=20 mg/kg, and XCO2=0.000285. The selection of the standard condition for carbon dioxide based on a fixed mole fraction ensures that standardized carbon dioxide transfer rates will be comparable even though the value of C*CO2 in the atmosphere is increasing with time. The computation of mass transfer for carbon dioxide is complicated by the impact of water depth and gas phase enrichment on the saturation concentration within the unit, although the importance of either factor depends strongly on the specific type of aerator. For some types of aerators, the most accurate gas phase model remains to be determined for carbon dioxide. The assumption that carbon dioxide can be treated as a non-reactive gas in packed columns may apply for cold acidic waters but not for warm alkaline waters.

  6. Hydromagnetic Falkner-Skan flow of Casson fluid past a moving wedge with heat transfer

    Directory of Open Access Journals (Sweden)

    Imran Ullah

    2016-09-01

    Full Text Available Numerical solutions are carried out for steady state two dimensional electrically conducting mixed convection flow of Casson fluid along non-isothermal moving wedge through porous medium in the presence of viscous dissipation and heat generation/absorption. The governing partial differential equations, subject to boundary conditions are transformed into ordinary differential equations using similarity transformations. The transformed equations are then solved numerically by Keller-box method. To check the validity of present method, numerical results for dimensionless local skin friction coefficient and rate of heat transfer are compared with results of available literature as special cases and revealed in good agreement. The influence of pertinent parameters on velocity, temperature profiles, as well as wall shear stress and heat transfer rate is displayed in graphical form and discussed. It is found that fluid velocity increases with increase of Eckert number in case of assisting flow, while it decreases in case of opposing flow. It is also noticed that heat generation/absorption parameter influence fluid velocity and temperature significantly. A significant result obtained from this study is that heat transfer rate reduces with increase of Prandtl number in the presence of viscous dissipation effect. Also, increasing values of Eckert number have no effects on force convection flow.

  7. Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux

    Directory of Open Access Journals (Sweden)

    I-Chung Liu

    2012-01-01

    Full Text Available We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM. The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.

  8. Mass transfer inside oblate spheroidal solids: modelling and simulation

    Directory of Open Access Journals (Sweden)

    J. E. F. Carmo

    2008-03-01

    Full Text Available A numerical solution of the unsteady diffusion equation describing mass transfer inside oblate spheroids, considering a constant diffusion coefficient and the convective boundary condition, is presented. The diffusion equation written in the oblate spheroidal coordinate system was used for a two-dimensional case. The finite-volume method was employed to discretize the basic equation. The linear equation set was solved iteratively using the Gauss-Seidel method. As applications, the effects of the Fourier number, the Biot number and the aspect ratio of the body on the drying rate and moisture content during the process are presented. To validate the methodology, results obtained in this work are compared with analytical results of the moisture content encountered in the literature and good agreement was obtained. The results show that the model is consistent and it may be used to solve cases such as those that include disks and spheres and/or those with variable properties with small modifications.

  9. Simulation of heat and mass transfer in boiling water with the Melodif code

    International Nuclear Information System (INIS)

    Freydier, P.; Chen, O.; Olive, J.; Simonin, O.

    1991-04-01

    The Melodif code is developed at Electricite de France, Research and Development Division. It is an eulerian two dimensional code for the simulation of turbulent two phase flows (a three dimensional code derived from Melodif, ASTRID, is currently being prepared). Melodif is based on the two fluid model, solving the equations of conservation for mass, momentum and energy, for both phases. In such a two fluid model, the description of interfacial transfers between phases is a crucial issue. The model used applies to a dominant continuous phase, and a dispersed phase. A good description of interfacial momentum transfer exists in the standard MELODIF code: the drag force, the apparent mass force... are taken into account. An important factor for interfacial transfers is the interfacial area per volume unit. With the assumption of spherical gas bubbles, an equation has been written for this variable. In the present wok, a model has been tested for interfacial heat and mass transfer in the case of boiling water: it is assumed that mass transfer is controlled by heat transfer through the latent massic energy taken in the phase that vaporizes (or condenses). This heat and mass transfer model has been tested in various configurations: - a cylinder with water flowing inside, is being heated. Boiling takes place near the wall, while bubbles migrating to the core of the flow recondense. This roughly simulates a sub-cooled boiling phenomenon. - a box containing liquid water is depressurized. Boiling takes place in the whole volume of the fluid. The Melodif code can simulate this configuration due to the implicitation of the relation between interphase mass transfer and the pressure variable

  10. Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation

    International Nuclear Information System (INIS)

    Jirkovsky, L.; Muriel, A.

    2012-01-01

    We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  11. Effective dark energy equation of state in interacting dark energy models

    International Nuclear Information System (INIS)

    Avelino, P.P.; Silva, H.M.R. da

    2012-01-01

    In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

  12. Effective dark energy equation of state in interacting dark energy models

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, P.P., E-mail: ppavelin@fc.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Silva, H.M.R. da, E-mail: hilberto.silva@gmail.com [Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)

    2012-07-24

    In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

  13. Radiative Transfer Equation for Anisotropic Spherical Medium with Specular Reflective Index

    International Nuclear Information System (INIS)

    Elghazaly, A.

    2009-01-01

    Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with diffuse and angular dependent (specular) reflecting boundaries is solved using the Pomraning-Eddington approximation method. The angular dependent specular reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0, and 10 mfp and for different scattering albedo. Two different weight functions are used to verify the boundary conditions. Our results are compared with the available data and give an excellent agreement for thick and highly scattering media

  14. An efficient method to calculate excitation energy transfer in light-harvesting systems: application to the Fenna-Matthews-Olson complex

    International Nuclear Information System (INIS)

    Ritschel, Gerhard; Roden, Jan; Eisfeld, Alexander; Strunz, Walter T

    2011-01-01

    A master equation derived from non-Markovian quantum state diffusion is used to calculate the excitation energy transfer in the photosynthetic Fenna-Matthews-Olson pigment-protein complex at various temperatures. This approach allows us to treat spectral densities that explicitly contain the coupling to internal vibrational modes of the chromophores. Moreover, the method is very efficient and as a result the transfer dynamics can be calculated within about 1 min on a standard PC, making systematic investigations w.r.t. parameter variations tractable. After demonstrating that our approach is able to reproduce the results of the numerically exact hierarchical equations of motion approach, we show how the inclusion of vibrational modes influences the transfer. (paper)

  15. Heat transfer modelling of two-phase bubbles swarm condensing in three - phase direct - contact condenser

    Directory of Open Access Journals (Sweden)

    Mahood Hameed B.

    2016-01-01

    Full Text Available An analytical model for the convective heat transfer coefficient and the two-phase bubble size of a three-phase direct contact heat exchanger was developed. Until the present, there has only been a theoretical model available that deals with a single two-phase bubble and a bubble train condensation in an immiscible liquid. However, to understand the actual heat transfer process within the three-phase direct contact condenser, characteristic models are required. A quasi - steady energy equation in a spherical coordinate system with a potential flow assumption and a cell model configuration has been simplified and solved analytically. The convective heat transfer in terms of Nu number has been derived, and it was found to be a function to Pe number and a system void fraction. In addition, the two-phase bubble size relates to the system void fraction and has been developed by solving a simple energy balance equation and using the derived convective heat transfer coefficient expression. Furthermore, the model correlates well with previous experimental data and theoretical results.

  16. Mixed convective heat transfer from a vertical plate embedded

    Indian Academy of Sciences (India)

    Abstract. The effect of melting and solute dispersion on heat and mass transfer in non-Darcy fluid flow over a vertical surface has been studied numerically in the present article. The flow is assumed to be laminar and steady state. Using similarity transformations, the governing boundary layer equations are transformed into ...

  17. Monte Carlo method for polarized radiative transfer in gradient-index media

    International Nuclear Information System (INIS)

    Zhao, J.M.; Tan, J.Y.; Liu, L.H.

    2015-01-01

    Light transfer in gradient-index media generally follows curved ray trajectories, which will cause light beam to converge or diverge during transfer and induce the rotation of polarization ellipse even when the medium is transparent. Furthermore, the combined process of scattering and transfer along curved ray path makes the problem more complex. In this paper, a Monte Carlo method is presented to simulate polarized radiative transfer in gradient-index media that only support planar ray trajectories. The ray equation is solved to the second order to address the effect induced by curved ray trajectories. Three types of test cases are presented to verify the performance of the method, which include transparent medium, Mie scattering medium with assumed gradient index distribution, and Rayleigh scattering with realistic atmosphere refractive index profile. It is demonstrated that the atmospheric refraction has significant effect for long distance polarized light transfer. - Highlights: • A Monte Carlo method for polarized radiative transfer in gradient index media. • Effect of curved ray paths on polarized radiative transfer is considered. • Importance of atmospheric refraction for polarized light transfer is demonstrated

  18. The determination of an unknown source for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer

    2014-09-01

    In this paper, we are interested in the estimation of the source term for a space fractional advection dispersion equation using concentration and flux measurements at final time. An example of application is the identification of contamination source in groundwater transport. We propose to use the socalled modulating functions method which has been introduced for parameters estimation. This method allows to transfer the estimation problem into solving a system of algebraic equations. Numerical examples are given to illustrate the effectiveness and the robustness of the proposed method. Finally, a comparison between a Tikhonov-based optimization method and the modulating functions approach is presented.

  19. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  20. Computational simulation of heat transfer in laser melted material flow

    International Nuclear Information System (INIS)

    Shankar, V.; Gnanamuthu, D.

    1986-01-01

    A computational procedure has been developed to study the heat transfer process in laser-melted material flow associated with surface heat treatment of metallic alloys to improve wear-and-tear and corrosion resistance. The time-dependent incompressible Navier-Stokes equations are solved, accounting for both convective and conductive heat transfer processes. The convection, induced by surface tension and high surface temperature gradients, sets up a counterrotating vortex flow within the molten pool. This recirculating material flow is responsible for determining the molten pool shape and the associated cooling rates which affect the solidifying material composition. The numerical method involves an implicit triple-approximate factorization scheme for the energy equation, and an explicit treatment for the momentum and the continuity equations. An experimental setup, using a continuous wave CO 2 laser beam as a heat source, has been carried out to generate data for validation of the computational model. Results in terms of the depth, width, and shape of the molten pool and the heat-affected zone for various power settings and shapes of the laser, and for various travel speeds of the workpiece, compare very well with experimental data. The presence of the surface tension-induced vortex flow is demonstrated

  1. Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

    International Nuclear Information System (INIS)

    Das, R.N.

    1980-01-01

    The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

  2. Concurrent hyperthermia estimation schemes based on extended Kalman filtering and reduced-order modelling.

    Science.gov (United States)

    Potocki, J K; Tharp, H S

    1993-01-01

    The success of treating cancerous tissue with heat depends on the temperature elevation, the amount of tissue elevated to that temperature, and the length of time that the tissue temperature is elevated. In clinical situations the temperature of most of the treated tissue volume is unknown, because only a small number of temperature sensors can be inserted into the tissue. A state space model based on a finite difference approximation of the bioheat transfer equation (BHTE) is developed for identification purposes. A full-order extended Kalman filter (EKF) is designed to estimate both the unknown blood perfusion parameters and the temperature at unmeasured locations. Two reduced-order estimators are designed as computationally less intensive alternatives to the full-order EKF. Simulation results show that the success of the estimation scheme depends strongly on the number and location of the temperature sensors. Superior results occur when a temperature sensor exists in each unknown blood perfusion zone, and the number of sensors is at least as large as the number of unknown perfusion zones. Unacceptable results occur when there are more unknown perfusion parameters than temperature sensors, or when the sensors are placed in locations that do not sample the unknown perfusion information.

  3. Transfer-matrix approach for modulated structures with defects

    International Nuclear Information System (INIS)

    Kostyrko, T.

    2000-01-01

    We consider scattering of electrons by defects in a periodically modulated, quasi-one-dimensional structure, within a tight-binding model. Combining a transfer matrix method and a Green function method we derive a formula for a Landauer conductance and show its equivalence to the result of Kubo linear response theory. We obtain explicitly unperturbed lattice Green functions from their equations of motion, using the transfer matrices. We apply the presented formalism in computations of the conductance of several multiband modulated structures with defects: (a) carbon nanotubes (b) two-dimensional (2D) superlattice (c) modulated leads with 1D wire in the tunneling regime. (c) 2000 The American Physical Society

  4. Exergy costs analysis of groundwater use and water transfers

    International Nuclear Information System (INIS)

    Carrasquer, Beatriz; Uche, Javier; Martínez-Gracia, Amaya

    2016-01-01

    Highlights: • A methodology to estimate the unit exergy cost of water supply alternatives is provided. • Two alternatives (water transfers and groundwaters) are defined. • The unit exergy costs are given as a function of design and operating parameters. • Unit exergy cost of groundwaters go from 1.01 to 2.67 and from 1 to 4.06 in water transfers. • Unit exergy costs are calculated and contrasted for the medium course of the Ebro. - Abstract: In the search for new alternatives to meet the water demands, it is interesting to analyze the cost of using alternatives different from those such as desalination and pumping. The exergy cost analysis can be a useful tool to estimate costs of those alternatives as a function of its energy efficiency and its relative abundance with respect to existing resources in their surroundings. This study proposes a methodology for assessing the costs of groundwaters and water transfers from surplus basins within the exergy perspective. An equation to assess the exergy costs of these alternatives is proposed. System boundaries are first identified to the assessment of input and output currents to the system in exergy values for the design and certain operating conditions. Next, an equation to assess water supply costs depending on design and operational parameters is proposed, from the analysis of different examples. Pumping efficiency, altitude gap and flow among other features are introduced in the calculations as those characteristics parameters. In the developed examples, unit exergy costs of groundwaters go from 1.01 to 2.67, and from 1 to 4.06 in case of water transfers. Maximum values, as expected within this perspective, are found at high pumped/transferred flows and high pumping levels and/or low pumping efficiency if pumping is required.

  5. ANALYSIS, OPTIMAL CONTROL, AND SIMULATION OF CONDUCTIVE-RADIATIVE HEAT TRANSFER

    Directory of Open Access Journals (Sweden)

    Peter Philip

    2011-01-01

    Full Text Available This article surveys recent results regarding the existence of weaksolutions to quasilinear partial differential equations(PDEcouplednonlocally by the integral operator of the radiosity equation, modeling conductive-radiative heat transfer. Both the stationary and the transient case are considered. For the stationary case, an optimal control problem with control constraints is presented withfirst-order necessary optimality conditions, where recent results on the solution theory of the linearized state equation allow to close a previous gap.Afinite volume scheme for the discretization of the stationary system is described and, based on this scheme, a numerical computation of the temperaturefield(solution of the state equationis shown as well as the numerical solution to a realistic control problem in the context of industrial applications in crystal growth.

  6. Free convection heat and mass transfer in a power law fluid past an inclined surface with thermophoresis

    Directory of Open Access Journals (Sweden)

    Medhat M. Helal

    2013-10-01

    Full Text Available The problem of heat and mass transfer in a power law, two-dimensional, laminar, boundary layer flow of a viscous incompressible fluid over an inclined plate with heat generation and thermophoresis is investigated by the characteristic function method. The governing non-linear partial differential equations describing the flow and heat transfer problem are transformed into a set of coupled non-linear ordinary differential equation which was solved using Runge–Kutta shooting method. Exact solutions for the dimensionless temperature and concentration profiles, are presented graphically for different physical parameters and for the different power law exponents 0  0.5.

  7. Frumkin–Butler–Volmer Theory and Mass Transfer in Electrochemical Cells1

    NARCIS (Netherlands)

    Van Soestbergen, M.

    2012-01-01

    An accurate mathematical description of the charge transfer rate at electrodes due to an electrochemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin-Butler–Volmer (gFBV) equation to describe electrochemical reactions, an

  8. Nucleate boiling heat transfer

    Energy Technology Data Exchange (ETDEWEB)

    Saiz Jabardo, J.M. [Universidade da Coruna (Spain). Escola Politecnica Superior], e-mail: mjabardo@cdf.udc.es

    2009-07-01

    Nucleate boiling heat transfer has been intensely studied during the last 70 years. However boiling remains a science to be understood and equated. In other words, using the definition given by Boulding, it is an 'insecure science'. It would be pretentious of the part of the author to explore all the nuances that the title of the paper suggests in a single conference paper. Instead the paper will focus on one interesting aspect such as the effect of the surface microstructure on nucleate boiling heat transfer. A summary of a chronological literature survey is done followed by an analysis of the results of an experimental investigation of boiling on tubes of different materials and surface roughness. The effect of the surface roughness is performed through data from the boiling of refrigerants R-134a and R-123, medium and low pressure refrigerants, respectively. In order to investigate the extent to which the surface roughness affects boiling heat transfer, very rough surfaces (4.6 {mu}m and 10.5 {mu}m ) have been tested. Though most of the data confirm previous literature trends, the very rough surfaces present a peculiar behaviour with respect to that of the smoother surfaces (Ra<3.0 {mu}m). (author)

  9. Nucleate boiling heat transfer

    International Nuclear Information System (INIS)

    Saiz Jabardo, J.M.

    2009-01-01

    Nucleate boiling heat transfer has been intensely studied during the last 70 years. However boiling remains a science to be understood and equated. In other words, using the definition given by Boulding, it is an 'insecure science'. It would be pretentious of the part of the author to explore all the nuances that the title of the paper suggests in a single conference paper. Instead the paper will focus on one interesting aspect such as the effect of the surface microstructure on nucleate boiling heat transfer. A summary of a chronological literature survey is done followed by an analysis of the results of an experimental investigation of boiling on tubes of different materials and surface roughness. The effect of the surface roughness is performed through data from the boiling of refrigerants R-134a and R-123, medium and low pressure refrigerants, respectively. In order to investigate the extent to which the surface roughness affects boiling heat transfer, very rough surfaces (4.6 μm and 10.5 μm ) have been tested. Though most of the data confirm previous literature trends, the very rough surfaces present a peculiar behaviour with respect to that of the smoother surfaces (Ra<3.0 μm). (author)

  10. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  11. A difference quotient-numerical integration method for solving radiative transfer problems

    International Nuclear Information System (INIS)

    Ding Peizhu

    1992-01-01

    A difference quotient-numerical integration method is adopted to solve radiative transfer problems in an anisotropic scattering slab medium. By using the method, the radiative transfer problem is separated into a system of linear algebraic equations and the coefficient matrix of the system is a band matrix, so the method is very simple to evaluate on computer and to deduce formulae and easy to master for experimentalists. An example is evaluated and it is shown that the method is precise

  12. Fuel-element temperature nonstationary distribution caused by local pulsations of the factor of heat transfer to a coolant

    International Nuclear Information System (INIS)

    Pupko, V.Ya.

    1978-01-01

    The equation of nonstationary heat transfer caused by the appearance of a local pulse jump in the factor of heat transfer to a coolant is solved analytically for a cylindrical fuel element. The problem solution is generalized to a case of the periodically pulsating factor of heat transfer according to its value in an arbitrary point of the fuel element surface

  13. Heat and mass transfer in porous cavity: Assisting flow

    Energy Technology Data Exchange (ETDEWEB)

    Badruddin, Irfan Anjum [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia); Quadir, G. A. [School of Mechatronic Engineering, University Malaysia Perlis, Pauh Putra, 02600 Arau, Perlis (Malaysia)

    2016-06-08

    In this paper, investigation of heat and mass transfer in a porous cavity is carried out. The governing partial differential equations are non-dimensionalised and solved using finite element method. The left vertical surface of the cavity is maintained at constant temperature and concentration which are higher than the ambient temperature and concentration applied at right vertical surface. The top and bottom walls of the cavity are adiabatic. Heat transfer is assumed to take place by natural convection and radiation. The investigation is carried out for assisting flow when buoyancy and gravity force act in same direction.

  14. Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

    Science.gov (United States)

    Liou, Tong-Miin; Wang, Chun-Sheng

    2018-01-01

    Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

  15. Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

    Science.gov (United States)

    Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

    2018-05-01

    Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

  16. A study of heat and mass transfer on magnetohydrodynamic (MHD flow of nanoparticles

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2018-03-01

    Full Text Available Investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate is presented using Buongiorno's model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticles volume fraction are passively controlled on the boundary rather than actively. The partial differential equations governing the flow are reduced to a system of nonlinear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters is provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. The passive control model can be used to control the boundary layer thickness as well as the rate of mass transfer at the wall. Keywords: Nanofluid, Brownian motion, Thermophoresis, Nusselt number, Sherwood number

  17. Two-dimensional numerical modeling and solution of convection heat transfer in turbulent He II

    Science.gov (United States)

    Zhang, Burt X.; Karr, Gerald R.

    1991-01-01

    Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.

  18. Flow and heat transfer of MHD graphene oxide-water nanofluid between two non-parallel walls

    Directory of Open Access Journals (Sweden)

    Azimi Mohammadreza

    2017-01-01

    Full Text Available The steady 2-D heat transfer and flow between two non-parallel walls of a graphene oxide nanofluid in presence of uniform magnetic field are investigated in this paper. The analytical solution of the non-linear problem is obtained by Galerkin optimal homotopy asymptotic method. At first a similarity transformation is used to reduce the partial differential equations modeling the flow and heat transfer to ordinary non-linear differential equation systems containing the semi angle between the plate’s parameter, Reynolds number, the magnetic field strength, nanoparticle volume fraction, Eckert and Prandtl numbers. Finally, the obtained analytical results have been compared with results achieved from previous works in some cases.

  19. Photo-induced charge transfer at heterogeneous interfaces: Dye-sensitized tin disulfide, the theory and the experiment

    International Nuclear Information System (INIS)

    Lanzafame, J.M.

    1993-01-01

    The study of photo-induced charge transfer is an endeavor that spans the entire industrial period of man's history. Its great importance demands an ever greater understanding of its underlying principles. The work discussed here attempts to probe elementary aspects of the charge transfer process. Investigations into the theory of charge transfer reactions are made in an attempt to isolate the relevant parameters. An analytical discussion is made of a simple Golden Rule type rate equation to describe the transfer kinetics. Then a quantum simulation is carried out to follow the wavefunction propagation as a test of the applicability of the assumptions made in deriving the simpler rate equation. Investigation of charge transfer at surfaces is bet served by the application of ultrafast optical spectroscopies to probe carrier dynamics. A discussion of the properties of the short pulse laser systems employed is included along with a discussion of the different optical spectroscopies available. These tools are then brought to bear upon dye-sensitized SnS 2 , a model system for the study of charge injection processes. The unique properties of the semiconductor are discussed with respect to the charge transfer process. The unique properties of the semiconductor are discussed with respect to the charge transfer process. The optical experiments performed on the dye/SnS 2 systems elucidate the fundamental carrier dynamics and these dynamics are discussed within the theoretical framework to provide a complete picture of the charge transfer kinetics

  20. A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.

    2012-01-01

    Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.