Integrability Estimates for Gaussian Rough Differential Equations
Cass, Thomas; Lyons, Terry
2011-01-01
We derive explicit tail-estimates for the Jacobian of the solution flow of stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H>1/4. We remark on the relevance of such estimates to a number of significant open problems.
Rough differential equations with unbounded drift term
Riedel, S.; Scheutzow, M.
2017-01-01
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly. Furthermore, we show that the semiflow exists assuming only appropriate one-sided growth conditions. We provide bounds for both the flow and the semiflow. Applied to stochastic analysis, our results imply strong completeness and the existence of a stochastic (semi)flow for a large class of stochastic differential equations. If the driving process is Gaussian, we can further deduce (essentially) sharp tail estimates for the (semi)flow and a Freidlin-Wentzell-type large deviation result.
Differential Equations driven by \\Pi-rough paths
Gyurkó, Lajos Gergely
2012-01-01
This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric \\Pi-rough paths in our terminology) sketched by Lyons ("Differential equations driven by rough signals", Revista Mathematica Iber. Vol 14, Nr. 2,215-310, 1998). Although geometric \\Pi-rough paths can be treated as p-rough paths for a sufficiently large p and the theory of integration of Lip-\\gamma one-forms (\\gamma>p-1) along geometric p-rough paths applies, we prove the existence of integrals of one-forms under weaker conditions. Moreover, we consider differential equations driven by geometric \\Pi-rough paths and give sufficient conditions for existence and uniqueness of solution.
Dependence of Convective Heat Flux Calculations on Roughness Lengths
Schieldge, John P.
1995-01-01
The zero plane displacement height (d) and aerodynamic roughness length (z0) can be determined separately for momentum, heat, and humidity by using a procedure based on the Levenberg-Marquardt method for solving non-linear equations. This procedure is used to analyze profile data previously collected by Lo (1977) in a forested area in Canada and by Morgan et al (1971) on a field at the University of California at Davis (UCD) in the United States. The UCD data base is used to show the effects of allowing for different roughness lengths (zom,z0h,z0q) in calculating sensible and latent heat flux densities from bulk transfer coefficients.
Rough solutions of Einstein vacuum equations in CMCSH gauge
Wang, Qian
2012-01-01
In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\\Box_\\bg \\phi=0$ directly.
Modified Wenzel and Cassie equations for wetting on rough surfaces
Xu, Xianmin
2016-01-01
We study a stationary wetting problem on rough and inhomogeneous solid surfaces. We derive a new formula for the apparent contact angle by asymptotic two-scale homogenization method. The formula reduces to a modified Wenzel equation for geometrically rough surfaces and a modified Cassie equation for chemically inhomogeneous surfaces. Unlike the classical Wenzel and Cassie equations, the modified equations correspond to local minimizers of the total interface energy in the solid-liquid-air system, so that they are consistent with experimental observations. The homogenization results are proved rigorously by a variational method.
Rough differential equations driven by signals in Besov spaces
Prömel, David J.; Trabs, Mathias
2016-03-01
Rough differential equations are solved for signals in general Besov spaces unifying in particular the known results in Hölder and p-variation topology. To this end the paracontrolled distribution approach, which has been introduced by Gubinelli, Imkeller and Perkowski [24] to analyze singular stochastic PDEs, is extended from Hölder to Besov spaces. As an application we solve stochastic differential equations driven by random functions in Besov spaces and Gaussian processes in a pathwise sense.
The influence of heat accumulation on the surface roughness in powder-bed additive manufacturing
Jamshidinia, Mahdi; Kovacevic, Radovan
2015-03-01
The influence of heat accumulation on surface roughness during powder-bed additive manufacturing was investigated. A series of Ti-6Al-4V thin plates were produced by using an identical heat input by electron beam melting® (EBM). Spacing distances of 5 mm, 10 mm, and 20 mm were used. The surface roughness of as-built thin plates was measured using a two-axis profilometer. A numerical model was developed to study the influence of spacing distance on heat accumulation. An inverse relationship between the spacing distance and surface roughness was revealed. The experimental and numerical results showed that the surface quality of buildups could be controlled not only by process parameters, but also by the arrangement of components in the buildup chamber. At a constant spacing distance, an increase in the number of powder layers resulted in the accumulation of more heat between the thin plates. An increase in the spacing distance resulted in an upward translation of the Bearing Area Curve (BAC) toward shallower depths, with a reduced core roughness depth (Rk) and peak height (Rpk). A logarithmic regression equation was established from the experimental data. This equation could be used to predict the surface roughness of parts fabricated by EBM® in the studied range of spacing distances.
Heat transfer between elastic solids with randomly rough surfaces.
Volokitin, A I; Lorenz, B; Persson, B N J
2010-01-01
We study the heat transfer between elastic solids with randomly rough surfaces.We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the non-contact regions.We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For solids with very smooth surfaces, as is typical in many modern engineering applications, the interfacial separation in the non-contact regions will be very small, and for this case we show the importance of the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies.
Effective disinfection of rough rice using infrared radiation heating
The objective of this study was to investigate the effect of infrared (IR) heating and tempering treatments on disinfection of Aspergillus flavus in freshly harvested rough rice and storage rice. Rice samples with initial moisture contents (IMCs) of 14.1 to 27.0% (wet basis) were infected with A. fl...
Heat Transfer Enhancement by Finned Heat Sinks with Micro-structured Roughness
Ventola, L.; Chiavazzo, E.; Calignano, F.; Manfredi, D.; Asinari, P.
2014-04-01
We investigated the benefits of micro-structured roughness on heat transfer performance of heat sinks, cooled by forced air. Heat sinks in aluminum alloy by direct metal laser sintering (DMLS) manufacturing technique were fabricated; values of the average surface roughness Ra from 1 to 25 microns (standard milling leads to roughness around 1 micron) under turbulent regimes (Reynolds number based on heating edge from 3000 to 17000) have been explored. An enhancement of 50% in thermal performances with regards to standard manufacturing was observed. This may open the way for huge boost in the technology of electronic cooling by DMLS.
Effective disinfection of rough rice using infrared radiation heating.
Wang, Bei; Khir, Ragab; Pan, Zhongli; El-Mashad, Hamed; Atungulu, Griffiths G; Ma, Haile; McHugh, Tara H; Qu, Wenjuan; Wu, Bengang
2014-09-01
The objective of this study was to investigate the effect of infrared (IR) heating and tempering treatments on disinfection of Aspergillus flavus in freshly harvested rough rice and storage rice. Rice samples with initial moisture contents (IMCs) of 14.1 to 27.0% (wet basis) were infected with A. flavus spores before the tests. The infected samples were heated by IR radiation to 60°C in less than 1 min, and then samples were tempered at 60°C for 5, 10, 20, 30, 60, or 120 min. High heating rates and corresponding high levels of moisture removal were achieved using IR heating. The highest total moisture removal was 5.3% for the fresh rice with an IMC of 27.0% after IR heating and then 120 min of tempering. IR heating followed by tempering for 120 min resulted in 2.5- and 8.3-log reductions of A. flavus spores in rough rice with the lowest and highest IMCs, respectively. To study the effect on disinfection of rewetting dried storage rice, the surface of the dry rice was rewetted to achieve IMCs of 14.7 to 19.4% (wet basis). The rewetting process for the dry rice had a significant effect on disinfection. IR heating followed by tempering for 60 min resulted in 7.2-log reductions in A. flavus on rewetted rough rice. The log-linear plus tail model was applied to estimate the tempering time needed to achieve a 5-log reduction of A. flavus in rice of different IMCs. At least 30 and 20 min of tempering were needed for fresh rice and rewetted rice, respectively, with the highest IMCs. The recommended conditions of simultaneous disinfection and drying for fresh rice was IR heating to 60°C followed by tempering for 120 min and natural cooling, resulting in a final MC of 16.5 to 22.0%, depending on the IMC. For the rewetted dry rice with an IMC of 19.4%, the recommended condition for disinfection and drying involved only 20 min of tempering. The final MC of the sample was 13.8%, which is a safe MC for storage rice.
Macroscopic heat transport equations and heat waves in nonequilibrium states
Guo, Yangyu; Jou, David; Wang, Moran
2017-03-01
Heat transport may behave as wave propagation when the time scale of processes decreases to be comparable to or smaller than the relaxation time of heat carriers. In this work, a generalized heat transport equation including nonlinear, nonlocal and relaxation terms is proposed, which sums up the Cattaneo-Vernotte, dual-phase-lag and phonon hydrodynamic models as special cases. In the frame of this equation, the heat wave propagations are investigated systematically in nonequilibrium steady states, which were usually studied around equilibrium states. The phase (or front) speed of heat waves is obtained through a perturbation solution to the heat differential equation, and found to be intimately related to the nonlinear and nonlocal terms. Thus, potential heat wave experiments in nonequilibrium states are devised to measure the coefficients in the generalized equation, which may throw light on understanding the physical mechanisms and macroscopic modeling of nanoscale heat transport.
Effect of surface roughness on rarefied-gas heat transfer in microbearings
Zhang, Wen-Ming, E-mail: wenmingz@sjtu.edu.cn [State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240 (China); Meng, Guang [State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240 (China); Wei, Xue-Yong [Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ (United Kingdom); Peng, Zhi-Ke [State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240 (China)
2012-01-30
In this Letter, the rarefaction and roughness effects on the heat transfer process in gas microbearings are investigated. A heat transfer model is developed by introducing two-variable Weierstrass–Mandelbrot (W–M) function with fractal geometry. The heat transfer problem in the multiscale self-affine rough microbearings at slip flow regime is analyzed and discussed. The results show that rarefaction has more significant effect on heat transfer in rough microbearings with lower fractal dimension. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. The heat transfer performance can be optimized with increasing fractal dimension of the rough surface. -- Highlights: ► A heat transfer model is described with fractal geometry. ► The rarefaction affects the heat transfer under lower fractal dimension. ► The negative influence of roughness on heat transfer is Nusselt number reduction. ► The heat transfer can be optimized with increasing fractal dimension.
J. H. Lee
2012-11-01
Full Text Available Aerodynamic roughness height (Z_{om} is a key parameter required in several land surface hydrological models, since errors in heat flux estimation are largely dependent on optimization of this input. Despite its significance, it remains an uncertain parameter which is not readily determined. This is mostly because of non-linear relationship in Monin-Obukhov similarity (MOS equations and uncertainty of vertical characteristic of vegetation in a large scale. Previous studies often determined aerodynamic roughness using a minimization of cost function over MOS relationship or linear regression over it, traditional wind profile method, or remotely sensed vegetation index. However, these are complicated procedures that require a high accuracy for several other related parameters embedded in serveral equations including MOS. In order to simplify this procedure and reduce the number of parameters in need, this study suggests a new approach to extract aerodynamic roughness parameter from single or two heat flux measurements analyzed via Ensemble Kalman Filter (EnKF that affords non-linearity. So far, to our knowledge, no previous study has applied EnKF to aerodynamic roughness estimation, while the majority of data assimilation study have paid attention to updates of other land surface state variables such as soil moisture or land surface temperature. The approach of this study was applied to grassland in semi-arid Tibetan Plateau and maize on moderately wet condition in Italy. It was demonstrated that aerodynamic roughness parameter can be inversely tracked from heat flux EnKF final analysis. The aerodynamic roughness height estimated in this approach was consistent with eddy covariance method and literature value. Through a calibration of this parameter, this adjusted the sensible heat previously overestimated and latent heat flux previously underestimated by the original Surface Energy Balance System (SEBS model. It was considered that
SPACE-TIME ESTIMATE TO HEAT EQUATION
2007-01-01
In this article, we prove the Strichartz type estimate for the solutions of linear heat equation with initial data in Hardy space H1(Rd). As an application, we obtain the full space-time estimate to the solutions of heat equation with initial data in LP(Rd) for 1＜p＜∞.
Heat and mass transfer during ice accretion on aircraft wings with an improved roughness model
Fortin, Guy; Ilinca, Adrian [Groupe eolien, Universite du Quebec a Rimouski, 300 allee des Ursulines, Rimouski, PQ (Canada); Laforte, Jean-Louis [Laboratoire international des materiaux Anti-givre, Universite du Quebec a Chicoutimi, 555 Boulevard Universite, Chicoutimi, PQ (Canada)
2006-06-15
This paper presents the thermodynamic model used in the numerical simulation of ice accreted on an airfoil surface in wet and dry regimes developed at AMIL (Anti-Icing Materials International Laboratory), in a joint project with CIRA (Italian Aerospace Research Center). The thermodynamic model combines mass and heat balance equations to an analytical representation of water states over the airfoil to calculate the surface roughness and masses of remaining, run-back, and shedding liquid water. The water state on the surface is represented in the form of beads, film or rivulets, each situation corresponding to a particular roughness height which has a major impact on the heat transfer coefficients necessary for the heat and mass balances. The model has been tested for severe icing conditions at six different temperatures corresponding to dry, mixed and wet accretion. Water mass, roughness and heat transfer convection coefficients over the airfoil surface are presented. The thermodynamic model combined with an air flow, water trajectory, and geometric model provides accurate results. It generates the complex ice shapes observed on the wing profile, and the numerical ice shapes profiles agree well with those obtained in wind tunnel experiments. (author)
Roughness Length of Water Vapor over Land Surfaces and Its Influence on Latent Heat Flux
Sang-Jong Park
2010-01-01
Full Text Available Latent heat flux at the surface is largely dependent on the roughness length for water vapor (z0q. The determination of z0q is still uncertain because of its multifaceted characteristics of surface properties, atmospheric conditions and insufficient observations. In this study, observed values from the Fluxes Over Snow Surface II field experiment (FLOSS-II from November 2002 to March 2003 were utilized to estimate z0q over various land surfaces: bare soil, snow, and senescent grass. The present results indicate that the estimated z0q over bare soil is much smaller than the roughness length of momentum (z0m; thus, the ratio z0m/z0q is larger than those of previous studies by a factor of 20 - 150 for the available flow regime of the roughness Reynolds number, Re* > 0.1. On the snow surface, the ratio is comparable to a previous estimation for the rough flow (Re* > 1, but smaller by a factor of 10 - 50 as the flow became smooth (Re* < 1. Using the estimated ratio, an optimal regression equation of z0m/z0q is determined as a function of Re* for each surface type. The present parameterization of the ratio is found to greatly reduce biases of latent heat flux estimation compared with that estimated by the conventional method, suggesting the usefulness of current parameterization for numerical modeling.
Blending Brownian motion and heat equation
Cristiani, Emiliano
2015-01-01
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
Surface roughness of Ti6Al4V after heat treatment evaluated by artificial neural networks
Altug, Mehmet [Inonu Univ., Malataya (Turkey). Dept. of Machine and Metal Technologies; Erdem, Mehmet; Bozkir, Oguz [Inonu Univ., Malataya (Turkey); Ozay, Cetin [Univ. of Firat Elazig (Turkey). Faculty of Tech. Education
2016-05-01
The study examines how, using wire electrical discharge machining (WEDM), the microstructural, mechanical and conductivity characteristics of the titanium alloy Ti6Al4V are changed as a result of heat treatment and the effect they have on machinability. Scanning electron microscope (SEM), optical microscope and X-ray diffraction (XRD) examinations were performed to determine various characteristics and additionally related microhardness and conductivity measurements were conducted. L{sub 18} Taquchi test design was performed with three levels and six different parameters to determine the effect of such alterations on its machinability using WEDM and post-processing surface roughness (Ra) values were determined. Micro-changes were ensured successfully by using heat treatments. Results obtained with the optimization technique of artificial neural network (ANN) presented minimum surface roughness. Values obtained by using response surface method along with this equation were completely comparable with those achieved in the experiments. The best surface roughness value was obtained from sample D which had a tempered martensite structure.
Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
Goloviznin, V. M.; Isakov, V. A.
2017-07-01
The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems.
Numerical analysis of choked converging nozzle ﬂows with surface roughness and heat ﬂux conditions
A Alper Ozalp
2006-02-01
Choked converging nozzle ﬂow and heat transfer characteristics are numerically investigated by means of a recent computational model that integrates the axisymmetric continuity, state, momentum and energy equations. To predict the combined effects of nozzle geometry, friction and heat transfer rates, analyses are conducted with sufﬁciently wide ranges of covergence half angle, surface roughness and heat ﬂux conditions. Numerical ﬁndings show that inlet Mach and Nusselt numbers decrease up to 23.1% and 15.8% with surface heat ﬂux and by 15.13% and 4.8% due to surface roughness. Considering each convergence half angle case individually results in a linear relation between nozzle discharge coefﬁcients and exit Reynolds numbers with similar slopes. Heat ﬂux implementation, by decreasing the shear stress values, lowers the risks due to wear hazards at upstream sections of ﬂow walls; however the ﬁnal 10% downstream nozzle portion is determined to be quite critical, where shear stress attains the highest magnitudes. Heat transfer rates are seen to increase in the streamwise direction up to 2.7 times; however high convergence half angles, heat ﬂux and surface roughness conditions lower inlet Nusselt numbers by 70%, 15.8% and 4.8% respectively.
Differential-algebraic solutions of the heat equation
Buchstaber, Victor M.; Netay, Elena Yu.
2014-01-01
In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.
Heat Transfer in a Forced Wall Jet on a heated Rough Surface
Marie－FrancoiseScibilia
2000-01-01
In this paper,an experimental investigation of a laminar wall jet in the presence of a heated wall with stationary particles on its surface,is reproted.The wall jet was submitted to external acoustic vibration amplifying the coherent structures appearing in the laminar region.A wind tunnel was used at very low Reynolds number,Mean velocity and turbulence intensity were measured by a constant temperature anemometer .Measurements were taken in the transition and turbulent regions.Embedded particles were outside the vissous sublayer and it was observed that their presence modifies significantly the flow characteristics in particular the boundary layer is thickened.This study can bring a better understanding of the structure of a flow when it is heated and forced on a rough wall.
Effects of rough boundary on the heat transfer in a thin-film flow
Pažanin, Igor; Suárez-Grau, Francisco Javier
In this Note, a heat flow through a rough thin domain filled with fluid (lubricant) is studied. The domain's thickness is considered as the small parameter ɛ, while the roughness is defined by a periodical function with a period of order ɛ2. We assume that the lubricant is cooled by the exterior medium and we describe the heat exchange on the rough part of the boundary by Newton's cooling law. Depending on the magnitude of the heat transfer coefficient with respect to ɛ, we obtain three different macroscopic models via formal asymptotic analysis. We identify the critical case explicitly acknowledging both roughness-induced effects and the effects of the surrounding medium on heat transfer at main order. We illustrate the obtained results by some numerical simulations.
Distributed Roughness Effects on Blunt-Body Transition and Turbulent Heating
Hollis, Brian R.
2014-01-01
An experimental program has been conducted to obtain data on the effects of surface roughness on blunt bodies at laminar, transitional, and turbulent conditions. Wind tunnel models with distributed surface roughness heights from 0.06 mm to 1.75 mm were tested and heating data were obtained using global surface thermography. Heating rates of up to 85% higher than predicted, smooth-surface turbulent levels were measured.
Zhang, Jianing; Bi, Lei; Liu, Jianping; Panetta, R. Lee; Yang, Ping; Kattawar, George W.
2016-07-01
Constructing an appropriate particle morphology model is essential for realistic simulation of optical properties of atmospheric particles. This paper presents a model for generating surface roughness based on a combination of methods from discrete differential geometry combined with a stochastic partial differential equation for surface evolution introduced by Edwards and Wilkinson. Scattering of light by roughened particles is simulated using the Invariant Imbedding T-Matrix (II-TM) method. The effects of surface roughness on the single-scattering properties, namely, the phase matrix, asymmetry factor, and extinction efficiency, are investigated for a single wavelength in the visible range and for a range of size parameters up to x=50. Three different smooth shapes are considered: spherical, spheroidal, and hexagonal, the latter two in just the "compact particle" case of unit aspect ratio. It is shown that roughness has negligible effects on the optical scattering properties for size parameters less than 20. For size parameters ranging from 20 to 50, the phase matrix elements are more sensitive to the surface roughness than are two important integral optical properties, the extinction efficiency and asymmetry factor. As has been seen in studies using other forms of roughening, the phase function is progressively smoothed as roughness increases. The effect on extinction efficiency is to increase it, and on asymmetry factor is to decrease it. Each of these effects is relatively modest in the size range considered, but the trend of results suggests that greater effects will be seen for size parameters larger than ones considered here.
Hyperbolic heat equation in Kaluza's magnetohydrodynamics
Sandoval-Villalbazo, A; García-Perciante, A L
2006-01-01
This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are briefly discussed.
Xu, Xianmin
2010-01-01
In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness becomes small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel and Cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition. The homogenization results are proved rigorously by the F-convergence theory. © 2010 Society for Industrial and Applied Mathematics.
Natrajan, V. K.; Christensen, K. T.
2009-11-01
The convective heat-transfer behavior of laminar flow through smooth- and rough-wall microchannels is investigated by performing non-intrusive measurements of fluid temperature using a microscale adaptation of two-color laser-induced fluorescent thermometry for flow through a heated copper microchannel testbed of hydraulic diameter Dh=600,μm. These measurements, in concert with pressure-drop measurements, are performed for a smooth-wall case and two different rough-wall cases with roughness that is reminiscent of the surface irregularities one might encounter due to imperfect fabrication methods. Pressure-drop measurements reveal the onset of transition above Recr=1800 for the smooth-wall case and deviation from laminar behavior at progressively lower Re with increasing surface roughness. The local Nusselt number (Nu) for smooth-wall flow over the range 200flow.
Persistence Diagrams and the Heat Equation Homotopy
Fasy, Brittany Terese
2010-01-01
Persistence homology is a tool used to measure topological features that are present in data sets and functions. Persistence pairs births and deaths of these features as we iterate through the sublevel sets of the data or function of interest. I am concerned with using persistence to characterize the difference between two functions f, g : M -> R, where M is a topological space. Furthermore, I formulate a homotopy from g to f by applying the heat equation to the difference function g-f. By stacking the persistence diagrams associated with this homotopy, we create a vineyard of curves that connect the points in the diagram for f with the points in the diagram for g. I look at the diagrams where M is a square, a sphere, a torus, and a Klein bottle. Looking at these four topologies, we notice trends (and differences) as the persistence diagrams change with respect to time.
Fem Formulation of Coupled Partial Differential Equations for Heat Transfer
Ameer Ahamad, N.; Soudagar, Manzoor Elahi M.; Kamangar, Sarfaraz; Anjum Badruddin, Irfan
2017-08-01
Heat Transfer in any field plays an important role for transfer of energy from one region to another region. The heat transfer in porous medium can be simulated with the help of two partial differential equations. These equations need an alternate and relatively easy method due to complexity of the phenomenon involved. This article is dedicated to discuss the finite element formulation of heat transfer in porous medium in Cartesian coordinates. A triangular element is considered to discretize the governing partial differential equations and matrix equations are developed for 3 nodes of element. Iterative approach is used for the two sets of matrix equations involved representing two partial differential equations.
Closed-Form Equations for Contact Force and Moment in Elastic Contact of Rough Surfaces
Ali Sepehri
2011-01-01
Full Text Available It is reasonable to expect that, when two nominally flat rough surfaces are brought into contact by an applied resultant force, they must support, in addition to the compressive load, an induced moment. The existence of a net applied moment would imply noneven distribution of contact force so that there are more asperities in contact over one region of the nominal area. In this paper, we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment, and thereby contact moment is derived. Through this scheme, it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force, however, is shown to be of a much smaller order than the contact normal force. Approximate closed-form equations are found for contact force and moment for the contact of rough surfaces.
Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles.
Khurana, Saheba; Thachuk, Mark
2013-10-28
Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues.
Probabilistic Representations of Solutions to the Heat Equation
B Rajeev; S Thangavelu
2003-08-01
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition , is given by the convolution of with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.
On the exact controllability of a nonlinear stochastic heat equation
Bui An Ton
2006-01-01
Full Text Available The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.
Effects of electrode surface roughness on motional heating of trapped ions
Lin, Kuan-Yu; Chuang, Issac L
2016-01-01
Electric field noise is a major source of motional heating in trapped ion quantum computation. While the influence of trap electrode geometries on electric field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating rate contributions from adsorbates are predicted to exhibit an exponential sensitivity to local surface curvature, leading to either a large net enhancement or suppression over smooth surfaces. For typical experimental parameters, orders-of-magnitude variations in total heating rates can occur depending on the spatial distribution of absorbates. Through careful engineering of electrode surface profiles, our results suggests that heating ra...
Limitations of Heat Conductivity in Cryogenic Sensors Due to Surface Roughness
Moktadir, Z.; Bruijn, M.P.; Wiegerink, Remco J.; Elwenspoek, Michael Curt; Ridder, M.; Mels, W.A.
2002-01-01
The limitation of heat conductivity in cryogenic sensors due to surface roughness was discussed. It was found that at macroscopic scale and high temperatures, the transport coefficients were characteristic properties of the material and were independent of the shape and size of specimen. An
Improvement in shelf life of rough and brown rice using infrared radiation heating
The objective of this study was to investigate the effect of IR heating and tempering treatments on storage stability of rough and brown rice. Samples of freshly harvested medium grain rice variety M206 with initial moisture content of 25.03±0.21% (d.b.) were used. They were dried using infrared (IR...
Heat Equation to 3D Image Segmentation
Nikolay Sirakov
2006-04-01
Full Text Available This paper presents a new approach, capable of 3D image segmentation and objects' surface reconstruction. The main advantages of the method are: large capture range; quick segmentation of a 3D scene/image to regions; multiple 3D objects reconstruction. The method uses centripetal force and penalty function to segment the entire 3D scene/image to regions containing a single 3D object. Each region is inscribed in a convex, smooth closed surface, which defines a centripetal force. Then the surface is evolved by the geometric heat differential equation toward the force's direction. The penalty function is defined to stop evolvement of those surface patches, whose normal vectors encountered object's surface. On the base of the theoretical model Forward Difference Algorithm was developed and coded by Mathematica. Stability convergence condition, truncation error and calculation complexity of the algorithm are determined. The obtained results, advantages and disadvantages of the method are discussed at the end of this paper.
On the strongly damped wave equation and the heat equation with mixed boundary conditions
Aloisio F. Neves
2000-01-01
Full Text Available We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
I E. Lobanov
2017-01-01
Full Text Available Objectives. The aim of present work was to carry out mathematical modelling of heat transfer with symmetrical heating in flat channels and round pipes with rough walls.Methods. The calculation was carried out using the L'Hôpital-Bernoulli's method. The solution of the problem of intensified heat transfer in a round tube with rough walls was obtained using the Lyon's integral.Results. Different from existing theories, a methodology of theoretical computational heat transfer determination for flat rough channels and round pipes with rough walls is developed on the basis of the principle of full viscosity superposition in a turbulent boundary layer. The analysis of the calculated heat transfer and hydroresistivity values for flat rough channels and round rough pipes shows that the increase in heat transfer is always less than the corresponding increase in hydraulic resistance, which is a disadvantage as compared to channels with turbulators, with all else being equal. The results of calculating the heat transfer for channels with rough walls in an extended range of determinant parameters, which differ significantly from the corresponding data for the channels with turbulators, determine the level of heat exchange intensification.Conclusion. An increase in the calculated values of the relative average heat transfer Nu/NuGL for flat rough channels and rough pipes with very high values of the relative roughness is significantly contributed by both an increase in the relative roughness height and an increase in the Reynolds number Re. In comparison with empirical dependencies, the main advantage of solutions for averaged heat transfer in rough flat channels and round pipes under symmetrical thermal load obtained according to the developed theory is that they allow the calculation of heat exchange in rough pipes to be made in the case of large and very large relative heights of roughness protrusions, including large Reynolds numbers, typical for pipes
Heat polynomial analogs for higher order evolution equations
G. N. Hile
2001-05-01
Full Text Available Polynomial solutions analogous to the heat polynomials are demonstrated for higher order linear homogeneous evolution equations with coefficients depending on the time variable. Further parallels with the heat polynomials are established when the equation is parabolic with constant coefficients and only highest order terms.
Further Result of Sideways Heat Equation and Wavelets
傅初黎; 邱春雨; 朱佑彬
2001-01-01
@@"Sideways heat equation and wavelets" written by Teresa Reginska[1] is one of the earliest important literatures about solving ill-posed problem by using wavelet regularization. In this paper a new approach of wavelet regularization for the following sideways heat equation[2] in the quarter plane (t≥0, x≥0) has been considered:
Behzadan, A
2015-01-01
In this article we consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF m...
Hall, Eric Joseph
2016-12-08
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.
Jing Cui
2015-06-01
Full Text Available The surface characteristics, such as wettability and roughness, play an important role in heat transfer performance in the field of microfluidic flow. In this paper, the process of a hot liquid flowing through a microchannel with cold walls, which possesses different surface wettabilities and microstructures, is simulated by a transient double-distribution function (DDF two-phase thermal lattice Boltzmann BGK (LBGK model. The Shan-Chen multiphase LBGK model is used to describe the flow field and the independent distribution function is introduced to solve the temperature field. The simulation results show that the roughness of the channel wall improves the heat transfer, no matter what the surface wettability is. These simulations reveal that the heat exchange characteristics are directly related to the flow behavior. For the smooth-superhydrophobic-surface flow, a gas film forms that acts as an insulating layer since the thermal conductivity of the gas is relatively small in comparison to that of a liquid. In case of the rough-superhydrophobic-surface flow, the vortex motion of the gas within the grooves significantly enhances the heat exchange between the fluid and wall.
Borisova Anastasia G.
2016-01-01
Full Text Available Using high-speed camera, the experiments were performed to research evaporation of 10 μl water droplets containing 2 mm solid inclusions in the shape of cube, when heated (up to 850 K in combustion products of technical ethanol. Adding solid inclusions in water droplets allowed considerably decreasing (by 70% their evaporation times. Also, the artificial irregularities (roughness and porosity at the surfaces of solid inclusions were manufactured to increase heat transfer area. Such approach enabled to decrease evaporation times of heterogeneous liquid droplets in high-temperature gases by 40% (when comparing inclusions with artificial irregularities and smooth surface.
Nevzat ÃƒÂ‡akÃ„Â±cÃ„Â±er
2008-09-01
Full Text Available Heat treatment is often used to improve the dimensional stability of wood. In this study, the effects of heat treatment on the physical properties and surface roughness of Turkish Hazel (Corylus colurna L. wood were examined. Samples obtained from Kastamonu Forest Enterprises, Turkey, were subjected to heat treatment at varying temperatures and for different durations. The physical properties of heat-treated and control samples were tested, and oven-dry density, air-dry density, and swelling properties were determined. A stylus method was employed to evaluate the surface characteristics of the samples. Roughness measurements, using the stylus method, wereb made in the direction perpendicular to the fiber. Four main roughness parameters, mean arithmetic deviation of profile (Ra, mean peak-to-valley height (Rz, root mean square roughness (Rq, and maximum roughness (Ry obtained from the surface of wood were used to evaluate the effect of heat treatment on the surface characteristics of the specimens. Significant difference was determined (p = 0.05 between physical properties and surface roughness parameters (Ra,Rz, Ry, Rq for three temperatures and three durations of heat treatment. The results showed that the values of density, swelling and surface roughness decreased with increasing temperature treatment and treatment times. Turkish Hazel wood could be utilized successfully by applying proper heat treatment techniques without any losses in investigated parameters. This is vital in areas, such as window frames, where working stability and surface smoothness are important factors.
Korkut, Derya Sevim; Korkut, Süleyman; Bekar, Ilter; Budakçi, Mehmet; Dilik, Tuncer; Cakicier, Nevzat
2008-09-01
Heat treatment is often used to improve the dimensional stability of wood. In this study, the effects of heat treatment on the physical properties and surface roughness of Turkish Hazel (Corylus colurna L.) wood were examined. Samples obtained from Kastamonu Forest Enterprises, Turkey, were subjected to heat treatment at varying temperatures and for different durations. The physical properties of heat-treated and control samples were tested, and oven-dry density, air-dry density, and swelling properties were determined. A stylus method was employed to evaluate the surface characteristics of the samples. Roughness measurements, using the stylus method, were made in the direction perpendicular to the fiber. Four main roughness parameters, mean arithmetic deviation of profile (Ra), mean peak-to-valley height (Rz), root mean square roughness (Rq), and maximum roughness (Ry) obtained from the surface of wood were used to evaluate the effect of heat treatment on the surface characteristics of the specimens. Significant difference was determined (p = 0.05) between physical properties and surface roughness parameters (Ra,Rz, Ry, Rq) for three temperatures and three durations of heat treatment. The results showed that the values of density, swelling and surface roughness decreased with increasing temperature treatment and treatment times. Turkish Hazel wood could be utilized successfully by applying proper heat treatment techniques without any losses in investigated parameters. This is vital in areas, such as window frames, where working stability and surface smoothness are important factors.
Najeeb, Umair
This thesis experimentally investigates the enhancement of single-phase heat transfer, frictional loss and pressure drop characteristics in a Single Heater Element Loop Tester (SHELT). The heater element simulates a single fuel rod for Pressurized Nuclear reactor. In this experimental investigation, the effect of the outer surface roughness of a simulated nuclear rod bundle was studied. The outer surface of a simulated fuel rod was created with a three-dimensional (Diamond-shaped blocks) surface roughness. The angle of corrugation for each diamond was 45 degrees. The length of each side of a diamond block is 1 mm. The depth of each diamond block was 0.3 mm. The pitch of the pattern was 1.614 mm. The simulated fuel rod had an outside diameter of 9.5 mm and wall thickness of 1.5 mm and was placed in a test-section made of 38.1 mm inner diameter, wall thickness 6.35 mm aluminum pipe. The Simulated fuel rod was made of Nickel 200 and Inconel 625 materials. The fuel rod was connected to 10 KW DC power supply. The Inconel 625 material of the rod with an electrical resistance of 32.3 kO was used to generate heat inside the test-section. The heat energy dissipated from the Inconel tube due to the flow of electrical current flows into the working fluid across the rod at constant heat flux conditions. The DI water was employed as working fluid for this experimental investigation. The temperature and pressure readings for both smooth and rough regions of the fuel rod were recorded and compared later to find enhancement in heat transfer coefficient and increment in the pressure drops. Tests were conducted for Reynold's Numbers ranging from 10e4 to 10e5. Enhancement in heat transfer coefficient at all Re was recorded. The maximum heat transfer co-efficient enhancement recorded was 86% at Re = 4.18e5. It was also observed that the pressure drop and friction factor increased by 14.7% due to the increased surface roughness.
Toporkov, Jakov V.
1998-01-01
A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects o...
Optimal Control of Non-well-posed Heat Equations
Geng Sheng WANG
2005-01-01
This work is concerned with Pontryagin's maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.
A new technology for solving diffusion and heat equations
Yang Xiao-Jun
2017-01-01
Full Text Available In this paper, a new technology combing the variational iterative method and an integral transform similar to Sumudu transform is proposed for the first time for solutions of diffusion and heat equations. The method is accurate and efficient in development of approximate solutions for the partial differential equations.
Finite approximate controllability for semilinear heat equations in noncylindrical domains
Menezes Silvano B. de
2004-01-01
Full Text Available We investigate finite approximate controllability for semilinear heat equation in noncylindrical domains. First we study the linearized problem and then by an application of the fixed point result of Leray-Schauder we obtain the finite approximate controllability for the semilinear state equation.
Multigrid waveform relaxation for the time-fractional heat equation
F.J. Gaspar Lorenz (Franscisco); C. Rodrigo (Carmen)
2017-01-01
textabstractIn this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the coefficient matrix is dense.
Green function diagonal for a class of heat equations
Kwiatkowski, Grzegorz
2011-01-01
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.
Korkut, Derya Sevim; Guller, Bilgin
2008-05-01
Heat treatment is often used to improve the dimensional stability of wood. In this study, the effects of heat treatment on physical properties and surface roughness of red-bud maple (Acer trautvetteri Medw.) wood were examined. Samples obtained from Düzce Forest Enterprises, Turkey, were subjected to heat treatment at varying temperatures and durations. The physical properties of heat-treated samples were compared against controls in order to determine their; oven-dry density, air-dry density, and swelling properties. A stylus method was employed to evaluate the surface characteristics of the samples. Roughness measurements, using the stylus method, were made in the direction perpendicular to the fiber. Three main roughness parameters; mean arithmetic deviation of profile (Ra), mean peak-to-valley height (Rz), and maximum roughness (Rmax) obtained from the surface of wood, were used to evaluate the effect of heat treatment on the surface characteristics of the specimens. Significant differences were determined (p>0.05) between surface roughness parameters (Ra, Rz, Rmax) at three different temperatures and three periods of heat treatment. The results showed that the values of density, swelling and surface roughness decreased with increasing temperature treatment and treatment times. Red-bud maple wood could be utilized successfully by applying proper heat treatment techniques without any losses in investigated parameters. This is vital in areas, such as window frames, where working stability and surface smoothness are important factors.
A Multi-Layer Extension of the Stochastic Heat Equation
O'Connell, Neil; Warren, Jon
2016-01-01
Motivated by recent developments on solvable directed polymer models, we define a `multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture.
Studies on Microwave Heated Drying-rate Equations of Foods
1990-01-01
In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...
Mahroo Vojdani
2012-09-01
Conclusion: Reinforcement of the conventional heat-cured acrylic resin with 2.5 wt% Al2O3 powder significantly increased its flexural strength and hardness with no adverse effects on the surface roughness.
Two-parameter Rankine Heat Pumps’ COP Equations
Samuel Sunday Adefila
2012-05-01
Full Text Available Equations for ideal vapour compression heat pump coefficient of performance (COPR which contain two fit-parameters are reported in this work. These equations contain either temperature term alone or temperature and pressure terms as the only thermodynamic variable(s. The best equation gave error ≥5% over wide range of temperature-lift and for different working fluid types that include fluorocarbons, hydrocarbons and inorganic fluids. In these respects the equation performs better than the one-parameter models reported earlier.
Poincar\\'e-Lelong equation via the Hodge Laplace heat equation
Ni, Lei
2011-01-01
In this article we start a new approach of solving the Poincar\\'e-Lelong equation via the large time study of the Hodge Laplace heat equation on $(1,1)$-forms. After a general theorem we construct the solution under three different assumptions.
Das, Sudev; Bhaumik, Swapan
2016-04-01
The influence of coating thickness and surface roughness on pool boiling heat transfer is experimentally studied over a range of surface roughness values with varied coating thickness with water at atmospheric pressure. Test surfaces used in this experiment are namely, untreated surface (Ra = 0.0899 µm), polished surface (Ra = 0.0493 µm), TiO2 nanoparticle coated surface with a roughness (Ra) ranging from 0.0338 to 0.289 µm. The surfaces were characterized with respect to contact angle, surface roughness and coating thickness. The contact angle, surface roughness and coating thickness were measured by sessile drop method, optical surface profiler and instrument thickness monitor respectively. Heat fluxes observed ranged from 52.63 to 144.73 W/cm2. Different trends were observed in the Heat Transfer Coefficient (HTC) with respect to the surface roughness and coating thickness values on the same set of heat flux. The HTC was found to increase with increasing the roughness values for untreated and polish surface but nanoparticle coated surfaces displayed different trend in HTCs. The HTC was found to increase with increasing coating thickness with all wall superheat.
Fourier's heat conduction equation: History, influence, and connections
Narasimhan, T. N.
1999-02-01
The equation describing the conduction of heat in solids has, over the past two centuries, proved to be a powerful tool for analyzing the dynamic motion of heat as well as for solving an enormous array of diffusion-type problems in physical sciences, biological sciences, earth sciences, and social sciences. This equation was formulated at the beginning of the nineteenth century by one of the most gifted scholars of modern science, Joseph Fourier of France. A study of the historical context in which Fourier made his remarkable contribution and the subsequent impact his work has had on the development of modern science is as fascinating as it is educational. This paper is an attempt to present a picture of how certain ideas initially led to Fourier's development of the heat equation and how, subsequently, Fourier's work directly influenced and inspired others to use the heat diffusion model to describe other dynamic physical systems. Conversely, others concerned with the study of random processes found that the equations governing such random processes reduced, in the limit, to Fourier's equation of heat diffusion. In the process of developing the flow of ideas, the paper also presents, to the extent possible, an account of the history and personalities involved.
Eigenvalue Expansion Approach to Study Bio-Heat Equation
Khanday, M. A.; Nazir, Khalid
2016-07-01
A mathematical model based on Pennes bio-heat equation was formulated to estimate temperature profiles at peripheral regions of human body. The heat processes due to diffusion, perfusion and metabolic pathways were considered to establish the second-order partial differential equation together with initial and boundary conditions. The model was solved using eigenvalue method and the numerical values of the physiological parameters were used to understand the thermal disturbance on the biological tissues. The results were illustrated at atmospheric temperatures TA = 10∘C and 20∘C.
Thermodynamic framework for a generalized heat transport equation
Guo Yangyu
2016-06-01
Full Text Available In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.
Dorari, Elaheh; Saffar-Avval, Majid; Mansoori, Zohreh
2015-12-01
In microfluidics, two important factors responsible for the differences between the characteristics of the flow and heat transfer in microchannels and conventional channels are rarefaction and surface roughness which are studied in the present work. An incompressible gas flow in a microchannel is simulated two dimensionally using the lattice Boltzmann method. The flow is in the slip regime and surface roughness is modeled by both regular and Gaussian random distribution of rectangular modules. The effects of relative surface roughness height and Knudsen number on gaseous flow and heat transfer are studied. It was shown that as the relative roughness height increases, the Poiseuille number increases and the Nusselt number has a decreasing or increasing trend, depending on the degree of rarefaction. A comparison between the flow and heat transfer characteristics in regular and random distribution of surface roughness demonstrates that in regular roughness, circular flows are more pronounced; Poiseuille number is higher and Nusselt number is lower than that of its equivalent random roughness.
Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force
Vega Reyes, Francisco, E-mail: fvega@unex.es; Santos, Andrés, E-mail: andres@unex.es [Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz (Spain)
2015-11-15
We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the direct simulation Monte Carlo method), we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called “lifted-tennis-ball” behavior)
Observer for heat equation with state-dependent switched parameters
Bendtsen, Jan Dimon; Leth, John-Josef
2016-01-01
This paper considers estimation of an unknown state function in the heat equation with state-dependent parameter values. The work is motivated by phase transitions in physical media, e.g., thawing of water or foodstuff, welding and casting processes. We point out that known solution to standard...
Schwarz waveform relaxation algorithm for heat equations with distributed delay
Wu Shu-Lin
2016-01-01
Full Text Available Heat equations with distributed delay are a class of mathematic models that has wide applications in many fields. Numerical computation plays an important role in the investigation of these equations, because the analytic solutions of partial differential equations with time delay are usually unavailable. On the other hand, duo to the delay property, numerical computation of these equations is time-consuming. To reduce the computation time, we analyze in this paper the Schwarz waveform relaxation algorithm with Robin transmission conditions. The Robin transmission conditions contain a free parameter, which has a significant effect on the convergence rate of the Schwarz waveform relaxation algorithm. Determining the Robin parameter is therefore one of the top-priority matters for the study of the Schwarz waveform relaxation algorithm. We provide new formula to fix the Robin parameter and we show numerically that the new Robin parameter is more efficient than the one proposed previously in the literature.
Heat Transfer Equation With Delay for Media With Thermal Memory
Anton Oleksandrovych Vasylenko
2013-04-01
Full Text Available A new model for heat transfer in this paper is proposed. It combines idea of medium with memory and phase-lag model. Equation for a temperature field based on new heat transfer model was obtained and investigated with wave-like solutions. New model was compared with common models for non-stationary heat transfer by its wave-like solutions amplitude attenuation, wave length and phase velocity. It was shown that model with memory is equivalent to a hyperbolic model of heat transfer. While new combined model is equivalent with a phase-lag model for a low frequencies but differs for a high frequencies. Both this models predict possibility of undamped thermal waves, but phase-lag model predict a numerous quantity of undumped thermal waves, while combined model predict undumped wave for a one frequency.
Younsi Ramdane
2015-01-01
Full Text Available In the present paper, three-dimensional equations for coupled heat and mass conservation equations for wood are solved to study the transient heat and mass transfer during high thermal treatment of wood. The model is based on Luikov’s approach, including pressure. The model equations are solved numerically by the commercial package FEMLfor the temperature and moisture content histories under different treatment conditions. The simulation of the proposed conjugate problem allows the assessment of the effect of the heat and mass transfer within wood. A parametric study was also carried out to determine the effects of several parameters such as initial moisture content and the sample thickness on the temperature, pressure and moisture content distributions within the samples during heat treatment.
Obot, N.T.; Esen, E.B. (Clarkson Univ., Potsdam, NY (USA). Fluid Mechanics, Heat and Mass Transfer Lab.); Rabas, T.J. (Argonne National Lab., IL (USA))
1990-04-01
It has been established that transition determines the attainable friction and heat transfer in smooth and rough passages. According to the proposed law of corresponding states for friction, different types of roughness exhibit the same general behavior for friction at the same reduced conditions. This is also true of different types of smooth passages. It has been fully demonstrated that, in rough passages, the marked increases in friction factor are intimately associated with early transition and that, under reduced similarity conditions, the friction factors are considerably lower than those deduced from the familiar f vs. Re plots. For all smooth or rough passages, the simple rule for heat transfer amounts to this: the lower the critical Reynolds number for transition, the greater the value for the average heat transfer coefficient. Consequently, for a given Reynolds number based on the hydraulic diameter, triangular passages can be expected to give heat transfer coefficients that are significantly higher than for circular, rectangular or annular tubes. For smooth and enhanced passages of complex shapes, it appears that heat transfer coefficients can be calculated accurately from the smooth circular tube relations, provided the critical Reynolds number is known. 61 refs., 25 figs., 1 tab.
Heat flow method to Lichnerowicz type equation on closed manifolds
Li MA; Sun, Yuhua
2010-01-01
In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M\\times\\mathbb{R}^{+}, u(x,0)=u_0,\\quad in\\quad M with the positive smooth initial da...
Qu Wei; Ma Tongze
2001-01-01
The surface of capillary wall can be treated to have a periodic microrelief mathematically. The roughness is micro enough compared with the thickness of the liquid film. So, the surface roughness only exerts influence on the adsorptive potential. Macroscopically, the flow field of the liquid film can be considered as that when the rough surface has an equivalent smooth surface, whose position is at the crests of the microrelief. The mechanism of heat transfer is in connection with two resistances: the thermal resistance of the liquid film conduction and the thermal resistance of the interfacial evaporation. The capillary pressure between the two sides of the vapor-liquid interface due to the interfacial curvature and the disjoining pressure owing to the thin liquid film are considered simultaneously. Several micro tubes with different micro rough surfaces are studied. The length of the evaporating interfacial region decreases with the increase of roughness angle and/or the increase of the roughness height. The heat transfer coefficient and the temperature of the vapor-liquid interface will change to fit the constant mass flow rate.
Ai-Min Yang
2014-03-01
Full Text Available The fractal heat flow within local fractional derivative is investigated. The nonhomogeneous heat equations arising in fractal heat flow are discussed. The local fractional Fourier series solutions for one-dimensional nonhomogeneous heat equations are obtained. The nondifferentiable series solutions are given to show the efficiency and implementation of the present method.
Modeling the Heating of Biological Tissue based on the Hyperbolic Heat Transfer Equation
Tung, M M; Molina, J A Lopez; Rivera, M J; Berjano, E J
2008-01-01
In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled by the bioheat equation introduced by Pennes, who considers Fourier's theory of heat conduction. We present an alternative and more realistic model established by the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the obtained results to different types of tissue heating with high energy fluxes, in particular radiofrequency heating and pulsed laser treatment of the cornea to correct refractive errors. Hopefully, the results of our approach help to refine surgical interventions in this novel field of medical treatment.
A NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATIONS
YANJINHAI
1996-01-01
The existenoe and limit hehaviour of the solution for a kind of nonloeal noulinear boundary value condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinks to a point in a certain way, this condition either results in a Dirac measure or simply disappears in the corresponding problem.
A numerical method for solving heat equations involving interfaces
Zhilin Li
2000-07-01
Full Text Available In 1993, Li and Mayo [3] gave a finite-difference method with second order accuracy for solving the heat equations involving interfaces with constant coefficients and discontinuous sources. In this paper, we expand their result by presenting a finite-difference method which allows each coefficient to take different values in different sub-regions of the interface. Our method is useful in physical applications, and has also second order accuracy.
The cost of approximate controllability for semilinear heat equations
Yuqing YAN; Yi ZHAO; Yu HUANG
2009-01-01
We consider the semilinear heat equation with globally Lipschitz non-linearity involving gradient terms in a bounded domain of Rn.In this paper,we obtain explicit bounds of the cost of approximate controllability,i.e.,of the minimal norm of a control needed to control the system approximately.The methods we used combine global Carleman estimates,the variational approach to approximate controllability and Schauder's fixed point theorem.
Solving Heat and Wave-Like Equations Using He's Polynomials
Syed Tauseef Mohyud-Din
2009-01-01
Full Text Available We use He's polynomials which are calculated form homotopy perturbation method (HPM for solving heat and wave-like equations. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that suggested technique solves nonlinear problems without using Adomian's polynomials is a clear advantage of this algorithm over the decomposition method.
Shayganpour, A.; Idris, M. H.; Izman, S.; Farahany, S.
2012-06-01
The effects of pouring temperature and slurry viscosity in terms of heat transfer on surface roughness during lost foam casting (LFC) of LM6 alloy were investigated experimentally. Heat transfer of molten materials is an important factors to changes the microstructure which is considered in the present study. It is primarily dependent on the pouring temperature, casting thickness, mould material, mould temperature and surrounding medium. The pouring temperature changed from 700 to740°C and slurry viscosity altered from 20 to 36 sec. A full 2-level factorial design experimental technique was used to identify the significant factors that effect on surface roughness of castings. The results show that surface roughness improved by lower pouring temperature, whereas slurry viscosity has less influence on the quality of surface.
Sensitivity of roughness length for heat transport (zoh) on evapotranspiration derived from SEBAL
Paul, G.; Gowda, P. H.; Prasad, V.; Howell, T. A.; Aiken, R. M.
2012-12-01
Thermal infrared remote sensing has greatly contributed to the development and improvement of remote sensing based evapotranspiration (RS-ET) mapping algorithms. The radiometric temperature derived from the thermal sensors were inherently different than the aerodynamic temperature required for solving the bulk formulation of sensible heat (H) based on the Monin-Obukhov similarity (MOS); this posed a critical problem. The TSM (Two Source Model), SEBS (Surface Energy Balance System) and SEBAL (Surface Energy Balance Algorithm) forms the three most widely applied RS-ET algorithm's differing in their conceptualization and parameterization of the soil-canopy-air heat exchange mechanism addressing the issue arising from aerodynamic-radiometric temperature differences. The scalar roughness length zoh, representing heat transport and described by the dimensionless parameter kB-1, was used as a correction factor to accommodate the discrepancy between radiometric and aerodynamic temperatures. In this study we looked into the sensitivity of zoh on the ET estimates using the SEBAL approach. ET estimates from four approaches namely, (i) zoh derived from constant kB-1 of 2.3, (ii) zoh=0.1, (iii) zoh=0.01, and (iv) zoh from kB-1 parameterization, were compared. SEBAL was executed for 10 high resolution airborne images acquired during BEAREX07-08 (Bushland Evapotranspiration and Agricultural Remote Sensing Experiment) field campaign and validated against large precision weighing lysimeters installed on two irrigated and two dryland fields. Statistical tests revealed no significant differences between the first three approaches, however, the fourth approach of kB-1 parameterization produced significantly different results. Model performance evaluation for all the components of the energy balance was conducted. Percent root mean square error (%RMSE) for instantaneous ET estimates from the four approaches were 33.7, 26.9, 27.7 and 23.2 respectively. Evaluation of the SEBAL
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik
2000-05-01
This paper studies nonlinear degenerate parabolic equations where the flux function does not depend Lipshitz continuously on the spatial position x. By properly adapting the 'doubling of variable' device due to Kruzkov and Carrillo, the authors prove a uniqueness result within the class of entropy solutions for the initial value problem. They also prove a result concerning the continuous dependence on the initial data and the flux function for degenerate parabolic equations with flux function of the form k(x)f(u), where k(x) is a vector-valued function and f(u) is a scalar function of the unknown scalar function u(x,t) which is sought.
Heat storage by phase transition, equation of state
Stunic, Z.
1984-01-01
Incongruent phase transitions accompanied by phase separation frequently cause a deterioration of heat-of-fusion storing systems. This kind of deterioration progresses, cycle after cycle, and is especially damaging in technical devices in which hydrated salts, e.g. CaCl/sub 2/ x 6H/sub 2/O, Na/sub 2/SO/sub 4/ x 10H/sub 2/O, Na/sub 2/S/sub 2/O/sub 3/ x 5H/sub 2/O, etc., are used as heat storing materials. Processes contributing to deterioration of hydrated-salt systems are analyzed, novel thermodynamic characteristics are proposed to enable unambiguous descriptions, and these are related in an equation of state for triads of characteristics so that any one of them can be calculated if the other two are known. State equations fo the three salts mentioned above are represented graphically in three-dimensional diagrams. Predictions deduced from state equations are tested experimentally with systems undergoing rapid (or purely incongruent) and slow (or pseudocongruent) phase transitions (CaCl/sub 2/ x 6H/sub 2/O and Na/sub 2/SO/sub 4/ 10H/sub 2/O, respectively). Good accordance between prognosis and experiment is shown.
Characteristic equation method for fractal heat-transfer problem via local fractional calculus
Liu Geng-Yuan
2016-01-01
Full Text Available In this paper the fractal heat-transfer problem described by the theory of local fractional calculus is considered. The non-differentiable-type solution of the heat-transfer equation is obtained. The characteristic equation method is proposed as a powerful technology to illustrate the analytical solution of the partial differential equation in fractal heat transfer.
Heat flow method to Lichnerowicz type equation on closed manifolds
Ma, Li
2010-01-01
In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M\\times\\mathbb{R}^{+}, u(x,0)=u_0,\\quad in\\quad M with the positive smooth initial data $u_0$.
Ahn, Sujung; Douglas, Peter; Doerr, Stefan; Gowenlock, Cathren; Hallin, Ingrid; Mabbett, Ian
2014-05-01
Manifestation of soil water repellency depends both on the surface chemistry and the physical structure of the particles making up the soil. In materials science the effect of physical structure on water repellency is often explained by the Cassie-Baxter equation. Recently, a few attempts have been made to explain water repellency of soil using the Cassie-Baxter equation for hexagonally-arrayed spheres on a flat plane. Experimental verification of this conceptual model using glass beads as model soil particles has been left somewhat incomplete, as the experimentally measured contact angles do not match well those expected from theory. This might be caused by a failure to generate a perfect arrangement of particles. Therefore, we have aimed to obtain highly precise arrangements of glass beads as model soil particles using 3D printing technology. Our aim is to generate particle frames of precise hexagonal arrangement with particles at differing separations, and to measure the water contact angles upon the particle arrays optically using a goniometer. In this contribution, we report our preliminary results in which we explore the applicability of the Cassie-Baxter equation to such regular arrays as both separation distance and surface roughness is varied. This research has been funded by Bridging the Gap in Swansea University, UK.
Similarity solution to a heat equation with convection in an infinite medium
Liancun Zheng; Xinxin Zhang; Jicheng He
2003-01-01
A second order heat equation with convection in an infinite medium is studied. Suitable similarity transformations are used to reduce the parabolic heat equation to a class of singular nonlinear boundary value problems. Numerical solutions are presented for different representations of heat conduction, heat convection, heat flux, and power law parameters by utilizing the shooting technique. The results reveal the heat transfer characteristic and the effect of parameters on the solutions.
Natrajan, V. K.; Christensen, K. T.
2010-11-01
The convective heat transfer behavior of laminar flow through a smooth- and two rough-wall microchannels is investigated by performing non-intrusive and spatially resolved measurements of fluid temperature via two-color fluorescent thermometry under constant heat flux conditions at three of the four microchannel walls. Pressure-drop measurements reveal that the apparent friction factors for all surfaces agree well with established macroscale predictions for laminar flow through rectangular ducts with the onset of transition at Re > Recr = 1,800 for smooth-wall flow and deviation from laminar behavior at progressively lower Re with increasing surface roughness. The local Nu for smooth-wall flow agrees well with macroscale predictions in both the thermally developing and developed regimes. With increasing roughness, while an enhancement in local Nu is noted for flow in the thermally developing regime, no measurable influence is noted upon attainment of a thermally developed state. These observations are supported by the examination of temperature profiles across the microchannel at various axial positions and Re, which suggest that the thermal boundary layer may be regenerated locally by roughness in the thermal entrance region of the flow resulting in an increased axial distance (compared to smooth-wall behavior) at which thermally developed flow is attained in the presence of roughness. Finally, estimates of the bulk Nu indicate enhancement in convective heat transfer over the smooth-wall case for laminar flow at higher Re while the smooth-wall bulk Nu data are found to agree well with macroscale predictions.
Sawicki Dominik
2015-09-01
Full Text Available One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES, which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems, as well as transient heat transfer problems. The purpose of this paper is to test the efficacy of the PIES method with time discretization in solving problem of laser heating of a material, with different pulse shape approximation functions.
McGinty, Sean; O'Connor, Gerard M.; Glynn, Thomas J.
2005-06-01
Excimer based laser ablation of micro-fluidic circuits for micro-total analysis systems (μTAS) is an alternative to more expensive techniques of LIGA or micro-moulding. In the interests of developing a rapid prototyping method for direct writing of micro-fluidic circuits in polymer materials the ablation process was characterised using Design of Experiment techniques and a robust full factorial model was developed. Input factors of pulse energy, repetition rate, scan speed and number of passes were considered. Output responses of trench bottom width, sidewall angle, trench depth and trench roughness were measured. From this a prediction equation was created to forecast the output responses prior to machining and to allow the development of a process prior to machining. The accuracy of the prediction equation is discussed for four materials; Polystyrene, Polycarbonate, Non-CQ grade PMMA and CQ grade PMMA. For the four materials studied the response of Polystyrene and Polycarbonate were similar while the two grades of PMMA behave differently.
Self-similar solution of the subsonic radiative heat equations using a binary equation of state
Heizler, Shay I; Malka, Elad
2016-01-01
Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in order to investigate the effect of the equation of state (EOS) on the propagation of radiation driven shocks. We find that using a single ideal gas EOS for both regions, as used in previous works, yields large errors in describing the shock wave. We use the fact that the solution is composed of two different self-similar solutions, one for the ablation region and one for the shock, and apply two ideal gas EOS (binary-EOS), one for each region, by fitting a detailed tabulated EOS to power laws at different regimes. By comparin...
Bayesian recovery of the initial condition for the heat equation
Knapik, B T; van Zanten, J H
2011-01-01
We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.
Fast numerical upscaling of heat equation for fibrous materials
Iliev, Oleg
2010-08-01
We are interested in numerical methods for computing the effective heat conductivities of fibrous insulation materials, such as glass or mineral wool, characterized by low solid volume fractions and high contrasts, i.e., high ratios between the thermal conductivities of the fibers and the surrounding air. We consider a fast numerical method for solving some auxiliary cell problems appearing in this upscaling procedure. The auxiliary problems are boundary value problems of the steady-state heat equation in a representative elementary volume occupied by fibers and air. We make a simplification by replacing these problems with appropriate boundary value problems in the domain occupied by the fibers only. Finally, the obtained problems are further simplified by taking advantage of the slender shape of the fibers and assuming that they form a network. A discretization on the graph defined by the fibers is presented and error estimates are provided. The resulting algorithm is discussed and the accuracy and the performance of the method are illusrated on a number of numerical experiments. © Springer-Verlag 2010.
Escobar, M.; Meyerovich, A. E., E-mail: Alexander-Meyerovich@uri.edu [University of Rhode Island, Department of Physics (United States)
2014-12-15
We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.
Lee, E.; Kim, Y.; jeong, H.; Chung, H.
2015-09-01
Aluminum alloy is a material with a high strength-weight ratio and excellent thermal conductivity. It neither readily corrodes nor quickly weakens at low temperatures, but can be easily recycled. Because of these features, aluminum heat exchangers are widely used in aluminum alloy. In addition, the aluminum alloy used in other areas is expected to gradually increase. As a result, researchers have been continuously studying the cutting patterns of aluminium alloy. However, such studies are fewer than those on the cutting patterns of ordinary steel. Moreover, the research on ball end milling with aluminium alloys has not received much attention. Therefore, in this study, an attempt was made to find the optimal cutting pattern among the seven cutting patterns for the machining of the commonly used aluminum alloy using ball end milling for a heat exchanger. The optimal pattern was found by comparing the different shapes and surface roughness values produced by the seven patterns.
Gündüz, Gökhan; Korkut, Süleyman; Korkut, Derya Sevim
2008-05-01
Heat treatment is often used to improve the dimensional stability of wood. In this study, the effects of heat treatment on physical properties and surface roughness of Camiyani Black Pine (Pinus nigra Arn. subsp. pallasiana var. pallasiana) wood were examined. Samples obtained from Yenice-Zonguldak Forest Enterprises, Turkey, were subjected to heat treatment at varying temperatures and for varying durations. The physical properties of heat-treated and control samples were tested, and oven-dry density, air-dry density, and swelling properties were determined. The mechanical properties of heat-treated and control samples were tested, and compression strength, and Janka-hardness were determined. A stylus method was employed to evaluate the surface characteristics of the samples. Roughness measurements by the stylus method were made in the direction perpendicular to the fiber. Four main roughness parameters, mean arithmetic deviation of profile (Ra), mean peak-to-valley height (Rz), root mean square roughness (Rq), and maximum roughness (Ry) obtained from the surface of wood were used to evaluate the effect of heat treatment on the surface characteristics of the specimens. Significant difference was determined (p=0.05) between physical and technological properties, and surface roughness parameters (Ra, Rz, Ry, Rq) for three temperatures and three durations of heat treatment. Based on the findings in this study, the results showed that density, swelling, compression strength, Janka-hardness and surface roughness values decreased with increasing treatment temperature and treatment times. Increase in temperature and duration further diminished technological strength values of the wood specimens. Camiyani Black Pine wood could be utilized by using proper heat treatment techniques without any losses in strength values in areas where working, stability, and surface smoothness, such as in window frames, are important factors.
Toporkov, Jakov V.
A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects of numerical simulations crucial to obtaining correct results in the demanding low grazing angle regime. It was found that when the MFIE propagator matrix is used with zeros on its diagonal (as has often been the practice) the results appear to show an unexpected sensitivity to the sampling interval. This sensitivity is especially pronounced in the case of horizontal polarization and at low grazing angles. We show---both numerically and analytically---that the problem lies not with the particular numerical technique used (MOMI) but rather with how the MFIE is discretized. It is demonstrated that the inclusion of so-called "curvature terms" (terms that arise from a correct discretization procedure and are proportional to the second surface derivative) in the diagonal of the propagator matrix eliminates the problem completely. A criterion for the choice of the sampling interval used in discretizing the MFIE based on both electromagnetic wavelength and the surface spectral cutoff is established. The influence of the surface spectral cutoff value on the results of scattering simulations is investigated and a recommendation for the choice of this spectral cutoff for numerical simulation purposes is developed. Also studied is the applicability of the tapered incident field at low grazing incidence angles. It is found that when a Gaussian-like taper with fixed beam waist is used there is a characteristic pattern (anomalous jump) in the calculated average backscattered cross section at
无
2003-01-01
Rough set is a new approach to uncertainties in spatial analysis.In this paper,rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication.Rough spatial entities and their topological relationships are also proposed in rough space,thus a universal intersected equation is developed,and rough membership function is further extended with the gray scale in our case study.We complete three works.First,a set of simplified rough symbols is advanced on the basis of existing rough symbols.Second,rough spatial entity is put forward to study the real world as it is,without forcing uncertainties into crisp set.Third,rough spatial topological relationships are studied by using rough matrix and their figures.The relationships are divided into three types,crisp entity and crisp entity (CC),rough entity and crisp entity (RC),and rough entity and rough entity (RR).A universal intersected equation is further proposed.Finally,the maximum and minimum maps of river thematic classification are generated via rough membership function and rough relationships in our case study.
A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
Spayd, Kimberly; Puckett, James
2016-01-01
This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…
Kinoshita, Hidetaka; Terada, Atsuhiko; Kaminaga, Masanori; Hino, Ryutaro [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2001-10-01
In the design of a spallation target system, the water cooling system, for example a proton beam window and a safety hull, is used with narrow channels, in order to remove high heat flux and prevent lowering of system performance by absorption of neutron. And in narrow channel, heat transfer enhancement using 2-D rib is considered for reduction the cost of cooling component and decrease inventory of water in the cooling system, that is, decrease of the amount of irradiated water. But few studies on CHF with rib have been carried out. Experimental and analytical studies with rib-roughened test section, in 10:1 ratio of pitch to height, are being carried out in order to clarify the CHF in rib-roughened channel. This paper presents the review of previous researches on heat transfer in channel with rib roughness, overview of the test facility and the preliminary experimental and analytical results. As a result, wall friction factors were about 3 times as large as that of smooth channel, and heat transfer coefficients are about 2 times as large as that of smooth channel. The obtained CHF was as same as previous mechanistic model by Sudo. (author)
Controllability and stability of 3D heat conduction equation in a submicroscale thin film
Heidari, H.; Zwart, Heiko J.; Malek, Alaeddin
We obtain a closed form analytic solution for the Dual Phase Lagging equation. This equation is a linear, time-independent partial differential equation modeling the heat distribution in a thin film. The spatial domain is of micrometer and nanometer geometries. We show that the solution is described
Heat Stress Equation Development and Usage for Dryden Flight Research Center (DFRC)
Houtas, Franzeska; Teets, Edward H., Jr.
2012-01-01
Heat Stress Indices are equations that integrate some or all variables (e.g. temperature, relative humidity, wind speed), directly or indirectly, to produce a number for thermal stress on humans for a particular environment. There are a large number of equations that have been developed which range from simple equations that may ignore basic factors (e.g. wind effects on thermal loading, fixed contribution from solar heating) to complex equations that attempt to incorporate all variables. Each equation is evaluated for a particular use, as well as considering the ease of use and reliability of the results. The meteorology group at the Dryden Flight Research Center has utilized and enhanced the American College of Sports Medicine equation to represent the specific environment of the Mojave Desert. The Dryden WBGT Heat Stress equation has been vetted and implemented as an automated notification to the entire facility for the safety of all personnel and visitors.
A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
Abimbola Abolarinwa
2014-08-01
Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.
Simultaneous rough rice drying and rice bran stabilization using infrared radiation heating
The objective of this study was to develop a new rice drying method by using IR heating followed by tempering. Freshly harvested medium grain rice (M206) samples with different initial moisture contents (IMCs) were used in this study. The samples were dried for one- and two-passes by using a catalyt...
Heat Equation with Memory in Anisotropic and Non-Homogeneous Media
Jiongmin YONG; Xu ZHANG
2011-01-01
A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory,heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics.
A heat equation for freezing processes with phase change
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef
2016-01-01
In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers’ equation. We show...
Nanofluids droplets evaporation kinetics and wetting dynamics on rough heated substrates.
Sefiane, K; Bennacer, R
2009-01-01
The influence of aluminium nanoparticles on the evaporation and wetting dynamics of ethanol sessile droplets on a heated PTFE surface is investigated experimentally. The experimental technique uses a goniometer to measure the evolution in time of the shape of the droplets (contact angle, base diameter and volume). The evaporation rate is deduced from the measurements of the evolution of volume in time. During the "pinning" phase and contrary to what is expected, the presence of nanoparticles leads to a reduction of the evaporation rate compared to the base fluid. It is found that the deposition of nanoparticles into the triple contact line wedge during the evaporation of the droplet causes a greater pinning time for nanofluid droplets. The overall evaporation time for base fluid droplets is found to be longer than for nanofluid ones. The wetting dynamics of the droplets throughout the evaporation process shows major influence of nanoparticles. Depinning contact angles tend to be larger for nanofluid droplets than for base liquid ones. Over a range of imposed substrate temperatures, no effect on the nanofluids depinning contact angle is observed. The alteration of contact line behavior as well as wettability can have important implications in a wide range of applications, e.g. two phase boiling heat transfer [Kim, S. J. et al., Appl. Phys. Lett., 2006, 89, 153107].
Uhlig, Ralf; Frantz, Cathy; Fritsch, Andreas
2016-05-01
External receiver configurations are directly exposed to ambient wind. Therefore, a precise determination of the convective losses is a key factor in the prediction and evaluation of the efficiency of the solar absorbers. Based on several studies, the forced convective losses of external receivers are modeled using correlations for a roughened cylinder in a cross-flow of air. However at high wind velocities, the thermal efficiency measured during the Solar Two experiment was considerably lower than the efficiency predicted by these correlations. A detailed review of the available literature on the convective losses of external receivers has been made. Three CFD models of different level of detail have been developed to analyze the influence of the actual shape of the receiver and tower configuration, of the receiver shape and of the absorber panels on the forced convective heat transfer coefficients. The heat transfer coefficients deduced from the correlations have been compared to the results of the CFD simulations. In a final step the influence of both modeling approaches on the thermal efficiency of an external tubular receiver has been studied in a thermal FE model of the Solar Two receiver.
Hongheng LI; Qi L(U)
2012-01-01
The authors establish the null controllability for some systems coupled by two backward stochastic heat equations.The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
Self-similar solution of the subsonic radiative heat equations using a binary equation of state
Heizler, Shay I.; Shussman, Tomer; Malka, Elad
2016-01-01
Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in orde...
Lp and L∞ Norm Estimates of the Cost of the Controllability for Heat Equations
Pei Dong LEI; Xu LIU; Hang GAO
2009-01-01
This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.
Controllability of the Heat Equation with a Control Acting on a Measurable Set
Hang YU
2012-01-01
The paper deals with the controllability of a heat equation.It is well-known that the heat equation yt - △y =uxE in (0,T) × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ＞ 0 and any open nonempty subset E of Ω.In this note,the author studies the case that E is an arbitrary measurable set with positive measure.
Solution of the two- dimensional heat equation for a rectangular plate
Nurcan BAYKUŞ SAVAŞANERİL
2015-11-01
Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.
Eddy Current Analysis of Thin Metal Container in Induction Heating by Line Integral Equations
Fujita, Hagino; Ishibashi, Kazuhisa
In recent years, induction-heating cookers have been disseminated explosively. It is wished to commercialize flexible and disposable food containers that are available for induction heating. In order to develop a good quality food container that is heated moderately, it is necessary to analyze accurately eddy currents induced in a thin metal plate. The integral equation method is widely used for solving induction-heating problems. If the plate thickness approaches zero, the surface integral equations on the upper and lower plate surfaces tend to become the same and the equations become ill conditioned. In this paper, firstly, we derive line integral equations from the boundary integral equations on the assumption that the electromagnetic fields in metal are attenuated rapidly compared with those along the metal surface. Next, so as to test validity of the line integral equations, we solve the eddy current induced in a thin metal container in induction heating and obtain power density given to the container and impedance characteristics of the heating coil. We compare computed results with those by FEM.
Yan Li-Mei
2013-01-01
Full Text Available The purpose of this paper is to extend the homotopy perturbation method to fractional heat transfer and porous media equations with the help of the Laplace transform. The fractional derivatives described in this paper are in the Caputo sense. The algorithm is demonstrated to be direct and straightforward, and can be used for many other non-linear fractional differential equations.
One-dimensional heat conduction equation of the polar bear hair
Zhu Wei-Hong
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus possess special membrane-pore structure. The structure enables the polar bear to survive in the harsh Arctic regions. In this paper, the membrane-pore structure be approximately considered as fractal space, 1-D heat conduction equation of the polar bear hair is established and the solution of the equation is obtained.
On the controllability of the semilinear heat equation with hysteresis
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it [Department of Mathematics, University of Trento, Via Sommarive 14, 38050-Trento (Italy)
2012-05-01
We study the null controllability problem for a semilinear parabolic equation, with hysteresis entering in the semilinearity. Under suitable hypotheses, we prove the controllability result and explicitly treat the cases where the hysteresis relationship is given by a Play or a Preisach operator.
A new method for solving a class of heat conduction equations
Tian Yi
2015-01-01
Full Text Available A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.
Applicability of heat transfer equations to hydrogen combustion
Shudo, Toshio; Suzuki, Hiroyuki
2002-01-01
Previous research by the authors showed that hydrogen combustion exhibits a higher cooling loss to the combustion chamber wall of an internal combustion engine compared to hydrocarbon combustion because of its higher burning velocity and shorter quenching distance. The high cooling loss means that reduction of the cooling loss is essential to establish a high thermal efficiency in hydrogen combustion engines. This research analyzed the applicability of equations to describe the h...
Simplified equations for transient heat transfer problems at low Fourier numbers
Christensen, Martin Gram; Adler-Nissen, Jens
2015-01-01
This paper proposes an analytical solution to transient heat transfer, which also applies for the initial heating/cooling period (Fo convective boundary conditions, with negligible mass transfer and phase-change. The new equation is presented...... 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...
Development and implementation of sensitivity coefficient equations for heat conduction problems
Blackwell, B.F.; Cochran, R.J.; Dowding, K.J.
1997-12-15
Three different methods are discussed for computing the sensitivity of the temperature field to changes in material properties and initial-boundary condition parameters for heat conduction problems. The most general method is to derive sensitivity equations by differentiating the energy equation with respect to the parameter of interest and numerically solving the resulting sensitivity equations. An example problem in which there are twelve parameters of interest is presented and the resulting sensitivity equations are derived. Numerical results are presented for thermal conductivity and volumetric heat capacity sensitivity coefficients for heat conduction in a 2-D orthotropic body. The numerical results are compared with the analytical solution to demonstrate that the numerical method is second order accurate as the mesh is refined spatially.
Asymptotic solution for heat convection-radiation equation
Mabood, Fazle; Ismail, Ahmad Izani Md [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Khan, Waqar A. [Department of Engineering Sciences, National University of Sciences and Technology, PN Engineering College, Karachi, 75350 (Pakistan)
2014-07-10
In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.
Role of heat equation in lap joint for welding process
Kumar, P.; Rohit, Sooraj
2017-07-01
Welding is predominantly used in industrial purposes and growth in their industry, which gives exact welding and more efficient. The major advantage of using this welding technique at initial stage it takes very low heat to weld the portion and gives a good result of low distortion in modules. In this context, two dissimilar metals copper and nickel are chosen for analysis in tungsten inert gas welding (TIG) in which length is 300 mm and breadth is 100 mm thickness 15 mm welded at room temperature a welded portion zone is formed simulation analysis has done on CATIA® and ANSYS®and MATLAB® code is generated for calculating temperatures at each node to calculate temperature at each node a new technique is used tri-diagonal matrix algorithm is used (TDMA) Steady state one dimension heat is calculated results compared between simulation analysis and analytical analysis temperature at each node is calculated both the temperatures are equal with error.
Madhukeshwara N., E. S. Prakash
2013-01-01
Full Text Available An experimental investigation of heat transfer augmentation and friction characteristics of fully developed turbulent flow in a rectangular duct of solar air heater with absorber plate having V-shaped wire ribs as artificial roughness on its underside is carried out. The investigation covers wide range of different parameters of wire ribbed roughness: relative roughness pitch (p/e from 10 to 40, relative roughness height (e/Dh from 0.01 to 0.04 and angle of attack of flow from 20° to 90°. Duct aspect ratio (W/B is kept 5 and Reynolds number (Re is varied from 2,500 to 8,500. The heat transfer and friction factor values obtained are compared with those of smooth duct under similar flow conditions. Expressions are developed for Nusselt number and friction factor for the roughness geometry. Enhancement of Nusselt number and friction factor for roughened duct are 1.5 and 2.7 times of smooth duct respectively.
Madhukeshwara, N. [Department of Mechanical Engineering, B.I.E.T, Davanagere, Karnataka (India); Prakash, E.S. [Department of Studies in Mechanical Engineering, U.B.D.T.C.E, Davanagere, Karnataka (India)
2013-07-01
An experimental investigation of heat transfer augmentation and friction characteristics of fully developed turbulent flow in a rectangular duct of solar air heater with absorber plate having V-shaped wire ribs as artificial roughness on its underside is carried out. The investigation covers wide range of different parameters of wire ribbed roughness: relative roughness pitch (p/e) from 10 to 40, relative roughness height (e/Dh) from 0.01 to 0.04 and angle of attack of flow from 20° to 90°. Duct aspect ratio (W/B) is kept 5 and Reynolds number (Re) is varied from 2,500 to 8,500. The heat transfer and friction factor values obtained are compared with those of smooth duct under similar flow conditions. Expressions are developed for Nusselt number and friction factor for the roughness geometry. Enhancement of Nusselt number and friction factor for roughened duct are 1.5 and 2.7 times of smooth duct respectively.
Sellitto, A.; Tibullo, V.; Dong, Y.
2017-03-01
By means of a nonlinear generalization of the Maxwell-Cattaneo-Vernotte equation, on theoretical grounds we investigate how nonlinear effects may influence the propagation of heat waves in isotropic thin layers which are not laterally isolated from the external environment. A comparison with the approach of the Thermomass Theory is made as well.
Fang, En; Wu, Xiaojie; Yu, Yuesen; Xiu, Junrui
2017-03-01
In this paper, a numerical model is developed by combining thermodynamics with heat transfer theory. Taking inner and external multi-irreversibility into account, it is with a complementary equation for heat circulation in air gaps of a steady cooling system with commercial thermoelectric modules operating in refrigeration mode. With two modes concerned, the equation presents the heat flowing through air gaps which forms heat circulations between both sides of thermoelectric coolers (TECs). In numerical modelling, a TEC is separated as two temperature controlled constant heat flux reservoirs in a thermal resistance network. In order to obtain the parameter values, an experimental apparatus with a commercial thermoelectric cooler was built to characterize the performance of a TEC with heat source and sink assembly. At constant power dissipation, steady temperatures of heat source and both sides of the thermoelectric cooler were compared with those in a standard numerical model. The method displayed that the relationship between Φf and the ratio Φ_{c}'/Φ_{c} was linear as expected. Then, for verifying the accuracy of proposed numerical model, the data in another system were recorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistances with temperature change and heat flux, heat loss of the device vertical surfaces and measurements.
POP, A. B.; ȚÎȚU, M. A.
2016-11-01
In the metal cutting process, surface quality is intrinsically related to the cutting parameters and to the cutting tool geometry. At the same time, metal cutting processes are closely related to the machining costs. The purpose of this paper is to reduce manufacturing costs and processing time. A study was made, based on the mathematical modelling of the average of the absolute value deviation (Ra) resulting from the end milling process on 7136 aluminium alloy, depending on cutting process parameters. The novel element brought by this paper is the 7136 aluminium alloy type, chosen to conduct the experiments, which is a material developed and patented by Universal Alloy Corporation. This aluminium alloy is used in the aircraft industry to make parts from extruded profiles, and it has not been studied for the proposed research direction. Based on this research, a mathematical model of surface roughness Ra was established according to the cutting parameters studied in a set experimental field. A regression analysis was performed, which identified the quantitative relationships between cutting parameters and the surface roughness. Using the variance analysis ANOVA, the degree of confidence for the achieved results by the regression equation was determined, and the suitability of this equation at every point of the experimental field.
Gaussian estimates for a heat equation on a network
Mugnolo, Delio
2010-01-01
We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of sub-Markovian and ultracontractive semigroups in order to obtain upper Gaussian estimates for the integral kernel. We conclude that the same diffusion problem is governed by an analytic semigroup acting on all $L^p$-type spaces as well as on suitable spaces of continuous functions. Stability and spectral issues are also discussed. As an application we discuss a system of semilinear equations on a network related to potential transmission problems arising in neurobiology.
A Theory for the Scalar Roughness and the Scalar Transfer Coefficients over Snow and Sea Ice,
1986-09-01
and camphor ... 7 4. Model predictions for an aerodynamically rough surface compared with the ex- perimental data of Dipprey and Sabersky (1963...stability 4.,. Ls Latent heat of sublimation of ice , . Pr v/D, Prandtl number Q Water vapor density Qr Water vapor density at an arbitrary reference height...specific heat of air at constant pressure L, = latent heat of sublimation of ice. Equations 1-3 define the roughness lengths. z0 is the familiar
Surface energy equation for heat transfer process in a pebble fuel
Espinosa-Paredes, G., E-mail: gepe@xanum.uam.mx [Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, DF 09340 (Mexico); Castillo-Jiménez, V. [Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, DF 09340 (Mexico); Herranz-Puebla, L.E. [División de Fisión Nuclear, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Avda. Complutense, 22, 28040 Madrid (Spain); Vázquez-Rodríguez, R. [Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, DF 09340 (Mexico)
2014-12-15
Highlights: • Steady and transient behaviors of the interfacial heat transfer in a fuel element. • Non-local averaging volume method for deriving the surface energy equation. • The method captures significant physical phenomena of the interfacial heat transfer. • Closure relationships are proposed in order to obtain the temperatures distribution. • The derived average equation represents an upscaling regarding the local description. - Abstract: In this paper the surface energy equation for the heat transfer process (HT) between the mixture of fuel (TRISO particles and graphite matrix) and coating in a fuel pebble is derived. The fuel pebble can be treated as a heterogeneous region (mixture of microspheres and graphite) interacting thermally with the homogeneous region (the coating or cladding). These two regions are separated by a boundary region where the properties and behavior differ from those of the adjoining regions. The methodology applied for deriving the surface energy equation is based on the classical theory on interfacial transport phenomena. The surface energy equation derived in this work is an average equation that represents an upscaling respect to the local description. The regions around the surface where changes in the physical phenomena are important are of the order of microns, in contrast with interfacial mass transfer between phases that may be several molecular diameters. The numerical analysis regarding the application of surface energy equation is presented in this work.
Fong, R.W.L.; Nitheanandan, T.; Bullock, C.D.; Slater, L.F.; McRae, G.A
2003-05-01
Glass-bead peening the outside surfaces of zirconium alloy tubes has been shown to increase the Critical Heat Flux (CHF) in pool boiling of water. The CHF is found to correlate with the fractal roughness of the metal tube surfaces. In this study on the effect of oxidation on glass-peened surfaces, test measurements for CHF, surface wettability and roughness have been evaluated using various glass-peened and oxidized zirconium alloy tubes. The results show that oxidation changes the solid-liquid contact angle (i.e., decreases wettability of the metal-oxide surface), but does not change the fractal surface roughness, appreciably. Thus, oxidation of the glass-peened surfaces of zirconium alloy tubes is not expected to degrade the CHF enhancement obtained by glass-bead peening. (author)
Meda, Adimurthy; Katti, Vadiraj V.
2017-08-01
The present work experimentally investigates the local distribution of wall static pressure and the heat transfer coefficient on a rough flat plate impinged by a slot air jet. The experimental parameters include, nozzle-to-plate spacing (Z /D h = 0.5-10.0), axial distance from stagnation point ( x/D h ), size of detached rib ( b = 4-12 mm) and Reynolds number ( Re = 2500-20,000). The wall static pressure on the surface is recorded using a Pitot tube and a differential pressure transmitter. Infrared thermal imaging technique is used to capture the temperature distribution on the target surface. It is observed that, the maximum wall static pressure occurs at the stagnation point ( x/D h = 0) for all nozzle-to-plate spacing ( Z/D h ) and rib dimensions studied. Coefficient of wall static pressure ( C p ) decreases monotonically with x/D h . Sub atmospheric pressure is evident in the detached rib configurations for jet to plate spacing up to 6.0 for all ribs studied. Sub atmospheric region is stronger at Z/D h = 0.5 due to the fluid accelerating under the rib. As nozzle to plate spacing ( Z/D h ) increases, the sub-atmospheric region becomes weak and vanishes gradually. Reasonable enhancement in both C p as well as Nu is observed for the detached rib configuration. Enhancement is found to decrease with the increase in the rib width. The results of the study can be used in optimizing the cooling system design.
Nonlinear heat conduction equations with memory: Physical meaning and analytical results
Artale Harris, Pietro; Garra, Roberto
2017-06-01
We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized Maxwell-Cattaneo law. Our main aim is to derive the governing equations of heat propagation, considering both the empirical temperature-dependence of the thermal conductivity coefficient (which introduces nonlinearity) and memory effects, according to the general theory of Gurtin and Pipkin of finite velocity thermal propagation with memory. In this framework, we consider in detail two different approaches to the generalized Maxwell-Cattaneo law, based on the application of long-tail Mittag-Leffler memory function and power law relaxation functions, leading to nonlinear time-fractional telegraph and wave-type equations. We also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some well-known results of the ordinary case.
Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations
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.
Alon, Leeor; Sodickson, Daniel K; Deniz, Cem M
2016-10-01
Deposition of radiofrequency (RF) energy can be quantified via electric field or temperature change measurements. Magnetic resonance imaging has been used as a tool to measure three dimensional small temperature changes associated with RF radiation exposure. When duration of RF exposure is long, conversion from temperature change to specific absorption rate (SAR) is nontrivial due to prominent heat-diffusion and conduction effects. In this work, we demonstrated a method for calculation of SAR via an inversion of the heat equation including heat-diffusion and conduction effects. This method utilizes high-resolution three dimensional magnetic resonance temperature images and measured thermal properties of the phantom to achieve accurate calculation of SAR. Accuracy of the proposed method was analyzed with respect to operating frequency of a dipole antenna and parameters used in heat equation inversion. Bioelectromagnetics. 37:493-503, 2016. © 2016 Wiley Periodicals, Inc.
Fundamental solutions to time-fractional heat conduction equations in two joint half-lines
Povstenko, Yuriy
2013-10-01
Heat conduction in two joint half-lines is considered under the condition of perfect contact, i.e. when the temperatures at the contact point and the heat fluxes through the contact point are the same for both regions. The heat conduction in one half-line is described by the equation with the Caputo time-fractional derivative of order α, whereas heat conduction in another half-line is described by the equation with the time derivative of order β. The fundamental solutions to the first and second Cauchy problems as well as to the source problem are obtained using the Laplace transform with respect to time and the cos-Fourier transform with respect to the spatial coordinate. The fundamental solutions are expressed in terms of the Mittag-Leffler function and the Mainardi function.
Heat-flow equation motivated by the ideal-gas shock wave.
Holian, Brad Lee; Mareschal, Michel
2010-08-01
We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.
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.
Cieśliński, Janusz T.; Fiuk, Artur; Typiński, Krzysztof; Siemieńczuk, Bartłomiej
2016-09-01
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.
Accurate numerical resolution of transients in initial-boundary value problems for the heat equation
Flyer, N
2003-01-01
If the initial and boundary data for a PDE do not obey an infinite set of compatibility conditions, singularities will arise in the solution at the corners of the initial time-space domain. For dissipative equations, such as the 1-D heat equation or 1-D convection-diffusion equations, the impacts of these singularities are short lived. However, they can cause a very severe loss of numerical accuracy if we are interested in transient solutions. The phenomenon has been described earlier from a theoretical standpoint. Here, we illustrate it graphically and present a simple remedy which, with only little extra cost and effort, restores full numerical accuracy.
Constitutive Equation Models of Hot-Compressed T122 Heat Resistant Steel
CA0Jin-rong; LIUZheng—dong; CHENGShi—chang; YANGGang; XIEJian-xin
2012-01-01
Based on dislocation reaction theory and Avrami equation, a constitutive equation model was developed to describe dynamic recovery and dynamic recrystallization during hot deformation of T122 heat resistant steel, which have taken the effect of dynamic strain aging into account. Uniaxial hot compression test had been carried out over a wide range of strain rate （0.01 to 10 s-1 ） and temperature （900 to 1 200 ~C） with the help of Gleeble 3500. Obtained experimental data was applied to determine the material parameters in proposed constitutive equations of T122 steel, by using the non-linear least square regress optimization method. The calculated constitutive equations are quantita- tively in good agreement with experimentally measured curves and microstructure observation. It shows that propose constitutive equation T122 steel is able to be used to predict flow stress of T122 steel during hot deformation in aus- tenite temperature scope.
Rajendra Karwa; Srivastava, V
2013-01-01
The paper presents results of thermal performance analysis of a solar air heater with v-down discrete rib roughness on the air flow side of the absorber plate, which supplies heated air for space heating applications. The air heater operates in a closed loop mode with inlet air at a fixed temperature of 295 K from the conditional space. The ambient temperature varied from 278 K to 288 K corresponding to the winter season of Western Rajasthan, India. The results of the analysis are presented ...
Górny Z.
2015-04-01
Full Text Available Decisions regarding appropriate methods for the heat treatment of bronzes affect the final properties obtained in these materials. This study gives an example of the construction of a knowledge base with application of the rough set theory. Using relevant inference mechanisms, knowledge stored in the rule-based database allows the selection of appropriate heat treatment parameters to achieve the required properties of bronze. The paper presents the methodology and the results of exploratory research. It also discloses the methodology used in the creation of a knowledge base.
DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR A FORWARD-BACKWARD HEAT EQUATION
LiHong; WeiXiaoxi
2005-01-01
A space-time finite element method,discontinuous in time but continuous in space, is studied to solve the nonlinear forward-backward heat equation. A linearized technique is introduced in order to obtain the error estimates of the approximate solutions. And the numerical simulations are given.
Robustness of the nonequilibrium entropy related to the Maxwell-Cattaneo heat equation
Àlvarez Calafell, Francesc Xavier
2008-01-01
The connection between the Maxwell-Cattaneo heat transport equation and a nonequilibrium entropy is examined through four different thermodynamic approaches, and it is shown that all of them lead to the same form of the nonequilibrium entropy. Furthermore, it is seen that this form is also consistent with three microscopic formalisms. This robustness underlines the consistency and relevance of the entropy.
MFE revisited : part 1: adaptive grid-generation using the heat equation
Zegeling, P.A.
2001-01-01
In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which
Solutions of the modification heating conduction equations of a kind of laser thermal effect
Lingyun Zhou(周凌云); Canbang Zhang(张灿邦); Yiying Zhou; Guangmin Wu(吴光敏)
2003-01-01
This paper has solved the Chester modified heat conduction equation of the different relaxation time τ value under different temperature conditions, different boundary conditions and the different initial conditions by different means of methods. These solutions can help to obtain temperature field of laser thermal effects.
MFE revisited : part 1: adaptive grid-generation using the heat equation
Zegeling, P.A.
1996-01-01
In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which
Yan Sheng-Ping
2015-01-01
Full Text Available In this article, we first propose the local fractional Laplace series expansion method, which is a coupling method of series expansion method and Laplace transform via local fractional differential operator. An illustrative example for handling the diffusion equation arising in fractal heat transfer is given.
Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
Payne LE
1999-01-01
Full Text Available Four different well-posed regularizations of the improperly posed Cauchy problem for the backward heat equation are investigated in order to determine whether solutions of these problems depend continuously on a perturbation parameter. Using differential inequality techniques, we derive results implying continuous dependence in each case.
A finite-element solver for the 2D heat equation with convection.
J. Wackers (Jeroen)
2004-01-01
textabstractA finite-element method is developed for the two-dimensional advection-diffusion heat equation. The method features up to cubic triangular elements with Lagrange polynomial basis functions and isoparametric elements for curved boundaries. First, test problems show that the error of the
Analytic Solution for Two-Dimensional Heat Equation for an Ellipse Region
Nurcan Baykus Savasaneril
2016-01-01
Full Text Available In this study, an altenative method is presented for the solution of two-dimensional heat equation in an ellipse region. In this method, the solution function of the problem is based on the Green, and therefore on elliptic functions. To do this, it is made use of the basic consepts associated with elliptic integrals, conformal mappings and Green functions.
Theeuwes, N.E.; Steeneveld, G.J.; Ronda, R.J.; Holtslag, A.A.M.
2016-01-01
The urban heat island (UHI) effect, defined as the air temperature difference between the urban canyon and the nearby rural area, is investigated. Because not all cities around the world are equipped with an extensive measurement network, a need exists for a relatively straightforward equation for t
Test of a new heat-flow equation for dense-fluid shock waves.
Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon
2010-09-21
Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.
Kot, V. A.
2016-07-01
On the basis of the consideration of the boundary-value problem for the generalized equation of heat conduction in bounded nonuniform spaces with Dirichlet, Neumann, and Robin boundary conditions, corresponding sequences of boundary characteristics have been obtained. For each of these sequences, definite integro-differential representations (relations) have been constructed. It has been shown that approximate analytical solutions can be obtained for bounded nonuniform regions with variable transfer coefficients in the Cartesian, cylindrical, and spherical coordinate systems. On the basis of systems of algebraic equations, approximate analytical solutions have been constructed with approximately equal accuracies independently of the calculation scheme used (with the introduction of the temperature-disturbance front or without it, i.e., by multiple integration of the heat-conduction equation over the whole computational region). These solutions have a negligibly small error and, therefore, can be considered as conditionally exact.
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
Transformed Fourier and Fick equations for the control of heat and mass diffusion
S. Guenneau
2015-05-01
Full Text Available We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves, the temperature (or mass concentration inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.
Transformed Fourier and Fick equations for the control of heat and mass diffusion
Guenneau, S.; Petiteau, D.; Zerrad, M.; Amra, C.; Puvirajesinghe, T.
2015-05-01
We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves, the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.
Shih, Tzu-Ching; Yuan, Ping; Lin, Win-Li; Kou, Hong-Sen
2007-11-01
This study focuses on the effect of the temperature response of a semi-infinite biological tissue due to a sinusoidal heat flux at the skin. The Pennes bioheat transfer equation such as rho(t)c(t)( partial differentialT/ partial differentialt)+W(b)c(b)(T-T(a))=k partial differential(2)T/ partial differentialx(2) with the oscillatory heat flux boundary condition such as q(0,t)=q(0)e(iomegat) was investigated. By using the Laplace transform, the analytical solution of the Pennes bioheat transfer equation with surface sinusoidal heating condition is found. This analytical expression is suitable for describing the transient temperature response of tissue for the whole time domain from the starting periodic oscillation to the final steady periodic oscillation. The results show that the temperature oscillation due to the sinusoidal heating on the skin surface is unstable in the initial period. Further, it is unavailable to predict the blood perfusion rate via the phase shifting between the surface heat flux and the surface temperature. Moreover, the lower frequency of sinusoidal heat flux on the skin surface induces a more sensitive phase shift response to the blood perfusion rate change, but extends the beginning time of sampling because of the avoidance of the unavailable first cyclic oscillation.
Coupled equations for transient water flow, heat flow, and deformation in hydrogeological systems
T N Narasimhan
2006-04-01
Hydrogeological systems are earth systems inﬂuenced by water.Their behaviors are governed by interacting processes,including ﬂow of ﬂuids,deformation of porous materials,chemical reactions, and transport of matter and energy.Here,coupling among three of these processes is considered: ﬂow of water,heat,and deformation,each of which is represented by a diffusion-type of partial differential equation.One side of the diffusion-type equation relates to motion of matter or energy, while the other relates to temporal changes of state variables at a given location.The coupling arises from processes that govern motion as well as those that relate to change of state.In this work, attention is devoted to coupling arising from changes in state.Partial derivatives of equations of state constitute the capacitance terms of diffusion-type equations.Of the many partial derivatives that are mathematically possible in physical systems characterized by several variables,only a few are physically signi ﬁcant.Because the state variables are related to each other through an equation of state,the partial derivatives must collectively satisfy a closure criterion.This framework offers a systematic way of developing the coupled set of equations that govern hydrogeological systems involving the ﬂow of water,heat,and deformation.Such systems are described in terms of four variables,and the associated partial derivatives.The physical import of these derivatives are discussed,followed by a description of partial derivatives that are of practical interest.These partial derivatives are then used as the basis to develop a set of coupled equations.A brief discussion is presented on coupled equations from a perspective of energy optimization.
Coupled Nosé-Hoover equations of motion to implement a fluctuating heat-bath temperature
Fukuda, Ikuo; Moritsugu, Kei
2016-03-01
The Nosé-Hoover (NH) equation provides a universal and powerful computer simulation protocol to realize an equilibrium canonical temperature for a target physical system. Here we demonstrate a general formalism to couple such NH equations. We provide a coupled NH equation that is constructed by coupling the NH equation of a target physical system and the NH equation of a temperature system. Thus, in contrast to the conventional single NH equation, the heat-bath temperature is a dynamical variable. The temperature fluctuations are not ad hoc, but instead are generated by the newly defined temperature system, and the statistical distribution of the temperature is completely described with an arbitrarily given probability function. The current equations of motion thus describe the physical system that develops with a predistributed fluctuating temperature, which allows enhanced sampling of the physical system. Since the total system is governed by a prescribed distribution, the equilibrium of the physical system is also reconstructed by reweighting. We have formulated a scheme for specifically setting the distribution of the dynamical inverse temperature and demonstrate the statistical relationship between the dynamical and physical temperatures. The statistical features, dynamical properties, and sampling abilities of the current method are demonstrated via the distributions, trajectories, dynamical correlations, and free energy landscapes for both a model system and a biomolecular system. These results indicated that the current coupled NH scheme works well.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity
Marcelo Fernandes de Almeida
2016-09-01
Full Text Available This article studies the existence, stability, self-similarity and symmetries of solutions for a superdiffusive heat equation with superlinear and gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type spaces. Unlike in previous works on such time-fractional partial differential equations of order $\\alpha\\in(1,2$, we take non null initial velocities into consideration, where new difficulties arise from. We overcome them by developing an appropriate decomposition of the two-parametric Mittag-Leffler function to obtain Mikhlin-type estimates and obtain our existence theorem.
A unified model for informetrics based on the wave and heat equations
Ye, Fred Y
2010-01-01
The function g(r,t) = p(r+q)^(-{\\beta}). e^(kt) is introduced as a basic informetric function describing the classical informetric laws (through its Mandelbrot part) and a time evolution. It is shown that this function is a solution of a wave-type and of a heat-type partial differential equation. It is suggested that our approach may lead to a description of informetrics in a partial differential equation setting, formally similar to that for well-known physical laws.
Zubov, V. I.
2016-10-01
The problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the initial-boundary value problem for the one-dimensional unsteady heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the experimental data on the left boundary of the domain is used as the objective functional. An analytical expression for the gradient of the objective functional is obtained. An algorithm for the numerical solution of the problem based on the modern fast automatic differentiation technique is proposed. Examples of solving the problem are discussed.
Shumaker, D E; Woodward, C S
2005-05-03
In this paper, the authors investigate performance of a fully implicit formulation and solution method of a diffusion-reaction system modeling radiation diffusion with material energy transfer and a fusion fuel source. In certain parameter regimes this system can lead to a rapid conversion of potential energy into material energy. Accuracy in time integration is essential for a good solution since a major fraction of the fuel can be depleted in a very short time. Such systems arise in a number of application areas including evolution of a star and inertial confinement fusion. Previous work has addressed implicit solution of radiation diffusion problems. Recently Shadid and coauthors have looked at implicit and semi-implicit solution of reaction-diffusion systems. In general they have found that fully implicit is the most accurate method for difficult coupled nonlinear equations. In previous work, they have demonstrated that a method of lines approach coupled with a BDF time integrator and a Newton-Krylov nonlinear solver could efficiently and accurately solve a large-scale, implicit radiation diffusion problem. In this paper, they extend that work to include an additional heating term in the material energy equation and an equation to model the evolution of the reactive fuel density. This system now consists of three coupled equations for radiation energy, material energy, and fuel density. The radiation energy equation includes diffusion and energy exchange with material energy. The material energy equation includes reaction heating and exchange with radiation energy, and the fuel density equation includes its depletion due to the fuel consumption.
The neutron star in Cassiopeia A: equation of state, superfluidity, and Joule heating
Bonanno, A; Burgio, G F; Urpin, V
2013-01-01
The thermomagnetic evolution of the young neutron star in Cassiopea A is studied by considering fast neutrino emission processes. In particular, we consider neutron star models obtained from the equation of state computed in the framework of the Brueckner-Bethe-Goldstone many-body theory and variational methods, and models obtained with the Akmal-Pandharipande-Ravenhall equation of state. It is shown that it is possible to explain a fast cooling regime as the one observed in the neutron star in Cassiopea A if the Joule heating produced by dissipation of the small-scale magnetic field in the crust is taken into account. We thus argue that it is difficult to put severe constraints on the superfluid gap if the Joule heating is considered.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
1986-01-01
1966). 3. Canale, R.P. and S.C. Chapra . Numerical Methods for Engineers with Personnel Computer Applications. New York: McGraw-Hill 509-533, ( 1985...This study looks at numerical % methods from an engineer’s view, a tool to be used in solving problems. This paper has given me much needed experience... numerical method in solving the transient heat conduction equation. The eigenvalue method was compared to five other numerical methods : Runge-Kutta
Heat flux solutions of the 13-moment approximation transport equations in a multispecies gas
Jian Wu [CRIRP, Henan Province (China); Taieb, C. [Centre de Recherche en Physique de l`Environnement (CRPE), Issy-les-Moulineaux (France)
1993-09-01
The authors study steady state heat flux equations by means of the 13-moment approximation for situations applicable to aeronomy and space plasmas. They compare their results with Fourier`s law applied to similar problems, to test validity conditions for it. They look at the flux of oxygen and hydrogen ions in the high-latitude ionosphere, and compare calculations with observations from EISCAT radar measurements. These plasma components are observed to have strongly non-Maxwellian distributions.
The heat flux from a relativistic kinetic equation with a simplified collision kernel
Sandoval-Villalbazo, A; García-Colin, L S
2009-01-01
We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.
ZHANG Hong-mei
2015-01-01
In this paper, a modified additive Schwarz finite difference algorithm is applied in the heat conduction equation of the compact difference scheme. The algorithm is on the basis of domain decomposition and the subspace correction. The basic train of thought is the introduction of the units function decomposition and reasonable distribution of the overlap of correction. The residual correction is conducted on each subspace while the computation is completely parallel. The theoretical analysis shows that this method is completely characterized by parallel.
Solution for a system of fractional heat equations of nanofluid along a wedge
Ibrahim Rabha W.
2015-01-01
Full Text Available In this article, authors set a new system of fractional heat equations of nanofluid along a wedge and establish the existence and uniqueness of a solution based on the Riemann-Liouville differential operators. Sufficient conditions on the parameters of the system are imposed. A numerical solution of the system is discussed, and applications are illustrated. The technique is based on the ability of Podlubny’s matrix in Matlab to formulate the operation of fractional calculus.
Rashidi, M. M.; Erfani, E.
2009-09-01
In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM [M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499] and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions.
On the Operator ⨁Bk Related to Bessel Heat Equation
Wanchak Satsanit
2010-01-01
Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.
Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions
Youtong Zhang; Changsong Zheng; Yongfeng Liu; Liang Shao; Chenhua Gou
2009-01-01
This paper presents two exact explicit solutions for the three dimensional dual-phase lag (DLP) heat conduction equation, during the derivation of which the method of trial and error and the authors' previous experiences are utilized. To the authors' knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth.In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Rajendra Karwa
2013-01-01
Full Text Available The paper presents results of thermal performance analysis of a solar air heater with v-down discrete rib roughness on the air flow side of the absorber plate, which supplies heated air for space heating applications. The air heater operates in a closed loop mode with inlet air at a fixed temperature of 295 K from the conditional space. The ambient temperature varied from 278 K to 288 K corresponding to the winter season of Western Rajasthan, India. The results of the analysis are presented in the form of performance plots, which can be utilized by a designer for calculating desired air flow rate at different ambient temperature and solar insolation values.
Sun, Hongbing; Feistel, Rainer; Koch, Manfred; Markoe, Andrew
2008-10-01
A set of fitted polynomial equations for calculating the physical variables density, entropy, heat capacity and potential temperature of a thermal saline fluid for a temperature range of 0-374 °C, pressure range of 0.1-100 MPa and absolute salinity range of 0-40 g/kg is established. The freshwater components of the equations are extracted from the recently released tabulated data of freshwater properties of Wagner and Pruß [2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387-535]. The salt water component of the equation is based on the near-linear relationship between density, salinity and specific heat capacity and is extracted from the data sets of Feistel [2003. A new extended Gibbs thermodynamic potential of seawater. Progress in Oceanography 58, 43-114], Bromley et al. [1970. Heat capacities and enthalpies of sea salt solutions to 200 °C. Journal of Chemical and Engineering Data 15, 246-253] and Grunberg [1970. Properties of sea water concentrates. In: Third International Symposium on Fresh Water from the Sea, vol. 1, pp. 31-39] in a temperature range 0-200 °C, practical salinity range 0-40, and varying pressure and is also calibrated by the data set of Millero et al. [1981. Summary of data treatment for the international high pressure equation of state for seawater. UNESCO Technical Papers in Marine Science 38, 99-192]. The freshwater and salt water components are combined to establish a workable multi-polynomial equation, whose coefficients were computed through standard linear regression analysis. The results obtained in this way for density, entropy and potential temperature are comparable with those of existing models, except that our new equations cover a wider temperature—(0-374 °C) than the traditional (0-40 °C) temperature range. One can apply these newly established equations to the calculation of in-situ or
Heat transfer analysis of skin during thermal therapy using thermal wave equation.
Kashcooli, Meisam; Salimpour, Mohammad Reza; Shirani, Ebrahim
2017-02-01
Specifying exact geometry of vessel network and its effect on temperature distribution in living tissues is one of the most complicated problems of the bioheat field. In this paper, the effects of blood vessels on temperature distribution in a skin tissue subjected to various thermal therapy conditions are investigated. Present model consists of counter-current multilevel vessel network embedded in a three-dimensional triple-layered skin structure. Branching angles of vessels are calculated using the physiological principle of minimum work. Length and diameter ratios are specified using length doubling rule and Cube law, respectively. By solving continuity, momentum and energy equations for blood flow and Pennes and modified Pennes bioheat equations for the tissue, temperature distributions in the tissue are measured. Effects of considering modified Pennes bioheat equation are investigated, comprehensively. It is also observed that blood has an impressive role in temperature distribution of the tissue, especially at high temperatures. The effects of different parameters such as boundary conditions, relaxation time, thermal properties of skin, metabolism and pulse heat flux on temperature distribution are investigated. Tremendous effect of boundary condition type at the lower boundary is noted. It seems that neither insulation nor constant temperature at this boundary can completely describe the real physical phenomena. It is expected that real temperature at the lower levels is somewhat between two predicted values. The effect of temperature on the thermal properties of skin tissue is considered. It is shown that considering temperature dependent values for thermal conductivity is important in the temperature distribution estimation of skin tissue; however, the effect of temperature dependent values for specific heat capacity is negligible. It is seen that considering modified Pennes equation in processes with high heat flux during low times is significant
Wang Yi
2008-01-01
The zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock is investigated. It is shown that when the heat ε→ 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier-Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].
Navier-Stokes turbine heat transfer predictions using two-equation turbulence
Ameri, Ali A.; Arnone, Andrea
1992-01-01
Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.
A simple numerical method for snowmelt simulation based on the equation of heat energy.
Stojković, Milan; Jaćimović, Nenad
2016-01-01
This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events.
Evaluating equations estimating change in swine feed intake during heat and cold stress.
White, Robin R; Miller, Phillip S; Hanigan, Mark D
2015-11-01
The objectives of this study were to evaluate heat stress feed intake models for growing swine using a data set assembled from the literature and to develop a series of new equations modeling the influence of the thermal environment and interactions between the thermal environmental and other factors on feed intake. A literature survey was conducted to identify studies assessing intake responses to temperature. The resulting data set comprised 35 studies containing 120 comparisons to thermoneutral intake. Intake as a fraction of thermoneutral intake (FFI) was the primary response variable, where a value of 1 represented no change from thermoneutral intake. The FFI predicted by NRC and a recent model from a meta-analysis (Renaudeau et al.,) were compared to observed values. New parameters for the NRC equation (NRCmod) were derived, and a series of new equations incorporating duration of exposure (TD), temperature cycling (TC), and floor type (TH) were also derived. Root-mean-square prediction error (RMSPE) and concordance correlation coefficients were used to evaluate all models. The RMSPE for the NRC model was 23.6 with mean and slope bias accounting for 12.6% and 51.1% of prediction error, respectively. The TD, TC, and TH models had reduced RMSPE compared with NRC: 12.9 for TD, 12.6 for TC, and 12.9 for TS. Substantial improvements were also made by refitting parameters (NRCmod; RMSPE 13.0%). In NRCmod, TD, TC, and TH, random error was the predominant source, accounting for over 97% of prediction error. The Renaudeau et al. model was also evaluated. Renaudeau et al. had relatively low RMSPE (22.3) for intake but higher RMSPE for FFI (22.6) than NRC, NRCmod, TD, TC, or TH. Additional parameters were derived for the Renaudeau et al. equation to account for housing system and diet characteristics. This adjustment reduced RMSPE of predicting feed intake (16.0) and FFI (16.3) and reduced systematic bias in the equation. This evaluation of equations highlights the
Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser
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.
Tatsii, R. M.; Pazen, O. Yu.
2016-03-01
A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.
García, Sergio; Trueba, Alfredo; Vega, Luis M; Madariaga, Ernesto
2016-11-01
The present study evaluated biofilm growth in AISI 316L stainless steel tubes for seawater-cooled exchanger-condensers that had four different arithmetic mean surface roughness values ranging from 0.14 μm to 1.2 μm. The results of fluid frictional resistance and heat transfer resistance regarding biofilm formation in the roughest surface showed increases of 28.2% and 19.1% respectively, compared with the smoothest surface. The biofilm thickness taken at the end of the experiment showed variations of up to 74% between the smoothest and roughest surfaces. The thermal efficiency of the heat transfer process in the tube with the roughest surface was 17.4% greater than that in the tube with the smoothest surface. The results suggest that the finish of the inner surfaces of the tubes in heat exchanger-condensers is critical for improving energy efficiency and avoiding biofilm adhesion. This may be utilised to reduce biofilm adhesion and growth in the design of heat exchanger-condensers.
Mark A. Dietenberger; Charles R. Boardman
2014-01-01
Several years ago the Laplace transform solutions of Luikovâs 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),...
S Pamuk; N Pamuk
2014-01-01
In this paper, we obtain the particular exact solutions of the two-dimensional heat and mass transfer equation with power-law temperature-dependent thermal con- ductivity using the Adomian's decomposition method...
Stochastic Heat Equation Limit of a (2 + 1)d Growth Model
Borodin, Alexei; Corwin, Ivan; Toninelli, Fabio Lucio
2017-03-01
We determine a {q to 1} limit of the two-dimensional q-Whittaker driven particle system on the torus studied previously in Corwin and Toninelli (Electron. Commun. Probab. 21(44):1-12, 2016). This has an interpretation as a (2 + 1)-dimensional stochastic interface growth model, which is believed to belong to the so-called anisotropic Kardar-Parisi-Zhang (KPZ) class. This limit falls into a general class of two-dimensional systems of driven linear SDEs which have stationary measures on gradients. Taking the number of particles to infinity we demonstrate Gaussian free field type fluctuations for the stationary measure. Considering the temporal evolution of the stationary measure, we determine that along characteristics, correlations are asymptotically given by those of the (2 + 1)-dimensional additive stochastic heat equation. This confirms (for this model) the prediction that the non-linearity for the anisotropic KPZ equation in (2 + 1)-dimension is irrelevant.
Effects of system-bath coupling on Photosynthetic heat engine: A polaron master equation approach
Qin, M; Zhao, X L; Yi, X X
2016-01-01
In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect charge transfer processes in Photosystem II reaction center (PSII RC) inspired quantum heat engine (QHE) model in a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in details. The results show a variety of dynamical behaviours. We interpret these results in terms of noise-assisted transport effect and dynamical localization which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization...
Stochastic Heat Equation Limit of a (2 + 1)d Growth Model
Borodin, Alexei; Corwin, Ivan; Toninelli, Fabio Lucio
2016-07-01
We determine a {q to 1} limit of the two-dimensional q-Whittaker driven particle system on the torus studied previously in Corwin and Toninelli (Electron. Commun. Probab. 21(44):1-12, 2016). This has an interpretation as a (2 + 1)-dimensional stochastic interface growth model, which is believed to belong to the so-called anisotropic Kardar-Parisi-Zhang (KPZ) class. This limit falls into a general class of two-dimensional systems of driven linear SDEs which have stationary measures on gradients. Taking the number of particles to infinity we demonstrate Gaussian free field type fluctuations for the stationary measure. Considering the temporal evolution of the stationary measure, we determine that along characteristics, correlations are asymptotically given by those of the (2 + 1)-dimensional additive stochastic heat equation. This confirms (for this model) the prediction that the non-linearity for the anisotropic KPZ equation in (2 + 1)-dimension is irrelevant.
Lie point symmetries of a general class of PDEs: The heat equation
Paliathanasis, Andronikos; Tsamparlis, Michael
2012-12-01
We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form {D}/{Ds}({Dxi(s)}/{Ds})=F(xi(s),x(s)) are subalgebras of the special projective and the homothetic algebra of the space respectively. We examine the possible extension of this result to partial differential equations (PDE) of the form Au-F(xi,u,ui)=0 where u(xi) and u stands for the second partial derivative. We find that if the coefficients A are independent of u(xi) then the Lie point symmetries of the PDE form a subgroup of the conformal symmetries of the metric defined by the coefficients A. We specialize the study to linear forms of F(xi,u,ui) and write the Lie symmetry conditions for this case. We apply this result to two cases. The wave equation in an inhomogeneous medium for which we derive the Lie symmetry vectors and check our results with those in the literature. Subsequently we consider the heat equation with a flux in an n-dimensional Riemannian space and show that the Lie symmetry algebra is a subalgebra of the homothetic algebra of the space. We discuss this result in the case of de Sitter space time and in flat space.
Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball
Le Minh Triet
2016-09-01
Full Text Available The backward heat problem (BHP has been researched by many authors in the last five decades; it consists in recovering the initial distribution from the final temperature data. There are some articles [1,2,3] related the axi-symmetric BHP in a disk but the study in spherical coordinates is rare. Therefore, we wish to study a backward problem for nonhomogenous heat equation associated with asymmetric final data in a ball. In this article, we modify the quasi-boundary value method to construct a stable approximate solution for this problem. As a result, we obtain regularized solution and a sharp estimates for its error. At the end, a numerical experiment is provided to illustrate our method.
Brear, D.J. [Power Reactor and Nuclear Fuel Development Corp., Oarai, Ibaraki (Japan). Oarai Engineering Center
1998-01-01
When liquid fuel makes contact with steel structure the liquid can freeze as a crust and the structure can melt at the surface. The melting and freezing processes that occur can influence the mode of fuel freezing and hence fuel relocation. Furthermore the temperature gradients established in the fuel and steel phases determine the rate at which heat is transferred from fuel to steel. In this memo the 1-D transient heat conduction equations are applied to the case of initially liquid UO{sub 2} brought into contact with solid steel using up-to-date materials properties. The solutions predict criteria for fuel crust formation and steel melting and provide a simple algorithm to determine the interface temperature when one or both of the materials is undergoing phase change. The predicted steel melting criterion is compared with available experimental results. (author)
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
On the generalized d'Alambert and Fourier heat equations
Dattoli, G. [ENEA, Centro Ricerche Frascati, Frascati, RM (Italy). Div. Fisica Applicata; Cesarano, C. [Ulm Univ., Ulm (Germany). Dept. of Mathematics
2000-07-01
In this paper is proposed a method employing the pseudo-hyperbolic functions. Hermite-Kampe' de Feriet polynomials and operational techniques, to find general solutions for extended forms of the D'Alambert and of the Fourier heat equations. [Italian] Si propone l'utilizzo di un metodo basato sulle funzioni pseudo iperboliche sui polinomi di Kampe' de Feriet e su tecniche operazionali per la ricerca di soluzioni generali delle equazioni di D'Alambert e Fourier generalizzate.
Hamid A. Jalab
2014-01-01
Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.
Xu Xinying
2012-01-01
In this paper; we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.
Measurement of the equation of state of solid-density copper heated with laser-accelerated protons
Feldman, S.; Dyer, G.; Kuk, D.; Ditmire, T.
2017-03-01
We present equation of state (EOS) measurements of solid-density copper heated to 5-10 eV. A copper sample was heated isochorically by hydrogen ions accelerated from an adjacent foil by a high intensity pulsed laser, and probed optically. The measured temperature and expansion are compared against simulations using the most up-to-date wide range EOS tables available.
Vandegehuchte, Maurits W; Steppe, Kathy
2012-05-01
Heat-pulse methods to determine sap flux density in trees are founded on the theory of heat conduction and heat convection in an isotropic medium. However, sapwood is clearly anisotropic, implying a difference in thermal conductivity along and across the grain, and hence necessitates the theory for an anisotropic medium. This difference in thermal conductivities, which can be up to 50%, is, however, not taken into account in the key equation leading to the currently available heat-pulse methods. Despite this major flaw, the methods remain theoretically correct as they are based on derivations of the key equation, ruling out any anisotropic aspects. The importance of specifying the thermal characteristics of the sapwood according to axial, tangential or radial direction is revealed as well as referring to and using the proper anisotropic theory in order to avoid confusion and misinterpretation of thermal properties when dealing with sap flux density measurements or erroneous results when modelling heat transport in sapwood.
Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation
Asma Yosaf
2016-01-01
Full Text Available The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.
Modeling Xenon Tank Pressurization using One-Dimensional Thermodynamic and Heat Transfer Equations
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.
Ibrahim Karatay
2012-01-01
Full Text Available We consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville fractional derivative of order α, where . The main purpose of this work is to extend the idea on Crank-Nicholson method to the time-fractional heat equations. We prove that the proposed method is unconditionally stable, and the numerical solution converges to the exact one with the order . Numerical experiments are carried out to support the theoretical claims.
Wenzel Wetting on Slippery Rough Surfaces
Stogin, Birgitt; Dai, Xianming; Wong, Tak-Sing
2015-11-01
Liquid repellency is an important surface property used in a wide range of applications including self-cleaning, anti-icing, anti-biofouling, and condensation heat transfer, and is characterized by apparent contact angle (θ*) and contact angle hysteresis (Δθ*). The Wenzel equation (1936) predicts θ* of liquids in the Wenzel state, and is one of the most fundamental equations in the wetting field. However, droplets in the Wenzel state on conventional rough surfaces exhibit large Δθ* , making it difficult to experimentally verify the model with precision. As a result, precise verification of the Wenzel wetting model has remained an open scientific question for the past 79 years. Here we introduce a new class of liquid-infused surfaces called slippery rough surfaces -- surfaces with significantly reduced Δθ* compared to conventional rough surfaces--and use them to experimentally assess the Wenzel equation with the highest precision to date. We acknowledge the funding support by National Science Foundation (NSF) CAREER Award #: 1351462 and Office of Navy Research MURI Award #: N00014-12-1-0875. Stogin acknowledges the support from the NSF Graduate Research Fellowship (Grant No. DGE1255832).
Conus, Daniel
2010-01-01
We study a family of non-linear stochastic heat equations in (1+1) dimensions, driven by the generator of a L\\'evy process and space-time white noise. We assume that the underlying L\\'evy process has finite exponential moments in a neighborhood of the origin and that the initial condition has exponential decay at infinity. Then we prove that under natural conditions on the non-linearity: (i) The absolute moments of the solution to our stochastic heat equation grow exponentially with time; and (ii) The distances to the origin of the farthest high peaks of those moments grow exactly linearly with time. Very little else seems to be known about the location of the high peaks of the solution to the non-linear stochastic heat equation. Finally, we show that these results extend to the stochastic wave equation driven by Laplacian.
Hu, Zhang-Mao; Tian, Hong; Li, Ben-Wen; Zhang, Wei; Yin, Yan-Shan; Ruan, Min; Chen, Dong-Lin
2017-10-01
The ray-effect is a major discretization error in the approximate solution method for the radiative transfer equation (RTE). To overcome this problem, the incident energy transfer equation (IETE) is proposed. The incident energy, instead of radiation intensity, is obtained by directly solving this new equation. Good numerical properties are found for the incident energy transfer equation. To show the properties of numerical solution, the collocation spectral method (CSM) is employed to solve the incident energy transfer equation. Three test cases are taken into account to verify the performance of the incident energy transfer equation. The result shows that the radiative heat flux obtained based on IETE is much more accurate than that based on RTE, which means that the IETE is very effective in eliminating the impacts of ray-effect on the heat flux. However, on the contrary, the radiative intensity obtained based on IETE is less accurate than that based on RTE due to the ray-effect. So, this equation is more suitable for those radiative heat transfer problems, in which the radiation heat flux and incident energy are needed rather than the radiation intensity.
Heat Transfer on a Film-Cooled Rotating Blade Using a Two Equation Turbulence Model
Garg, Vijay K.
1998-01-01
A three-dimensional Navier-Stokes code has been used to compare the heat transfer coefficient on a film-cooled, rotating turbine blade. The blade chosen is the ACE rotor with five rows containing 93 film cooling holes covering the entire span. This is the only film-cooled rotating blade over which experimental data is available for comparison. Over 2.278 million grid points are used to compute the flow over the blade including the tip clearance region, using Coakley's q-omega turbulence model. Results are also compared with those obtained by Garg and Abhari (1997) using the zero-equation Baldwin-Lomax (B-L) model. A reasonably good comparison with the experimental data is obtained on the suction surface for both the turbulence models. At the leading edge, the B-L model yields a better comparison than the q-omega model. On the pressure surface, however, the comparison between the experimental data and the prediction from either turbulence model is poor. A potential reason for the discrepancy on the pressure surface could be the presence of unsteady effects due to stator-rotor interaction in the experiments which are not modeled in the present computations. Prediction using the two-equation model is in general poorer than that using the zero-equation model, while the former requires at least 40% more computational resources.
Davies, Ian M.; Truman, Aubrey; Zhao, Huaizhong
2005-04-01
We study the inviscid limit, μ →0, of the stochastic viscous Burgers equation, for the velocity field vμ(x,t), t >0, x εRd, (∂vμ/∂t)+(vμ.∇)vμ=-∇c(x,t)-ε∇k(x,t)Ẇt+(μ2/2)Δvμ, for small ε, with vμ(x,0)≡∇S0(x) for some given S0, Ẇt representing white noise. Here we use the Hopf-Cole transformation, vμ=-μ2∇lnuμ, where uμ satisfies the stochastic heat equation of Stratonovich-type and the Feynmac-Kac Truman-Zhao formula for uμ, where dutμ(x )=[(μ2/2)Δutμ(x)+μ-2c(x,t)utμ(x)]dt+εμ-2k(x,t)utμ(x)∘dWt, with u0μ(x)=T0(x)exp(-S0(x)/μ2), S0 as before and T0 a smooth positive function. In an earlier paper, Davies, Truman, and Zhao [J. Math. Phys. 43, 3293 (2002)], an exact solution of the stochastic viscous Burgers equation was used to show how the formal "blow-up" of the Burgers velocity field occurs on random shockwaves for the vμ =0 solution of Burgers equation coinciding with the caustics of a corresponding Hamiltonian system with classical flow map Φ. Moreover, the uμ =0 solution of the stochastic heat equation has its wavefront determined by the behavior of the Hamilton principal function of the corresponding stochastic mechanics. This led in particular to the level surface of the minimizing Hamilton-Jacobi function developing cusps at points corresponding to points of intersection of the corresponding prelevel surface with the precaustic, "pre" denoting the preimage under Φ determined algebraically. These results were primarily of a geometrical nature. In this paper we consider small ε and derive the shape of the random shockwave for the inviscid limit of the stochastic Burgers velocity field and also give the equation determining the random wavefront for the stochastic heat equation both correct to first order in ε. In the case c (x,t)=1/2xTΩ2x, ∇k(x,t)=-a(t), we obtain the exact random shockwave and prove that its shape is unchanged by the addition of noise, it merely being displaced by a random Brownian vector
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef
2014-01-01
In this work the stability properties of a nonlinear partial differential equation (PDE) with state–dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers’ Equation. We show that for certain forms...
Conjugate heat and mass transfer in the lattice Boltzmann equation method.
Li, Like; Chen, Chen; Mei, Renwei; Klausner, James F
2014-04-01
An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved
N. Nesenchuk
2013-01-01
Full Text Available Directions pertaining to intensification of convective heat transfer in a soft heating device have been experimentally investigated in the paper and the most efficient one has been selected that is creation of artificial roughness on the device surface. The considered heating device for a heat supply system of a mobile object has been made of soft polymer material (polyvinyl chloride. Following evaluation results of heat exchange intensification a criteria equation has been obtained for calculation of external heat transfer with due account of heat transfer intensification.
Existence and non-existence results for a nonlinear heat equation
Canan Celik
2007-02-01
Full Text Available In this study, we consider the nonlinear heat equation $$displaylines{ u_{t}(x,t = Delta u(x,t + u(x,t^p quad hbox{in } Omega imes (0,T,cr Bu(x,t = 0 quad hbox{on } partialOmega imes (0,T,cr u(x,0 = u_0(x quad hbox{in } Omega,}$$ with Dirichlet and mixed boundary conditions, where $Omega subset mathbb{R}^n$ is a smooth bounded domain and $p = 1+ 2 /n$ is the critical exponent. For an initial condition $u_0 in L^1$, we prove the non-existence of local solution in $L^1$ for the mixed boundary condition. Our proof is based on comparison principle for Dirichlet and mixed boundary value problems. We also establish the global existence in $L^{1+epsilon}$ to the Dirichlet problem, for any fixed $epsilon > 0$ with $|u_0|_{1+epsilon}$ sufficiently small.
Optimal actuator location of minimum norm controls for heat equation with general controlled domain
Guo, Bao-Zhu; Xu, Yashan; Yang, Dong-Hui
2016-09-01
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L2 (Ω × (0 , T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks.
Simple equation for estimating actual evapotranspiration using heat units for wheat in arid regions
M.A. Salama
2015-07-01
Application of treatment (B resulted in highly significant increase in yield production of Gemmeza10 and Misr2 as compared to treatment (A. Grain yield of different wheat varieties grown under treatment (B could be ranked in the following descending order: Misr2 > Gemmeza10 > Sids12. While under treatment (A it could be arranged in the following descending order: Misr2 > Sids12 > Gemmeza10. On the other hand, the overall means indicated non-significant difference between all wheat verities. The highest values of water and irrigation use efficiency as well as heat use efficiency were obtained with treatment (B. The equation used in the present study is available to estimate ETa under arid climate with drip irrigation system.
Pacheco-Vega, Arturo
2016-09-01
In this work a new set of correlation equations is developed and introduced to accurately describe the thermal performance of compact heat exchangers with possible condensation. The feasible operating conditions for the thermal system correspond to dry- surface, dropwise condensation, and film condensation. Using a prescribed form for each condition, a global regression analysis for the best-fit correlation to experimental data is carried out with a simulated annealing optimization technique. The experimental data were taken from the literature and algorithmically classified into three groups -related to the possible operating conditions- with a previously-introduced Gaussian-mixture-based methodology. Prior to their use in the analysis, the correct data classification was assessed and confirmed via artificial neural networks. Predictions from the correlations obtained for the different conditions are within the uncertainty of the experiments and substantially more accurate than those commonly used.
Blow-up in p-Laplacian heat equations with nonlinear boundary conditions
Ding, Juntang; Shen, Xuhui
2016-10-01
In this paper, we investigate the blow-up of solutions to the following p-Laplacian heat equations with nonlinear boundary conditions: {l@{quad}l}(h(u))_t =nabla\\cdot(|nabla u|pnabla u)+k(t)f(u) &{in } Ω×(0,t^{*}), |nabla u|ppartial u/partial n=g(u) &on partialΩ×(0,t^{*}), u(x,0)=u0(x) ≥ 0 & {in } overline{Ω},. where {p ≥ 0} and {Ω} is a bounded convex domain in {RN}, {N ≥ 2} with smooth boundary {partialΩ}. By constructing suitable auxiliary functions and using a first-order differential inequality technique, we establish the conditions on the nonlinearities and data to ensure that the solution u( x, t) blows up at some finite time. Moreover, the upper and lower bounds for the blow-up time, when blow-up does occur, are obtained.
Kamajaya, Ketut; Umar, Efrizon; Sudjatmi, K. S.
2012-06-01
This study focused on natural convection heat transfer using a vertical rectangular sub-channel and water as the coolant fluid. To conduct this study has been made pipe heaters are equipped with thermocouples. Each heater is equipped with five thermocouples along the heating pipes. The diameter of each heater is 2.54 cm and 45 cm in length. The distance between the central heating and the pitch is 29.5 cm. Test equipment is equipped with a primary cooling system, a secondary cooling system and a heat exchanger. The purpose of this study is to obtain new empirical correlations equations of the vertical rectangular sub-channel, especially for the natural convection heat transfer within a bundle of vertical cylinders rectangular arrangement sub-channels. The empirical correlation equation can support the thermo-hydraulic analysis of research nuclear reactors that utilize cylindrical fuel rods, and also can be used in designing of baffle-free vertical shell and tube heat exchangers. The results of this study that the empirical correlation equations of natural convection heat transfer coefficients with rectangular arrangement is Nu = 6.3357 (Ra.Dh/x)0.0740.
Parallelization of 2-D IADE-DY Scheme on Geranium Cadcam Cluster for Heat Equation
Simon Uzezi Ewedafe
2013-06-01
Full Text Available A parallel implementation of the Iterative Alternating Direction Explicit method by D’Yakonov (IADE-DY for solving 2-D heat equation on a distributed system of Geranium Cadcam cluster (GCC using the Message Passing Interface (MPI is presented. The implementation of the scheduling of n tri-diagonal system of equations with the above method was used to show improvement on speedup, effectiveness, and efficiency. The Master/Worker paradigm and Single Program Multiple Data (SPMD model is employed to manage the whole computation based on the use of domain decomposition. The completion of the execution can need task recovery and favorable configuration. The above mentioned details consist of a main report about the numerical validation of the parallelization through simulation to demonstrate the proposed method effectiveness on the cluster system. It was found that the rate of convergence decreases as the number of processors increases. The result of this paper suggests that the 2-D IADE-DY scheme is a good approach to solving problems, particularly when it is simulation with more processors.
Two-Equation Turbulence Models for Prediction of Heat Transfer on a Transonic Turbine Blade
Garg, Vijay K.; Ameri, Ali A.; Gaugler, R. E. (Technical Monitor)
2001-01-01
Two versions of the two-equation k-omega model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier-Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k-w models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multiblock grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.
On the Stochastic Heat Equation with Spatially-Colored Random forcing
Foondun, Mohammud
2010-01-01
We consider the stochastic heat equation of the following form \\frac{\\partial}{\\partial t}u_t(x) = (\\sL u_t)(x) +b(u_t(x)) + \\sigma(u_t(x))\\dot{F}_t(x)\\quad \\text{for}t>0, x\\in \\R^d, where $\\sL$ is the generator of a L\\'evy process and $\\dot{F}$ is a spatially-colored, temporally white, gaussian noise. We will be concerned mainly with the long-term behavior of the mild solution to this stochastic PDE. For the most part, we work under the assumptions that the initial data $u_0$ is a bounded and measurable function and $\\sigma$ is nonconstant and Lipschitz continuous. In this case, we find conditions under which the preceding stochastic PDE admits a unique solution which is also \\emph{weakly intermittent}. In addition, we study the same equation in the case that $\\mathcal{L}u$ is replaced by its massive/dispersive analogue $\\mathcal{L}u-\\lambda u$ where $\\lambda\\in\\R$. Furthermore, we extend our analysis to the case that the initial data $u_0$ is a measure rather than a function. As it turns out, the stochastic...
Numerical solutions for the one-dimensional heat-conduction equation using a spreadsheet
Gvirtzman, Zohar; Garfunkel, Zvi
1996-12-01
We show how to use a spreadsheet to calculate numerical solutions of the one-dimensional time-dependent heat-conduction equation. We find the spreadsheet to be a practical tool for numerical calculations, because the algorithms can be implemented simply and quickly without complicated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mathematical operations. We implement the explicit and the Crank-Nicholson forms of the finite-difference approximations and discuss the geological applications of both methods. We also show how to adjust these two algorithms to a nonhomogeneous lithosphere in which the thermal properties (thermal conductivity, density, and radioactive heat generation) change from the upper crust to the lower crust and to the mantle. The solution is presented in a way that can fit any spreadsheet (Lotus-123, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macros that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix.
A.K.Alomari; M.S.M.Noorani; R.Nazar
2008-01-01
We employ the homotopy analysis method(HAM)to obtain approximate analytical solutions to the heat-like and wave-like equations.The HAM contains the auxiliary parameter h,which provides a convenient way of controlling the convergence region of series solutions.The analysisis accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems.The results obtained prove that HAM is very effectiw and simple with less error than the Adomian decomposition method and the variational iteration method.
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.
Duan, Ran; Guo, Ai; Zhu, Changjiang
2017-04-01
We obtain existence and uniqueness of global strong solution to one-dimensional compressible Navier-Stokes equations for ideal polytropic gas flow, with density dependent viscosity and temperature dependent heat conductivity under stress-free and thermally insulated boundary conditions. Here we assume viscosity coefficient μ (ρ) = 1 +ρα and heat conductivity coefficient κ (θ) =θβ for all α ∈ [ 0 , ∞) and β ∈ (0 , + ∞).
Singh, Brajesh K; Srivastava, Vineet K
2015-04-01
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
Ai-Min Yang
2014-01-01
Full Text Available The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.
Baker, Charles
2012-01-01
One method available to prove the Schauder estimates is Neil Trudinger's method of mollification. In the case of second order elliptic equations, the method requires little more than mollification and the solid mean value inequality for subharmonic functions. Our goal in this article is show how the mean value property of subsolutions of the heat equation can be used in a similar fashion as the solid mean value inequality for subharmonic functions in Trudinger's original elliptic treatment, providing a relatively simple derivation of the interior Schauder estimate for second order parabolic equations.
Shukla Shailndra Kumar
2013-01-01
Full Text Available This paper presents a theoretical analysis of thermal storage unit using phase change material (PCM as storage medium. Storage unit consists of parallel rectangular channels for the air flow which are separated by phase change storage material. The purpose of storage unit is to absorb the night coolness and to provide cooled air at comfort temperature during day time in summer season. MATLsimulation tool has been used to compute the air temperature variation with location as well as time, charging and discharging time of storage unit. Phase change material used for analysis is selected in such a way that it’s Melting point lies between comfort temperature and minimum night ambient temperatures. The air flow rate needed for charging of PCM is approximately four times greater than the flow rate required during day time to achieve comfort temperature for approximately eight hours, due to limited summer night time (only eight hours. The length of storage unit for which NTU value is greater than or equal to five will give the exit air temperature equal to PCM temperature for the case of latent heat utilization. It is found that artificial roughness on the duct surface effectively reduces the length of storage unit in the cost of some extra pressure drop across the duct.
Abdulla Ugur G
2005-01-01
Full Text Available This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of ( for the diffusion (or heat equation. The result implies asymptotic probability law for the standard -dimensional Brownian motion.
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Green's function of the heat equation with periodic and antiperiodic boundary conditions
Imanbaev, Nurlan; Erzhanov, Nurzhan
2016-12-01
In this work a non-local initial-boundary value problem for a non-homogeneous one-dimensional heat equation is con-sidered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A non-local periodic boundary condition with respect to a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the non-local initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions
Collot, Charles; Merle, Frank; Raphaël, Pierre
2016-11-01
We consider the energy critical semilinear heat equation partial_tu = Δ u + |u|^{4/d-2}u, quad x in R^d and give a complete classification of the flow near the ground state solitary wave Q(x) = 1/(1+{|x|^2/{d(d-2)})^{d-2/2}} in dimension {d ≥ 7} , in the energy critical topology and without radial symmetry assumption. Given an initial data {Q + ɛ_0} with {|nabla ɛ_0|_{L^2} ≪ 1} , the solution either blows up in the ODE type I regime, or dissipates, and these two open sets are separated by a codimension one set of solutions asymptotically attracted by the solitary wave. In particular, non self similar type II blow up is ruled out in dimension {d ≥ 7} near the solitary wave even though it is known to occur in smaller dimensions (Schweyer, J Funct Anal 263(12):3922-3983, 2012). Our proof is based on sole energy estimates deeply connected to Martel et al. (Acta Math 212(1):59-140, 2014) and draws a route map for the classification of the flow near the solitary wave in the energy critical setting. A by-product of our method is the classification of minimal elements around Q belonging to the unstable manifold.
Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation
Michael S. Hughes
2015-05-01
Full Text Available Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information”, as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined as the mean variation (i.e., observed change divided by mean variance (i.e., noise. Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an “optimal” reference for the joint entropy emerges, which also has been validated in several studies.
Shaojun Xia, Lingen Chen, Fengrui Sun
2012-01-01
Full Text Available A multistage endoreversible Carnot heat engine system operating with a finite thermal capacity high-temperature black photon fluid reservoir and the heat transfer law is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the general optimization results, the analytical solution for the case with pseudo-Newtonian heat transfer law is further obtained. Since there are no analytical solutions for the radiative heat transfer law, the continuous HJB equations are discretized and the dynamic programming (DP algorithm is adopted to obtain the complete numerical solutions, and the relationships among the maximum power output of the system, the process period and the fluid temperatures are discussed in detail. The optimization results obtained for the radiative heat transfer law are also compared with those obtained for pseudo-Newtonian heat transfer law and stage-by-stage optimization strategy. The obtained results can provide some theoretical guidelines for the optimal designs and operations of solar energy conversion and transfer systems.
Stochastic control with rough paths
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
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.
Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v = kSt R2/3 I1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughn...
Gülcan Özkum
2013-01-01
Full Text Available The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM. We apply ADM to determine the continuous right hand side functions fx and ft in the heat-like diffusion equations Dtαux,t=hxuxxx,t+fx and Dtαux,t=hxuxxx,t+ft, respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
无
2002-01-01
The apparent activation energies and frequency factors of the double reversible transformations occurring in heating CuZnAlMnNi shape memory alloy (SMA) were deduced as AEx .M = 62.597 8 kJ/mol, AEm.A 153.92 kJ'mol,Ax-m = 5.223 2 × 109s 1, and AM-A = 2.325 1 × l023 s 1, respectively. The kinetic equations of the two transfornations during heating were established simultaneously.
Aursand, Eskil; Lervåg, Karl Yngve; Lund, Halvor
2016-01-01
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.
Rough function model and rough membership function
Wang Yun; Guan Yanyong; Huang Zhiqin
2008-01-01
Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower (upper) approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
Ioku, Norisuke, E-mail: ioku@ehime-u.ac.jp [Ehime University, Graduate School of Science Engineering (Japan); Ruf, Bernhard; Terraneo, Elide [Università degli Studi di Milano, Dipartimento di Matematica “F. Enriques” (Italy)
2015-12-15
We consider a semilinear heat equation with exponential nonlinearity in ℝ{sup 2}. We prove that local solutions do not exist for certain data in the Orlicz space exp L{sup 2}(ℝ{sup 2}), even though a small data global existence result holds in the same space exp L{sup 2}(ℝ{sup 2}). Moreover, some suitable subclass of exp L{sup 2}(ℝ{sup 2}) for local existence and uniqueness is proposed.
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations
J. Bajars (Janis); J.E. Frank (Jason); B.J. Leimkuhler (Ben)
2013-01-01
textabstractThermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers–Hopf or Korteweg–de Vries equation, we introduce auxiliary variables and stochastic
The Effect of Surface Roughness on Thermohydrodynamic Performance in Misaligned Journal Bearings
Mustafa Mohammed K.
2010-01-01
Full Text Available In this work an approach has been developed to investigate the influence of surface roughness on thermohydrodynamic performance in aligned and misaligned journal bearings by considering an average flow model and deriving the shear flow factor for various roughness configurations, similar to the pressure flow factor. An average Reynolds equation for rough surfaces is defined in term of pressure and shear flow factors, which can be obtained by numerical flow simulation, though the use of measured or numerically generated rough surfaces. Reynolds, heat conduction and energy equations are solved simultaneously by using a suitable numerical technique (Finite Difference Method to obtain the pressure and temperature distribution through the oil film thickness of the journal bearing. These equations are obtained for isotropic surfaces and for surfaces with directional patterns. The flow factors for these surfaces are expressed as empirical relations in term of normalized oil film thickness (h/σ and surface characteristic (γ defined as the ratio of x and z correlation lengths . The results of this approach showed increase in load carrying capacity and maximum pressure and decrease in maximum temperature in the case of stationary surface roughness (rough bearing and smooth journal with transverse pattern. The results obtained through this work have been compared with that published by other works and found to be in a good agreement.
Garg, Vijay K.; Ameri, Ali A.
1997-01-01
A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely, the VKI rotor with six rows of cooling holes, including three rows on the shower head and the C3X vane with nine rows of holes, including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence model specifically, Coakley's q-omega model, Chien's k-epsilon model and Wilcox's k-omega model with Menter's modifications, have been compared with the experimental data of Camci and Arts for the VKI rotor, and of Hylton et al. for the C3X vane along with predictions using the Baldwin-Lomar (B-L) model taken from Garg and Gaugler. It is found that for the cases considered here the two equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooled holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-omega and k-epsilon models need 40% more computer time than the B-L model the k-omega model requires at least 65% more time because of the slower rate of convergence. It is found that the heat transfer coefficient exhibit a strong spanwise as well as streamwise variation for both blades and all turbulence models.
Simplified Approach to Predicting Rough Surface Transition
Boyle, Robert J.; Stripf, Matthias
2009-01-01
Turbine vane heat transfer predictions are given for smooth and rough vanes where the experimental data show transition moving forward on the vane as the surface roughness physical height increases. Consiste nt with smooth vane heat transfer, the transition moves forward for a fixed roughness height as the Reynolds number increases. Comparison s are presented with published experimental data. Some of the data ar e for a regular roughness geometry with a range of roughness heights, Reynolds numbers, and inlet turbulence intensities. The approach ta ken in this analysis is to treat the roughness in a statistical sense , consistent with what would be obtained from blades measured after e xposure to actual engine environments. An approach is given to determ ine the equivalent sand grain roughness from the statistics of the re gular geometry. This approach is guided by the experimental data. A roughness transition criterion is developed, and comparisons are made with experimental data over the entire range of experimental test co nditions. Additional comparisons are made with experimental heat tran sfer data, where the roughness geometries are both regular as well a s statistical. Using the developed analysis, heat transfer calculatio ns are presented for the second stage vane of a high pressure turbine at hypothetical engine conditions.
A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media
Salama, Amgad
2013-03-20
In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described. Copyright © 2013 by ASME.
Fuel rod model based on Non-Fourier heat conduction equation
Espinosa-Paredes, G. [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico DF., CP 09340 (Mexico)], E-mail: gepe@xanum.uam.mx; Espinosa-Martinez, E-G. [Retorno Quebec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor. (Mexico)
2009-05-15
In this paper we explore the applicability of a fuel rod mathematical model based on Non-Fourier transient heat conduction as constitutive law for the Light Water Reactors transient analysis (LWRs). In the classical theory of diffusion, Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The motivation for this research was to eliminate the paradox of an infinite thermal wave speed. The time-dependent heat sources were considered in the fuel rod heat transfer model. The close of the Main Steam Isolated Valves (MSIV) transient in a Boiling Water Reactor (BWR) was analyzed by different relaxation times. The results show that for long-times the heat fluxes on the clad surface under Non-Fourier approach can be important, while for short-times and from the engineering point of view the changes are very small. Some results from transient calculations are examined.
Exact solutions of time-fractional heat conduction equation by the fractional complex transform
Li Zheng-Biao
2012-01-01
Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.
ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS
Tan Zhong; Wu Guochun
2011-01-01
In this paper,we consider the heat flow for the H-system with constant mean curvature in higher dimensions.We give sufficient conditions on the initial data such that the heat flow develops finite time singularity.We also provide a new set of initial data to guarantee the existence of global regular solution to the heat flow,that converges to zero in W1,n with the decay rate t2/2-n as time goes to infinity.
Nucleate boiling heat transfer
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)
Rough Sets in Approximate Solution Space
Hui Sun; Wei Tian; Qing Liu
2006-01-01
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and in complete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set. A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
Leontev, K. L.
1981-07-01
An expression is obtained for heat capacity differences of materials at a constant pressure and volume, on the basis of the rigorous thermodynamic equation (Kittel, 1976), and by using the Grueneisen law (Kikoin and Kikoin, 1976) of constancy of the ratio of the cubic expansion coefficient to the molar heat capacity. Conditions are determined, where the empirical Nernst and Lindemann (Filippov, 1967) equation is regarded as rigorous.
Application of the heat-balance and refined integral methods to the Korteweg-de Vries equation
Myers Timothy G.
2009-01-01
Full Text Available In this paper we consider approximate travelling wave solutions to the Korteweg-de Vries equation. The heat-balance integral method is first applied to the problem, using two different quartic approximating functions, and then the refined integral method is investigated. We examine two types of solution, chosen by matching the wave speed to that of the exact solution and by imposing the same area. The first set of solutions is generally better with an error that is fixed in time. The second set of solutions has an error that grows with time. This is shown to be due to slight discrepancies in the wave speed.
Zhensheng GAO; Zhong TAN; Guochun WU
2014-01-01
In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.
Lodi, C.; Bacher, Peder; Cipriano, J.
2012-01-01
This paper deals with grey-box modelling of the energy transfer of a double skin Building Integrated Photovoltaic (BIPV) system. Grey-box models are based on a combination of prior physical knowledge and statistics, which enable identification of the unknown parameters in the system and accurate...... and heat transfer coefficients is fundamental in order to improve the thermo-electrical production.The considered grey-box models are composed of a set of continuous time stochastic differential equations, holding the physical description of the system, combined with a set of discrete time measurement...
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
Lie point symmetries of a general class of PDEs: The heat equation
Paliathanasis, Andronikos; Tsamparlis, Michael
2012-01-01
We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form (D/(Ds))(((Dx^{i}(s))/(Ds)))=F(x^{i}(s),x^{j}(s)) are subalgebras of the special projective and the homothetic algebra of the space respectively. We examine the possible extension of this result to partial differential equations (PDE) of the form A^{ij}u_{ij}-F(x^{i},u,u_{i})=0 where u(x^{i}) and u_{ij} stands for the second partial derivative. We find tha...
Ritchie, R.H.; Sakakura, A.Y.
1956-01-01
The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.
Modelling the heat dynamics of a building using stochastic differential equations
Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik
2000-01-01
estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
Galerkin and weighted Galerkin methods for a forward-backward heat equation
Lu, H.
1997-01-01
Galerkin and weighted Galerkin methods are proposed for the numerical solution of parabolic partial differential equations where the diffusion coefficient takes different signs. The approach is based on a simultaneous discretization of space and time variables by using continuous finite element
Davies, I M; Zhao, H
2004-01-01
We study the inviscid limit, $\\mu\\to 0$, of the stochastic viscous Burgers equation, for the velocity field $v^{\\mu}(x,t)$, $t>0$, $x\\in\\mathbb R^d$,\\frac{\\partial{v^{\\mu}}}{\\partial{t}} + (v^{\\mu}\\cdot\
Malherbe, J.M. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1963-02-15
The effect of various types of roughness on the wall of an axial tube in an annular space of 15-25 mm cooled by an air-flow has been studied in the case of steady turbulence. Roughness of the type 'disrupter of the boundary layer' was set up using triangular threads of 0.2 to 0.4 mm thickness machined in the tube itself, or brass or glass wire wound on a smooth tube. Tests were also carried out using the roughness provided by regularly spaced pyramids 0.4 mm high. The results obtained showed that the heat exchange increased because of the presence of this roughness. A maximum in the heat exchange and pressure-drop coefficients was observed when the pitch equals about eight times the height of the thread. An analytical method has been developed and experiments have been carried out in which the two walls of the annular space were heated in such a way as to transmit unequal heat flows. The region considered is limited to Reynolds's numbers of between 5 X 10{sup 3} and 5 x 10{sup 4} and wall temperatures of under 250 deg C. (author) [French] L'effet de diverses rugosites sur la paroi du tube central d'un espace annulaire de diametre 15-25 mm refroidi par un ecoulement d'air a ete etudie en regime turbulent etabli. Des rugosites du type 'interrupteur de couche limite' etaient realisees au moyen de filets triangulaires, de 0,2 a 0,4 mm de hauteur usines dans l'epaisseur du tube ou de fils de laiton, ou de verre, enroules sur un tube lisse. Les essais ont porte egalement sur des rugosites constituees par des pyramides de 0,4 mm de hauteur et regulierement espacees. Les resultats obtenus ont mis en evidence une augmentation de transfert de chaleur due a la presence des elements rugueux. L'existence d'un maximum pour les coefficients d'echange thermique et de perte de charge a ete constate lorsque le pas atteint huit fois la hauteur des rugosites. Une methode analytique a ete etablie et des experiences ont ete
Determination temperature of a heat equation from the final value data
Tuan H. Nguyen
2012-08-01
Full Text Available We introduce the truncation method for solving a backward heat conduction problem. For this method, we give the stability analysis with new error estimates. Meanwhile, we investigate the roles of regularization parameters in these two methods. These estimates prove that our method is effective.
1983-02-01
Anthony Ralston and Herbert S. Wilf. New York: John Wiley and Sons, Inc., 95-115, 1967. 15. Patankar, Suhas V.. Numerical Heat Transfer and Fluid Flow...Series in Computational Methods in Mechanics and Thermal Sciences. New York: McGraw- Hill Book Company, 1980. 16. Patankar, Suhas V. and B. R
Svetushkov, N. N.
2016-11-01
The paper deals with a numerical algorithm to reduce the overall system of integral equations describing the heat transfer process at any geometrically complex area (both twodimensional and three-dimensional), to the iterative solution of a system of independent onedimensional integral equations. This approach has been called "string method" and has been used to solve a number of applications, including the problem of the detonation wave front for the calculation of heat loads in pulse detonation engines. In this approach "the strings" are a set of limited segments parallel to the coordinate axes, into which the whole solving area is divided (similar to the way the strings are arranged in a tennis racket). Unlike other grid methods where often for finding solutions, the values of the desired function in the region located around a specific central point here in each iteration step is determined by the solution throughout the length of the one-dimensional "string", which connects the two end points and set them values and determine the temperature distribution along all the strings in the first step of an iterative procedure.
A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations
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.
Singular solutions to the heat equations with nonlinear absorption and Hardy potentials
Liskevich, Vitali; Sobol, Zeev
2010-01-01
We study the existence and nonexistence of singular solutions to the equation $u_t-\\Delta u - \\frac{\\kappa}{|x|^2}u+|x|^\\alpha u|u|^{p-1}=0$, $p>1$, in $\\R^N\\times[0,\\infty)$, $N\\ge 3$, with a singularity at the point $(0,0)$, that is, nonnegative solutions satisfying $u(x,0)=0$ for $x\
The heat equation source determination for the case of non-smooth boundary and initial conditions
Solovi’ev, V. V.; Tkachenko, D. S.
2017-01-01
An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.
Meshless Least-Squares Method for Solving the Steady-State Heat Conduction Equation
LIU Yan; ZHANG Xiong; LU Mingwan
2005-01-01
The meshless weighted least-squares (MWLS) method is a pure meshless method that combines the moving least-squares approximation scheme and least-square discretization. Previous studies of the MWLS method for elastostatics and wave propagation problems have shown that the MWLS method possesses several advantages, such as high accuracy, high convergence rate, good stability, and high computational efficiency. In this paper, the MWLS method is extended to heat conduction problems. The MWLS computational parameters are chosen based on a thorough numerical study of 1-dimensional problems. Several 2-dimensional examples show that the MWLS method is much faster than the element free Galerkin method (EFGM), while the accuracy of the MWLS method is close to, or even better than the EFGM. These numerical results demonstrate that the MWLS method has good potential for numerical analyses of heat transfer problems.
Respiration Rate Predictive Equation and Effective Heat Stress Relief Ways for Hanwoo Steers
Gutierrez, Winson-Montanez; Oh, Taek-Kuen; Kim, Dong-Hyeok; Lee, Jin-Ju; Kim, Suk; Min, Wong; Lee, Seung-Joo; Kim, Byeong-Woo; Chang, Hong-Hee; Chikushi, Jiro
2012-01-01
Normalizing respiration rate in heat–stress challenged cattle during summer season is very important. In this study, we investigated the contribution of different thermal factors such as skin temperature, dew–point temperature, solar radiation, dry–bulb temperature and wind speed on its influence to the respiration rate dynamics of 45 Hanwoo steers in 2010. Secondly, the heat insulation efficiencies of the three kinds of roofing materials such as sandwich panel (SP), master panel (MP), and fi...
Wei-zhong Dai; Raja Nassar
2003-01-01
Heat transport at the microscale is of vital importance in microtechnology applications.The heat transport equation is different from the traditional heat transport equation sincea second order derivative of temperature with respect to time and a third-order mixedderivative of temperature with respect to space and time are introduced. In this study,we develop a hybrid finite element-finite difference (FE-FD) scheme with two levels intime for the three dimensional heat transport equation in a cylindrical thin film with sub-microscale thickness. It is shown that the scheme is unconditionally stable. The scheme isthen employed to obtain the temperature rise in a sub-microscale cylindrical gold film. Themethod can be applied to obtain the temperature rise in any thin films with sub-microscalethickness, where the geometry in the planar direction is arbitrary.
Global representations of the Heat and Schrodinger equation with singular potential
Jose A. Franco
2013-07-01
Full Text Available The n-dimensional Schrodinger equation with a singular potential $V_lambda(x=lambda |x|^{-2}$ is studied. Its solution space is studied as a global representation of $widetilde{SL(2,mathbb{R}}imes O(n$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for $lambda$ so that this space is non-empty. The direct sum of solution spaces over such admissible values of $lambda$ is studied as a representation of the (2n+1-dimensional Heisenberg group.
Solution of the Boltzmann Equation for Electrons in Laser-Heated Metals
Pietanza, L. D.; Colonna, G.; Capitelli, M.
2005-05-01
A kinetic study of the electron relaxation dynamic inside a noble metal film (Ag) subjected to a femtosecond laser pulse has been performed. A time dependent numerical algorithm for the solution of the Boltzmann equations for electrons and phonons inside the film has been developped, considering electron-electron and electron-phonon collisions and the laser perturbation. The dependence of electron-electron and electron-phonon characteristic time-scales on the screening parameter values has been investigated. Electron-electron relaxation times are also compared with experimental data obtained through time-resolved two-photon photoemission technique.
Heat Transfer on a Film-Cooled Rotating Blade Using a Two-Equation Turbulence Model
Vijay K Garg
1998-01-01
A three-dimensional Navier–Stokes code has been used to compare the heat transfer coefficient on a film-cooled, rotating turbine blade. The blade chosen is the ACE rotor with five rows containing 93 film cooling holes covering the entire span. This is the only filmcooled rotating blade over which experimental data is available for comparison. Over 2.278 million grid points are used to compute the flow over the blade including the tip clearance region, using Coakley's q-ω turbulence model. Res...
Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation
Cortazar, C.; Elgueta, M. [Universidad Catolica, Santiago (Chile); Felmer, P. [Universidad de Chile, Santiago (Chile)
1996-12-31
We will consider in this paper a semilinear elliptic equation {triangle}u + f(u) = 0 in {Omega}, (1.5) where the function f is locally Lipschitz in (0,{infinity}) and continuous in (0,{infinity}). We study symmetry properties of nonnegative solutions of this equation in two different situations: first we assume {Omega} = IR{sup N}, and second we consider {Omega} {ne} IR{sup N} and we provide (1.5) with overdetermined boundary conditions. Next we describe our results in the first case, that is, when {Omega} = IR{sup N}. We will consider the following hypothesis on the nonlinear function f (F) f(0) {le} 0, f continuous in (0,+{infinity}), locally Lipschitz in (0,+{infinity}) and there exists {alpha} > 0 so that f is strictly decreasing in [0,{alpha}]. We note that the support of a solution of (1.5) is not known a priori and so we have in fact a free boundary involved. Our goal is to determine the shape of this support and the symmetry properties of the solution.
Efficient high-order immersed interface methods for heat equations with interfaces
刘建康; 郑洲顺
2014-01-01
An efficient high-order immersed interface method (IIM) is proposed to solve two-dimensional (2D) heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact (HOC) difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit (ADI) scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
Denisov, A. M.
2016-10-01
An initial-boundary value problem for the two-dimensional heat equation with a source is considered. The source is the sum of two unknown functions of spatial variables multiplied by exponentially decaying functions of time. The inverse problem is stated of determining two unknown functions of spatial variables from additional information on the solution of the initial-boundary value problem, which is a function of time and one of the spatial variables. It is shown that, in the general case, this inverse problem has an infinite set of solutions. It is proved that the solution of the inverse problem is unique in the class of sufficiently smooth compactly supported functions such that the supports of the unknown functions do not intersect. This result is extended to the case of a source involving an arbitrary finite number of unknown functions of spatial variables multiplied by exponentially decaying functions of time.
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.
O S IYIOLA; F D ZAMAN
2016-10-01
In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Kolesnichenko, A. V.
2010-08-01
This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism, this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects. Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002-2004; Kolesnichenko and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative
Boudesocque-Dubois, C.; Clarisse, J.M
2007-07-01
In the context of linear perturbation computations of planar or spherically symmetric flows, we propose numerical methods, in Lagrangian coordinates, for integrating the one-dimensional gas dynamics equations with nonlinear heat conduction and their linear perturbations. Numerical results are presented for different configurations, with or without flow motion. (authors)
Surface Roughness Effects on Vortex Torque of Air Supported Gyroscope
LIANG Yingchun; LIU Jingshi; SUN Yazhou; LU Lihua
2011-01-01
In order to improve the drift precision of air supported gyroscope, effects of surface roughness magnitude and direction on vortex torque of air supported gyroscope are studied. Based on Christensen's rough surface stochastic model and consistency transformation method, Reynolds equation of air supported gyroscope containing surface roughness information is established.Also effects of mathematical models of main machining errors on vortex torque are established. By using finite element method,the Reynolds equation is solved numerically and the vortex torque in the presence of machining errors and surface roughness is calculated. The results show that surface roughness of slit has a significant effect on vortex torque. Transverse surface roughness makes vortex torque greater, while longitudinal surface roughness makes vortex torque smaller. The maximal difference approaches 11.4％ during the range analyzed in this article. However surface roughness of journal influences vortex torque insignificantly. The research is of great significance for designing and manufacturing air supported gyroscope and predicting its performance.
Adriana C. Briozzo
2006-02-01
Full Text Available We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.
张薇; 刘娟; 李长福
2012-01-01
Objective:To study the staining of heat-cured base resin with different surface roughness by different coloring agents. Methods; 64 specimens ( 20 mm×20 mm×5 mm) made of heat- cured base resin were divided into 4 groups ( n = 16 ) and then different surface roughness degree were produced for different groups. A surface roughness tester was used to measure Ra along 3 tracks on each surface. The specimens in the 4 groups were immersed in coffee, tea, vinegar and water( n= 4 for each coloring agent) respectively and treated for 4 weeks. The initial and further color values of each specimen were measured using a colorimeter. The CIE L * a * b* values were recorded and color differences (△E) after staining were calculated. Data were statistically analyzed using analysis of variance ( ANOVA). Results; The △E of the specimens in coffee and tea was significantly affected by the immersion solutions (P 0. 05). The specimens with greater surface roughness demonstrated the higher AE(P< 0.05). Conclusion;Extrinsic pigment may stain heat-cured base resin, the rough surface can increase the staining susceptibility.%目的:研究4种着色介质对不同表面粗糙度的热固化基托树脂的表面着色状况.方法:制作64个热固化基托树脂试件,随机分成4组,不同组试件的测试面打磨出不同的粗糙度等级,用表面粗糙度轮廓仪测量其表面粗糙度参数Ra并记录,然后将每组试件分别浸泡于蒸馏水(对照)、咖啡、茶和陈醋中,用分光光度比色仪测量试件浸泡前及浸泡4周后的颜色,得到L*、a *、b*值,计算浸泡前后的色差△E,采用统计学方法,分析热固化基托树脂着色与上述因素的关系.结果:除对照组外,咖啡组和茶组试件的色差值△E均增大(P＜0.05),且咖啡组的△E大于茶组(P＜0.05),陈醋组的△E无明显改变(P＞0.05)；同一浸泡液中不同表面粗糙度的试件的△E值差异有显著性(P＜0.05),表面粗糙度越大,△E越大.结论
Modeling surface roughness scattering in metallic nanowires
Moors, Kristof, E-mail: kristof@itf.fys.kuleuven.be [KU Leuven, Institute for Theoretical Physics, Celestijnenlaan 200D, B-3001 Leuven (Belgium); IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Sorée, Bart [IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Physics Department, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium); KU Leuven, Electrical Engineering (ESAT) Department, Kasteelpark Arenberg 10, B-3001 Leuven (Belgium); Magnus, Wim [IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Physics Department, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)
2015-09-28
Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.
Minimal axiom group of similarity-based rough set model
DAI Jian-hua; PAN Yun-he
2006-01-01
Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups.Thus,rough set theory can be studied by logic and axiom system methods.The classical rough set theory is based on equivalence relation,but the rough set theory based on similarity relation has wide applications in the real world.To characterize similarity-based rough set theory,an axiom group named S,consisting of 3 axioms,is proposed.The reliability of the axiom group,which shows that characterizing of rough set theory based on similarity relation is rational,is proved.Simultaneously,the minimization of the axiom group,which requests that each axiom is an equation and independent,is proved.The axiom group is helpful to research rough set theory by logic and axiom system methods.
A methodology for including wall roughness effects in k-ε low-Reynolds turbulence models
Ambrosini, W., E-mail: walter.ambrosini@ing.unipi.it; Pucciarelli, A.; Borroni, I.
2015-05-15
Highlights: • A model for taking into account wall roughness in low-Reynolds k-ε models is presented. • The model is subjected to a first validation to show its potential in general applications. • The application of the model in predicting heat transfer to supercritical fluids is also discussed. - Abstract: A model accounting for wall roughness effects in k-ε low-Reynolds turbulence models is described in the present paper. In particular, the introduction in the transport equations of k and ε of additional source terms related to roughness, based on simple assumptions and dimensional relationships, is proposed. An objective of the present paper, in addition to obtaining more realistic predictions of wall friction, is the application of the proposed model to the study of heat transfer to supercritical fluids. A first validation of the model is reported. The model shows the capability of predicting, at least qualitatively, some of the most important trends observed when dealing with rough pipes in very different flow conditions. Qualitative comparisons with some DNS data available in literature are also performed. Further analyses provided promising results concerning the ability of the model in reproducing the trend of friction factor when varying the flow conditions, though improvements are necessary for achieving better quantitative accuracy. First applications of the model in simulating heat transfer to supercritical fluids are also described, showing the capability of the model to affect the predictions of these heat transfer phenomena, in particular in the vicinity of the pseudo-critical conditions. A more extended application of the model to relevant deteriorated heat transfer conditions will clarify the usefulness of this modelling methodology in improving predictions of these difficult phenomena. Whatever the possible success in this particular application that motivated its development, this approach suggests a general methodology for accounting
Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach
Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.
2017-07-01
Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather
Generalization Rough Set Theory
XIAO Di; ZHANG Jun-feng; HU Shou-song
2008-01-01
In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed.At first, the degree of general importance of an attribute and attribute subsets are presented.Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method.At last, a generalization rough set theory based on the general near neighborhood relation is proposed.The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.
Gupta, Shamik; Bandyopadhyay, Malay
2011-10-01
We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
Analytical skin friction and heat transfer formula for compressible internal flows
Dechant, Lawrence J.; Tattar, Marc J.
1994-01-01
An analytic, closed-form friction formula for turbulent, internal, compressible, fully developed flow was derived by extending the incompressible law-of-the-wall relation to compressible cases. The model is capable of analyzing heat transfer as a function of constant surface temperatures and surface roughness as well as analyzing adiabatic conditions. The formula reduces to Prandtl's law of friction for adiabatic, smooth, axisymmetric flow. In addition, the formula reduces to the Colebrook equation for incompressible, adiabatic, axisymmetric flow with various roughnesses. Comparisons with available experiments show that the model averages roughly 12.5 percent error for adiabatic flow and 18.5 percent error for flow involving heat transfer.
Measurement of surface roughness
De Chiffre, Leonardo
This document is used in connection with two 3 hours laboratory exercises that are part of the course GEOMETRICAL METROLOGY AND MACHINE TESTING. The laboratories include a demonstration of the function of roughness measuring instruments plus a series of exercises illustrating roughness measurement...
Said Broumi; Florentin Smarandache; Mamoni Dhar
2013-01-01
Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information. In this paper we develop an hybrid structure called rough neutrosophic sets and studied their properties.
Hu, Kainan; Geng, Shaojuan
2016-01-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e. the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion...
J. H. Lee
2012-04-01
Full Text Available Aerodynamic roughness height (Z_{om} is a key parameter required in land surface hydrological model, since errors in heat flux estimations are largely dependent on accurate optimization of this parameter. Despite its significance, it remains an uncertain parameter that is not easily determined. This is mostly because of non-linear relationship in Monin-Obukhov Similarity (MOS and unknown vertical characteristic of vegetation. Previous studies determined aerodynamic roughness using traditional wind profile method, remotely sensed vegetation index, minimization of cost function over MOS relationship or linear regression. However, these are complicated procedures that presume high accuracy for several other related parameters embedded in MOS equations. In order to simplify a procedure and reduce the number of parameters in need, this study suggests a new approach to extract aerodynamic roughness parameter via Ensemble Kalman Filter (EnKF that affords non-linearity and that requires only single or two heat flux measurement. So far, to our knowledge, no previous study has applied EnKF to aerodynamic roughness estimation, while a majority of data assimilation study has paid attention to land surface state variables such as soil moisture or land surface temperature. This approach was applied to grassland in semi-arid Tibetan area and maize on moderately wet condition in Italy. It was demonstrated that aerodynamic roughness parameter can inversely be tracked from data assimilated heat flux analysis. The aerodynamic roughness height estimated in this approach was consistent with eddy covariance result and literature value. Consequently, this newly estimated input adjusted the sensible heat overestimated and latent heat flux underestimated by the original Surface Energy Balance System (SEBS model, suggesting better heat flux estimation especially during the summer Monsoon period. The advantage of this approach over other methodologies is
Sabaeian, Mohammad
2012-10-20
The problem of finding analytical solutions for time-dependent or time-independent heat equations, especially for solid-state laser media, has required a lot of work in the field of thermal effects. However, to calculate the temperature distributions analytically, researchers often have to make some approximations or employ complex methods. In this work, we present full analytical solutions for anisotropic time-dependent heat equations in the Cartesian coordinates with various source terms corresponding to various pumping schemes. Moreover, the most general boundary condition of Robin (or impedance boundary condition), corresponding to the convection cooling mechanism, was applied. This general condition can be easily switched to constant temperature and thermal insulation as special cases. To this end, we first proposed a general approach to solving time-dependent heat equations with an arbitrary heat source. We then applied our approach to explore the temperature distribution for three cases: steady-state pumping or long transient, single-shot pumping or short transient, and repetitively pulsed pumping. Our results show the possibility of an easier and more accurate approach to analytical calculations of the thermal dispersion, thermal stresses (strains), thermal bending, thermal phase shift, and other thermal effects.
Thermodynamics of capillary adhesion between rough surfaces.
de Boer, M P; de Boer, P C T
2007-07-01
According to the Dupré equation, the work of adhesion is equal to the surface energy difference in the separated versus the joined materials minus an interfacial energy term. However, if a liquid is at the interface between two solid materials, evaporation or condensation takes place under equilibrium conditions. The resulting matter exchange is accompanied by heat flow, and can reduce or increase the work of adhesion. Accounting for the energies requires an open-system control volume analysis based on the first law of thermodynamics. Depending on whether evaporation or condensation occurs during separation, a work term that is negative or positive must be added to the surface energy term to calculate the work of adhesion. We develop and apply this energy balance to several different interface geometries and compare the work of adhesion to the surface energy created. The model geometries include a sphere on a flat with limiting approximations and also with an exact solution, a circular disc, and a combination of these representing a rough interface. For the sphere on a flat, the work of adhesion is one half the surface energy created if equilibrium is maintained during the pull-off process.
F-rough law and the discovery of rough law
Qiu Jinming; Shi Kaiquan
2009-01-01
By using function one direction S-rough sets (function one direction singular rough sets), this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.
Automatic Determination of Roughness
无
2002-01-01
During the second development and the design of AutoCAD, it's necessary for us to choose roughness according to the part's precision grade, it's connecting relationship, and look up the list. In order to make the designer and programmer get the precision grade quickly and accurately, and decide the roughness in the drawing, this article analyze the relationship between the precision and roughness on the basis of analyzing method, and consider the experience in practice, then carry out a set of method formul...
Thermal smoothing of rough surfaces in vacuo
Wahl, G.
1986-01-01
The derivation of equations governing the smoothing of rough surfaces, based on Mullins' (1957, 1960, and 1963) theories of thermal grooving and of capillarity-governed solid surface morphology is presented. As an example, the smoothing of a one-dimensional sine-shaped surface is discussed.
Surface roughness evolution of nanocomposite thin films
Turkin, A; Pei, Y.T.; Shaha, K.P.; Chen, C.Q.; Vainchtein, David; Hosson, J.Th.M. De
2009-01-01
An analysis of dynamic roughening and smoothening mechanisms of thin films grown with pulsed-dc magnetron sputtering is presented. The roughness evolution has been described by a linear stochastic equation, which contains the second- and fourth-order gradient terms. Dynamic smoothening of the growin
Mixed convection of nanofluids in a lid-driven rough cavity
Guo, Zhimeng; Wang, Jinyu; Mozumder, Aloke K.; Das, Prodip K.
2017-06-01
Mixed convection heat transfer and fluid flow of air, water or oil in enclosures have been studied extensively using experimental and numerical means for many years due to their ever-increasing applications in many engineering fields. In comparison, little effort has been given to the problem of mixed convection of nanofluids in spite of several applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. Mixed convection of nanofluids is a challenging problem due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, mixed convection of nanofluids in a lid-driven square cavity with sinusoidal roughness elements at the bottom is studied numerically using the Navier-Stokes equations with the Boussinesq approximation. The numerical model is developed using commercial finite volume software ANSYS-FLUENT for Al2O3-water and CuO-water nanofluids inside a square cavity with various roughness elements. The effects of number and amplitude of roughness elements on the heat transfer and fluid flow are analysed for various volume concentrations of Al2O3 and CuO nanoparticles. The flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers. The outcome of this study provides some important insight into the heat transfer behaviour of Al2O3-water and CuO-water nanofluids inside a lid-driven rough cavity. This knowledge can be further used in developing novel geometries with enhanced and controlled heat transfer for solar collectors, electronic cooling, and food processing industries.
Umatilla - Rough Fish Eradication
US Fish and Wildlife Service, Department of the Interior — In order to enhance environmental conditions in the McCormack Slough on Umatilla NWR, the population of rough fish, including common carp (Cyprinus carpio) and...
Wu, Guochun
2017-01-01
In this paper, we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3D compressible Navier-Stokes equations without heat conductivity in a bounded domain with slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
Khan, Sabeel M.; Hammad, M.; Sunny, D. A.
2017-08-01
In this article, the influence of thermal relaxation time and chemical reaction is studied on the MHD upper-convected viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation for the first time in the literature. The flow-governing equations are formulated and are converted into their respective ordinary differential equations (ODEs) with the application of similarity functions. The resulting system of coupled nonlinear ODEs is solved along with the prescribed conditions at boundary using a finite-difference code in MATLAB. Influence of chemical reaction, thermal relaxation time and internal material parameter on the macroscopic and micropolar velocities as well as on the temperature and concentration profiles is examined along with other physical parameters ( e.g., magnetic parameter, Eckert number, Prandtl number and fluid relaxation time). The accuracy of the obtained numerical solution is shown by comparing the physical parameters of interest with particular cases of existing results in the literature.
P.C. Mishra
2014-06-01
Full Text Available Performance characteristics of a rough elliptic bore journal bearing are studied. The bearing bore of isotropic roughness orientation is characterized by stochastic function and the film geometry is quantified to elliptic shape. There after the Reynolds equation and energy equation are descretized for pressure and temperature respectively. A finite difference model is developed to evaluate hydrodynamic pressure and oil temperature. Solution to this model is done using effective influence Newton-Raphson method. Performance parameters such as load bearing ability, friction, flow-in and side leakages are computed and discussed.
Abdollahi, Ali; Reza Salimpour, Mohammad
2016-11-01
In this paper, the pool boiling heat transfer of Fe3O4 -deionized (DI) water as a magnetic nanofluid has been experimentally analyzed in the atmospheric pressure. The applied nanofluid within this research has been synthesized through a single step to retain a high stability. The repeatability and precision of the testing device with deionized water show a good agreement with the equations introduced in previous studies. Parametric studies on magnetic field, surface roughness, and magnetic nanofluid concentration are performed to reveal various aspects of the boiling heat transfer. In order to study the surface roughness, two surfaces with high average roughness (480nm) and low average roughness (7.3nm) were used. The obtained results indicate that the boiling heat transfer on the rough surface increases when raising the nanofluid concentration up to 0.1% volume concentration. In addition, it is observed that there is an optimum 0.1% volume concentration for the nanofluid which makes the boiling heat transfer coefficient increase up to 43%. Moreover, the heat transfer of a nanofluid with volume concentration of 0.1% is greater for the rough surface compared with the smooth one. The results of the experiments indicate that adding nanoparticles would not necessarily increase the boiling heat transfer coefficient. In fact, the surface roughness and the magnetic field gradient on the boiling surface were the main factors that could affect the boiling heat transfer coefficient significantly. The simultaneous analysis of magnetic field, surface roughness, and nanofluid concentration reveals that the boiling heat transfer coefficient of the magnetic nanofluid with 0.1% volume concentration in the presence of a magnetic field on the rough surface is higher than on the smooth surface. Our findings show that this increase is associated to the increase of nucleation sites concentration and bubble formation sites for the rough surface.
Influence of random roughness on cantilever resonance frequency
Ergincan, O.; Palasantzas, G.
2010-01-01
In this paper we investigate the influence of random roughness on the oscillation frequency of cantilevers coated with thin film overlayers. First the theory expressions for the roughness-induced frequency shift are derived using the cantilever equation of motion. Subsequently it is shown that the r
Multidimensional Heat Conduction
Rode, Carsten
1998-01-01
Analytical theory of multidimensional heat conduction. General heat conduction equation in three dimensions. Steay state, analytical solutions. The Laplace equation. Method of separation of variables. Principle of superposition. Shape factors. Transient, multidimensional heat conduction....
Heatshield Ablation Pattern Roughness Onset and Effects Project
National Aeronautics and Space Administration — This project will develop a practical method for predicting pattern roughness onset and quantitative effects on heat and mass transfer rates for heatshield materials...
Subcellular fractionation of rough microsomes.
Sabatini, David D
2014-09-02
When eukaryotic cells are homogenized, the rough endoplasmic reticula are converted into small vesicles, called rough microsomes. Strategies for the isolation of rough microsomes are introduced here, as are methods for evaluating the purity and intactness of an isolated rough microsomal fraction.
Dualities in Covering Rough Operations
William Zhu
2006-01-01
Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[ 1,40-43 ] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.
2017-01-01
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...
An efficient threshold dynamics method for wetting on rough surfaces
Xu, Xianmin; Wang, Dong; Wang, Xiao-Ping
2017-02-01
The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary. Direct generalization of MBO-type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original MBO method. The dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary. In this paper, we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces. This method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase. The method is simple, stable with O (Nlog N) complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary.
Bollerslev, Tim; Li, Sophia Zhengzi; Todorov, Viktor
Motivated by the implications from a stylized equilibrium pricing framework, we investigate empirically how individual equity prices respond to continuous, or \\smooth," and jumpy, or \\rough," market price moves, and how these different market price risks, or betas, are priced in the cross-section...
Influence of metal roughness on SPR sensor performance
Agarwal, Sajal; Prajapati, Y. K.; Singh, V.
2017-01-01
Roughness of the nano-layer greatly affects the sensor performance. This study is done to quantify the effect of roughness on the sensor performance experimentally. It is seen that the increased thickness of the top metal layer degrades the sensor performance i.e. sensitivity and detection accuracy. The roughness effect on the surface is seen by varying the thickness of intermediate and top metal layers separately. It is seen that 2-5 nm thick intermediate layer and 50 nm thick top layer provides better performance of sensor. Also, mathematical equations are included for the sake of theoretical analysis which indicates the effect of surface roughness on the sensor performance.
End depth in steeply sloping rough rectangular channels
Subhasish Dey
2000-02-01
The paper presents a theoretical model to compute the end depth of a free overfall in steeply sloping rough rectangular channels. A momentum equation based on the Boussinesq approximation is applied to obtain the equation of the end depth. The effect ofstreamline curvature at the free surface is utilized to develop the differential equation for the flow profile upstream of the free overfall of a wide rectangular channel. As direct solutions for the end depth and flow profile cannot be obtained owing to implicit forms of the developed equations, an auto-recursive search scheme is evolved to solve these equations simultaneously. A method for estimation of discharge from the known end depth and Nikuradse equivalent sand roughness is also presented. Results from the present model correspond satisfactorily with experimental observations except for some higher roughnesses.
Zhang, Chuanqian; Johnson, Duane T; Brazel, Christopher S
2008-12-01
This study develops and solves two-dimensional convective-conductive coupled partial differential equations based on Pennes' bio-heat transfer model using low Curie temperature nanoparticles (LCTNPs) to illustrate thermal behavior quantitatively within tumor-normal composite tissue by establishing a multi-region finite difference algorithm. The model combines NEel relaxation and temperature-variant saturation magnetization derived from Brillouin Equation and Curie-Weiss Law. The numerical results indicate that different deposition patterns of LCTNP and boundary conditions directly effect the steady state temperature distribution. Compared with high Curie temperature nanoparticles (HCTNPs), optimized distributions of LCTNPs within tumorous tissue can be used to control the temperature increase in tumors for hyperthermia treatment using an external magnetic field while healthy tissue surrounding a tumor can be kept closer to normal body tissue, reducing the side effects observed in whole body and regional hyperthermia therapy.
Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan
2016-10-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.
Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan
2016-10-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.
Parand, K; Kazem, S; Rezaei, A R; 10.1016/j.cnsns.2010.07.011
2010-01-01
In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the two approaches on natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear wastes disposal. Numerical results show that the IRBF be performed much better than the common DRBF, and show good accuracy and high rate of convergence of IRBF process.
Rough similarity degree and rough close degree in rough fuzzy sets and the applications
Li Jian; Xu Xiaojing; Shi Kaiquan
2008-01-01
Based on rough similarity degree of rough sets and close degree of fuzzy sets,the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given,which can be used to measure the similar degree between two rough fuzzy sets.The properties and theorems are listed.Using the two new measures,the method of clustering in the rough fuzzy system can be obtained.After clustering,the new fuzzy sample can be recognized by the principle of maximal similarity degree.
Sacripanti, A. [ENEA, Rome (Italy). Direzione Sicurezza Nazionale e Protezione Sanitaria; Dal Monte, A. [CONI, Rome (Italy). Ist. di Scienza dello Sport; Rossi, L.; Fabbri, M. [ENEA, Casaccia (Italy)
1993-12-31
The foundation, evolution and related improvements of the new heat and mass transfer equation, used in the joint research of CONI-ENEA (the Italian National Agency for Energy, New Technologies and the Environment) - FILPJ are shown in this report. Emphasis is given to the experimental history and the changes that are justified in a more formal approach on the basis of theoretical thermodynamics or similarity and dimensional theory. The new form of the equation in the computer code actually utilized in the research is given in the appendix.
Jin Yaqin; Li Zhongxin
2001-01-01
As a Gaussian beam is incident upon a rough surface at low grazing angle, the Helmholts scalar wave equation may be replaced by the parabolic approximate equation. As the incident field is known, the scattered field and surface current give the Volterra integral equation.Surface roughness profile can be formulated by the integral equation of the surface currents. These two coupled equations are applied to invert the roughness profile of heterogeneous fractal surface.Using Monte Carlo method, the fractal rough surfaces with a band-limited Weistrass-Manderbrot function are numerically simulated and the scattered fields along a line parallel to the mean surface are solved. The Gaussian beam incidence and scattered fields are used to progressively invert the surface roughness profile. Reconstructed profile and its inverted fractal dimension,roughness variance and correlation length are well matched with the simulated surfaces.
Hydrodynamic Noise from Flexible Roughness Elements
2015-06-29
approach. The specialized plumage features believed to be responsible for this noise suppression are a leading-edge comb of evenly spaced feathers, the...turbulent structures of the boundary layer, and control not only the source of roughness noise but Trailing-Edge Fringe Leading-Edge Comb Velvety Down...0=1/2. The mapping relationship between the z- and f-planes is completed by equating the background mean flows far from the fiber, which yields V
IMPROVED ACCURACY AND ROUGHNESS MEASURES FOR ROUGH SETS
Zhou Yuming; Xu Baowen
2002-01-01
Accuracy and roughness, proposed by Pawlak(1982), might draw a conclusion inconsistent with our intuition in some cases. This letter analyzes the limitations in these measures and proposes improved accuracy and roughness measures based on information theory.
R. T. Al-Khairy
2009-01-01
source, whose capacity is given by (,=((1−− while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.
Pavement roughness and skid properties
Road roughness and roadway safety as it relates to both surface and air transportation are discussed. The role of road roughness in vehicle ride, the measurement of roughness, the evaluation of riding confort, and the effect of grooving pavements are discussed. The effects of differential pavement friction on the response of cars in skidding maneuvers is discussed.
Modelling dynamic roughness during floods
Paarlberg, Andries; Dohmen-Janssen, Catarine M.; Hulscher, Suzanne J.M.H.; Termes, A.P.P.
2007-01-01
In this paper, we present a dynamic roughness model to predict water levels during floods. Hysteresis effects of dune development are explicitly included. It is shown that differences between the new dynamic roughness model, and models where the roughness coefficient is calibrated, are most
Andrzej Skowron
2006-01-01
Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Computing(GC). We discuss the Rough-Granular Computing(RGC) approach to modeling of computations in complex adaptive systems and multiagent systems as well as for approximate reasoning about the behavior of such systems. The RGC methods have been successfully applied for solving complex problems in areas such as identification of objects or behavioral patterns by autonomous systems, web mining, and sensor fusion.
Weizhi Wu
2006-01-01
In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced. It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures, and vice versa. And for a random approximation space generated from a totally random set, its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.
Explicit Numerical Modeling of Heat Transfer in Glacial Channels
Jarosch, A. H.; Zwinger, T.
2015-12-01
Turbulent flow and heat transfer of water in englacial channels is explicitly modelelled and the numerical results are compared to the most commonly used heat transfer parameterization in glaciology, i.e. the Dittus-Boelter equation. The three-dimensional flow is simulated by solving the incompressible Navier-Stokes equations utilizing a variational multiscale method (VMS) turbulence model and the finite-element method (i.e. Elmer-FEM software), which also solves the heat equation. By studying a wide range of key parameters of the system, e.g. channel diameter, Reynolds number, water flux, water temperature and Darcy-Weisbach wall roughness (which is explicitly represented on the wall geometry), it is found that the Dittus-Boelter equation is inadequate for glaciological applications and a new, highly suitable heat transfer parameterization for englacial/subglacial channels will be presented. This new parameterization utilizes a standard combination of dimensionless numbers describing the flow and channel (i.e. Reynolds number, Prandtl number and Darcy-Weisbach roughness) to predict a suitable Nusselt number describing the effective heat transfer and thus can be readily used in existing englacial/subglacial hydrology models.
Kong Linghua; Wang Jinhuan; Zheng Sining
2012-01-01
This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the criterion for simultaneous blow-up of solutions,and then establish the uniform blow-up profiles of solutions near the blow-up time.It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmetric,but also the blow-up rates of the same component u (or v) may be in different levels under different dominations.
NONE
2002-07-01
This report, which was commissioned by the Offshore Division of the Health and Safety Executive, reviews the type of equipment and techniques used to rescue people from the water around offshore platforms in rough weather. It also examines the limitations of the equipment in extreme conditions and reports the views of the various industry sectors (as determined by a questionnaire survey). The type of incidents covered by the report include: man overboard; helicopter ditching; and evacuation from totally enclosed motor propelled survival craft (TEMPSC) and life rafts. The report considers: the approach taken by other oil-producing countries; current escape, evacuation and rescue (EER) practices for the UK Continental Shelf (UKCS); environmental limits; methods for rescue and recovery from the water and TEMPSC; launch and recovery systems; fast rescue craft (FSC) and daughter craft; emergency response and rescue vessels; helicopters; casualty personal protection equipment; claimed versus actual equipment performance; training and practice procedures; attitudes to environmental limits; lessons learnt from incidents; mechanical recovery devices; equipment design and use in rough weather; and recommendations for improvements.
Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2009-01-01
This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of
Irmak, A.; Singh, R.K.; Walter-Shea, Elizabeth; Verma, S.B.; Suyker, A.E.
2011-01-01
We evaluated the performance of four models for estimating soil heat flux density (G) in maize (Zea mays L.) and soybean (Glycine max L.) fields under different irrigation methods (center-pivot irrigated fields at Mead, Nebraska, and subsurface drip irrigated field at Clay Center, Nebraska) and rainfed conditions at Mead. The model estimates were compared against measurements made during growing seasons of 2003, 2004, and 2005 at Mead and during 2005, 2006, and 2007 at Clay Center. We observed a strong relationship between the G and net radiation (Rn) ratio (G/Rn) and the normalized difference vegetation index (NDVI). When a significant portion of the ground was bare soil, G/Rn ranged from 0.15 to 0.30 and decreased with increasing NDVI. In contrast to the NDVI progression, the G/Rn ratio decreased with crop growth and development. The G/Rn ratio for subsurface drip irrigated crops was smaller than for the center-pivot irrigated crops. The seasonal average G was 13.1%, 15.2%, 10.9%, and 12.8% of Rn for irrigated maize, rainfed maize, irrigated soybean, and rainfed soybean, respectively. Statistical analyses of the performance of the four models showed a wide range of variation in G estimation. The root mean square error (RMSE) of predictions ranged from 15 to 81.3 W m-2. Based on the wide range of RMSE, it is recommended that local calibration of the models should be carried out for remote estimation of soil heat flux.
Surface Roughness Effects on Discharge Coefficient of Broad Crested Weir
Shaker A. Jalil
2014-06-01
Full Text Available The aim of this study is to investigate the effects of surface roughness sizes on the discharge coefficient for a broad crested weirs. For this purpose, three models having different lengths of broad crested weirs were tested in a horizontal flume. In each model, the surface was roughed four times. Experimental results of all models showed that the logical negative effect of roughness increased on the discharge (Q for different values of length. The performance of broad crested weir improved with decrease ratio of roughness to the weir height (Ks/P and with the increase of the total Head to the Length (H/L. An empirical equation was obtained to estimate the variation of discharge coefficient Cd in terms total head to length ratio, with total head to roughness ratio.
Xanming Wang
1996-01-01
Full Text Available A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/rdy/dr+λ2(β−r2y=0 which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow (β>1. A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case of β>1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values of β were obtained.
Ye, Xia; Zhang, Jianwen
2016-08-01
This paper concerns the asymptotic behavior of the solution to an initial-boundary value problem of the cylindrically symmetric Navier-Stokes equations with large data for compressible heat-conducting ideal fluids, as the shear viscosity μ goes to zero. A suitable corrector function (the so-called boundary-layer type function) is constructed to eliminate the disparity of boundary values. As by-products, the convergence rates of the derivatives in L 2 are obtained and the boundary-layer thickness (BL-thickness) of the value O≤ft({μα}\\right) with α \\in ≤ft(0,1/2\\right) is shown by an alternative method, compared with the results proved in Jiang and Zhang (2009 SIAM J. Math. Anal. 41 237-68) and Qin et al (2015 Arch. Ration. Mech. Anal. 216 1049-86).
T Nguyen
2017-06-01
Full Text Available This paper studies the contact of general rough curved surfaces having nearly identical geometries, assuming the contact at each differential area obeys the model proposed by Greenwood and Williamson. In order to account for the most general gross geometry, principles of differential geometry of surface are applied. This method while requires more rigorous mathematical manipulations, the fact that it preserves the original surface geometries thus makes the modeling procedure much more intuitive. For subsequent use, differential geometry of axis-symmetric surface is considered instead of general surface (although this “general case” can be done as well in Chapter 3.1. The final formulas for contact area, load, and frictional torque are derived in Chapter 3.2.
A minimal axiom group for rough set based on quasi-ordering
代建华; 陈卫东; 潘云鹤
2004-01-01
Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups.Thus,rough set theory can be studied by logic and axiom system methods.The classic rough set theory is based on equivalent relation,but rough set theory based on reflexive and transitive relation(called quasi-ordering)has wide applications in the real world.To characterize topological rough set theory,an axiom group named RT,consisting of 4 axioms,is proposed.It is proved that the axiom group reliability in characterizing rough set theory based on similai relation is reasonable.Simultaneously,the minimization of the axiom group,which requires that each axiom is an equation and each is independent,is proved.The axiom group is helpful for researching rough set theory by logic and axiom system methods.
A minimal axiom group for rough set based on quasi-ordering
代建华; 陈卫东; 潘云鹤
2004-01-01
Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world. To characterize topological rough set theory, an axiom group named RT, consisting of 4 axioms, is proposed. It is proved that the axiom group reliability in characterizing rough set theory based on similar relation is reasonable. Simultaneously, the minimization of the axiom group, which requires that each axiom is an equation and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.
Analytical large deformation shear strength for bolted rough discontinuous rock
LIU Bo(刘波); TAO Long-guang(陶龙光); YUE Zhong-qi(岳中琦)
2004-01-01
Presented a new analytical model for studying the shear-tensile large deformation behavior near the vicinity of joint interface for bolted rough discontinuous rock, and presented the formulation estimating global shear strength for bolted joints under shearing-tensile loads. The analytical strength curves of bolts contribution on reinforced discontinuous rocks as the function of joint displacements or deformation angle of a bolt at rock joints was obtained. Based on Barton's equation on JRC roughness profiles, the theoretical shearing strength of bolted rough joints was also established. Test results on bolted granite and marble specimen confirm the validity of the analytical approach.
无
2007-01-01
It is well-known that rough set theory can be applied successfully to rough classification and knowledge discovery. Our work is concerned with finding methods for using rough sets to identify classes in datasets, finding dependencies in relations and discovering rules which are hidden in databases by means of decision tables and algorithm D. We use these methods to analyze and control aspects of nuclear energy generation.
Roughness Measurement of Dental Materials
Shulev Assen
2016-06-01
Full Text Available This paper presents a roughness measurement of zirconia ceramics, widely used for dental applications. Surface roughness variations caused by the most commonly used dental instruments for intraoral grinding and polishing are estimated. The applied technique is simple and utilizes the speckle properties of the scattered laser light. It could be easily implemented even in dental clinic environment. The main criteria for roughness estimation is the average speckle size, which varies with the roughness of zirconia. The algorithm used for the speckle size estimation is based on the normalized autocorrelation approach.
Roughness Measurement of Dental Materials
Shulev, Assen; Roussev, Ilia; Karpuzov, Simeon; Stoilov, Georgi; Ignatova, Detelina; See, Constantin von; Mitov, Gergo
2016-06-01
This paper presents a roughness measurement of zirconia ceramics, widely used for dental applications. Surface roughness variations caused by the most commonly used dental instruments for intraoral grinding and polishing are estimated. The applied technique is simple and utilizes the speckle properties of the scattered laser light. It could be easily implemented even in dental clinic environment. The main criteria for roughness estimation is the average speckle size, which varies with the roughness of zirconia. The algorithm used for the speckle size estimation is based on the normalized autocorrelation approach.
Heat transfer and fluid flow in microchannels
Mala, Ghulam Mohiuddin
Fluid flow and heat transfer characteristics in microchannels of different cross-sections; parallel plate, cylindrical and trapezoidal microchannels were studied. The trapezoidal microchannels were etched in silicon and glass by photolithographic techniques. The cylindrical microchannels of fused silica and stainless steel were readily available. Channels with depths of 18 μm to 300 μm were studied. The study was divided into three parts viz. theoretical modeling, numerical simulation and experimentation. Electrokinetic effects such as the effects of electrical double layer (EDL) at the solid-liquid interface and surface roughness effects were considered. An experimental apparatus was constructed and a procedure devised to measure the flow rate, pressure drop, temperatures and electrokinetic parameters like streaming potential, streaming current, and conductivity of the working fluid. Great care was taken so that the measurements were accurate and repeatable. For steady state laminar flow and heat transfer in microchannels, mathematical models were developed that consider the effects of electrical double layer and surface roughness at the microchannel walls. The non- linear, 2-D, Poisson-Boltzmann equation that describes the potential distribution at the solid liquid interface was solved numerically and results were compared with a linear approximate solution that overestimates the potential distribution for higher values of zeta potential. Effects of the EDL field at the solid-liquid interface, surface roughness at the microchannel walls and the channel size, on the velocity distribution, streaming potential, apparent viscosity, temperature distribution and heat transfer characteristics are discussed. The experimental results indicate significant departure in flow characteristics from the predictions of the Navier-Stokes equations, referred to as conventional theory. The difference between the experimental results and theoretical predictions decreases as the
ROUGHNESS ON WOOD SURFACES AND ROUGHNESS MEASUREMENT METHODS
İsmail Aydın
2003-04-01
Full Text Available Some visual characteristics of wood such as color, pattern and texture determine the quality of manufactured products. Surface properties of wood material are important both in production and marketing after production. Initial studies related to the roughness of wood surface were begun in early 1950’s. However, no general agreed standardization can not have been developed for wood surfaces. Surface roughness of wood is function of the production process, product type and the natural anatomical properties of wood. Contact and non-contact tracing methods are used to measure of wood surface roughness. Surface roughness also affects the gluability and wettability of wood surfaces. The success in finishing also depends on the surface roughness of wood.
Influence of Nanoscale Surface Roughness on Colloidal Force Measurements.
Zou, Yi; Jayasuriya, Sunil; Manke, Charles W; Mao, Guangzhao
2015-09-29
Forces between colloidal particles determine the performances of many industrial processes and products. Colloidal force measurements conducted between a colloidal particle AFM probe and particles immobilized on a flat substrate are valuable in selecting appropriate surfactants for colloidal stabilization. One of the features of inorganic fillers and extenders is the prevalence of rough surfaces-even the polymer latex particles, often used as model colloidal systems including the current study, have rough surfaces albeit at a much smaller scale. Surface roughness is frequently cited as the reason for disparity between experimental observations and theoretical treatment but seldom verified by direct evidence. This work reports the effect of nanoscale surface roughness on colloidal force measurements carried out in the presence of surfactants. We applied a heating method to reduce the mean surface roughness of commercial latex particles from 30 to 1 nm. We conducted force measurements using the two types of particles at various salt and surfactant concentrations. The surfactants used were pentaethylene glycol monododecyl ether, Pluronic F108, and a styrene/acrylic copolymer, Joncryl 60. In the absence of the surfactant, nanometer surface roughness affects colloidal forces only in high salt conditions when the Debye length becomes smaller than the surface roughness. The adhesion is stronger between colloids with higher surface roughness and requires a higher surfactant concentration to be eliminated. The effect of surface roughness on colloidal forces was also investigated as a function of the adsorbed surfactant layer structure characterized by AFM indentation and dynamic light scattering. We found that when the layer thickness exceeds the surface roughness, the colloidal adhesion is less influenced by surfactant concentration variation. This study demonstrates that surface roughness at the nanoscale can influence colloidal forces significantly and should be taken
A.S.J.AL-SAIF; 朱正佑
2003-01-01
The traditional differential quadrature method was improved by using the upwind difference scheme for the convectiveterms to solve the coupled two-dimensional incompressible Navier-stokes equations and heat equation. The new method was comparedwith the conventional differential quadrature method in the aspects of convergence and accuracy. The results show that the newmethod is more accurate, and has better convergence than the conventional differential quadrature method for numerically computingthe steady-state solution.
Bankruptcy Prediction with Rough Sets
J.C. Bioch (Cor); V. Popova (Viara)
2001-01-01
textabstractThe bankruptcy prediction problem can be considered an or dinal classification problem. The classical theory of Rough Sets describes objects by discrete attributes, and does not take into account the order- ing of the attributes values. This paper proposes a modification of the Rough Set
Bounds for convection between rough boundaries
Goluskin, David
2016-01-01
We consider Rayleigh-B\\'enard convection in a layer of fluid between no-slip rough boundaries, where the top and bottom boundary heights are functions of the horizontal coordinates with bounded gradients. We use the background method to derive an upper bound on mean heat flux across the layer for all admissible boundary geometries. This flux, normalized by the temperature difference between the boundaries, can grow with the Rayleigh number ($Ra$) no faster than $Ra^{1/2}$ as $Ra \\rightarrow \\infty$. Coefficients of the bound are given explicitly in terms of the geometry, and evaluation of the coefficients is illustrated for sinusoidal boundaries.
Wave-driven Hydrodynamics for Different Reef Geometries and Roughness Scenarios
Franklin, G. L.; Marino-Tapia, I.; Torres-Freyermuth, A.
2013-05-01
In fringing reef systems where a shallow lagoon is present behind the reef crest, wave breaking appears to dominate circulation, controlling numerous key processes such as the transport and dispersion of larvae, nutrients and sediments. Despite their importance, there is a need for more detailed knowledge on the hydrodynamic processes that take place within the surf zone of these systems and the effects different combinations of geometries and roughness have on them. The present study focuses on the use of two-dimensional (2DV) numerical model simulations and data obtained during a field campaign in Puerto Morelos, Quintana Roo, Mexico to better understand the detailed surf zone processes that occur over a fringing reef. The model used is Cornell Breaking Wave and Structures (COBRAS), which solves Reynolds-Averaged Navier-Stokes (RANS) equations. Reef geometries implemented in the model include a reef flat and two different reef crests. The effect of roughness on wave setup, radiation stress, mean flows, and cross-shore spectral evolution for the model results was studied using different roughness coefficients (Nikuradse) and a bathymetric profile obtained in the field using the bottom track option of an Acoustic Doppler Current Profiler. Field data were also analysed for the configuration and roughness of Puerto Morelos. Model results reveal that for all profiles wave setup increased significantly (~22%) with increasing bed roughness, in agreement with previous findings for sandy beaches.For all wave heights and periods studied, increasing roughness also affected spectral wave evolution across the reef, with a significant reduction in energy, particularly at infragravity frequencies. The presence of a reef crest in the profile resulted in differences in behaviour at infragravity frequencies. For example, preliminary results suggest that there is a shift towards higher frequencies as waves progress into the lagoon when a crest is present, something that does not
Paloma, Cynthia S.
The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the
Maher Abourabia, Aly; Hassan, Kawsar Mohammad; Abo-Elghar, Eman Mohammad
2015-02-01
We investigate a bio-system composed of a shape memory alloy (SMA) immersed and subjected to heat convection in a blood vessel, affected by heart beats that create a wave motion of long wavelength. The tackled model in (2+1)-D is based on the continuity and momentum equations for the fluid phase, besides; the state of the SMA are described via previous works in the form of statistical distributions of energy for both Martensite and Austenite phases. The solution based on the reductive perturbation technique gives a thermal diffusion-like equation as a key for expressing the temperature and velocity components of the blood. In terms of two cases concerning the difference between the wave numbers in the perpendicular directions, it is found that the system's temperature increases nonlinearly from a minimum initial temperature 293 K (20 °C) up to a maximum value about 316.68 K (43.68 °C), then tends to decrease along the blood flow (anisotropy of K and L) direction. In both cases it is observed that the SMA acquires most of this temperature raising not the blood because of its conventional biological limits (37-40 °C). The range of the heart beats wave numbers characteristic for each person plays an important role in realizing phase changes in the anisotropic case leading to the formation of the hysteresis loops Martensite-Austenite-Martensite or vice versa, according to the energy variation. The entropy generation σ is investigated for the system (Blood + SMA), it predicts that along the flow direction the system gains energy convectively up to a maximum value, then reverses his tendency to gradually loosing energy passing by the equilibrium state, then the system looses energy to the surroundings by the same amount which was gained beforehand. The loss diminishes but stops before arriving to equilibrium again. For certain differences in wave numbers the system starts to store energy again after it passes by the state of equilibrium for the second time. In the
李宏; 魏小溪
2005-01-01
A space-time finite element method,discon tinuous in time but continuous in space,is studied to solve the nonlinear forwar d-backward heat equation.A linearized technique is introduced in order to obtai n the error estimates of the approximate solutions.And the numerical simulations are given.
S-Rough communication and its characteristics
Hu Haiqing; Wang Yan; Shi Kaiquan
2007-01-01
In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model.S-rough communication has two kinds of forms: one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method,and it is a novel research direction in rough sets field.
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Bi-Spectrum Scattering Model for Dielectric Randomly Rough Surface
刘宁; 李宗谦
2003-01-01
The bistatic scattering model is offen used for remote microwave sensing. The bi-spectrum model (BSM) for conducting surfaces was used to develop a scattering model for dielectric randomly rough surfaces to estimate their bistatic scattering coefficients. The model for dielectric rough surfaces differs from the BSM for a conducting surface by including Fresnell reflection and transmission from dielectric rough surfaces. The bistatic scattering coefficients were defined to satisfy the reciprocal theorem. Values calculated using the BSM for dielectric randomly rough surfaces compare well with those of the integral equation model (IEM) and with experimental data, showing that the BSM accuracy is acceptable and its range of validity is similar to that of IEM while the BSM expression is simpler than that of IEM.
Bi-Spectrum Scattering Model for Conducting Randomly Rough Surface
刘宁; 李宗谦
2002-01-01
A scattering model is developed to predict the scattering coefficient of a conducting randomly rough surface by analyzing the randomly rough surface in the spectral domain using the bi-spectrum method. For common randomly rough surfaces without obvious two-scale characteristics, a scale-compression filter can divide the auto-correlation spectrum into two parts with different correlation lengths. The Kirchhoff approximation and the small perturbation method are used to obtain the surface field, then a bistatic scattering model, the bi-spectrum model (BSM), is used to derive an explicit expression from the surface field. Examples using the integral equation model (IEM), finite difference of the time domain (FDTD) method, and BSM show that the BSM accuracy is acceptable and its range of validity is similar to IEM. BSM can also be extended to a scattering model for dielectric randomly rough surfaces.
Tatiana Petrova
2016-08-01
Full Text Available An extremely interesting problem in aero-hydrodynamics is the sound radiation of a single vortical structure. Currently, this type of problem is mainly considered for an incompressible medium. In this paper a method was developed to take into account the viscosity and thermal conductivity of gas. The acoustic radiation frequency of a cylindrical vortex on a flat wall in viscous heat-conducting gas (air has been investigated. The problem is solved on the basis of the Navier–Stokes equations using the small initial vorticity approach. The power expansion of unknown functions in a series with a small parameter (vorticity is used. It is shown that there are high-frequency oscillations modulated by a low-frequency signal. The value of the high frequency remains constant for a long period of time. Thus the high frequency can be considered a natural frequency of the vortex radiation. The value of the natural frequency depends only on the initial radius of the cylindrical vortex, and does not depend on the intensity of the initial vorticity. As expected from physical considerations, the natural frequency decreases exponentially as the initial radius of the cylinder increases. Furthermore, the natural frequency differs from that of the oscillations inside the initial cylinder and in the outer domain. The results of the paper may be of interest for aeroacoustics and tornado modeling.
ROUGHNESS ON WOOD SURFACES AND ROUGHNESS MEASUREMENT METHODS
İsmail Aydın; Gürsel Çolakoğlu
2003-01-01
Some visual characteristics of wood such as color, pattern and texture determine the quality of manufactured products. Surface properties of wood material are important both in production and marketing after production. Initial studies related to the roughness of wood surface were begun in early 1950’s. However, no general agreed standardization can not have been developed for wood surfaces. Surface roughness of wood is function of the production process, product type and the natural anatomic...
Enhanced thermoelectric performance of rough silicon nanowires.
Hochbaum, Allon I; Chen, Renkun; Delgado, Raul Diaz; Liang, Wenjie; Garnett, Erik C; Najarian, Mark; Majumdar, Arun; Yang, Peidong
2008-01-10
Approximately 90 per cent of the world's power is generated by heat engines that use fossil fuel combustion as a heat source and typically operate at 30-40 per cent efficiency, such that roughly 15 terawatts of heat is lost to the environment. Thermoelectric modules could potentially convert part of this low-grade waste heat to electricity. Their efficiency depends on the thermoelectric figure of merit ZT of their material components, which is a function of the Seebeck coefficient, electrical resistivity, thermal conductivity and absolute temperature. Over the past five decades it has been challenging to increase ZT > 1, since the parameters of ZT are generally interdependent. While nanostructured thermoelectric materials can increase ZT > 1 (refs 2-4), the materials (Bi, Te, Pb, Sb, and Ag) and processes used are not often easy to scale to practically useful dimensions. Here we report the electrochemical synthesis of large-area, wafer-scale arrays of rough Si nanowires that are 20-300 nm in diameter. These nanowires have Seebeck coefficient and electrical resistivity values that are the same as doped bulk Si, but those with diameters of about 50 nm exhibit 100-fold reduction in thermal conductivity, yielding ZT = 0.6 at room temperature. For such nanowires, the lattice contribution to thermal conductivity approaches the amorphous limit for Si, which cannot be explained by current theories. Although bulk Si is a poor thermoelectric material, by greatly reducing thermal conductivity without much affecting the Seebeck coefficient and electrical resistivity, Si nanowire arrays show promise as high-performance, scalable thermoelectric materials.
Industrial characterization of nano-scale roughness on polished surfaces
Feidenhans'l, Nikolaj Agentoft; Hansen, Poul-Erik; Pilny, Lukas
2015-01-01
We report a correlation between the scattering value “Aq” and the ISO standardized roughness parameter Rq. The Aq value is a measure for surface smoothness, and can easily be determined from an optical scattering measurement. The correlation equation extrapolates the Aq value from a narrow...
Bayesian approach to rough set
Marwala, Tshilidzi
2007-01-01
This paper proposes an approach to training rough set models using Bayesian framework trained using Markov Chain Monte Carlo (MCMC) method. The prior probabilities are constructed from the prior knowledge that good rough set models have fewer rules. Markov Chain Monte Carlo sampling is conducted through sampling in the rough set granule space and Metropolis algorithm is used as an acceptance criteria. The proposed method is tested to estimate the risk of HIV given demographic data. The results obtained shows that the proposed approach is able to achieve an average accuracy of 58% with the accuracy varying up to 66%. In addition the Bayesian rough set give the probabilities of the estimated HIV status as well as the linguistic rules describing how the demographic parameters drive the risk of HIV.
Evaporative heat transfer in beds of sensible heat pellets
Arimilli, R.V.; Moy, C.A. [Univ. of Tennessee, Knoxville, TN (United States)
1989-03-01
An experimental study of boiling/evaporative heat transfer from heated spheres in vertical packed beds with downward liquid-vapor flow of Refrigerant-113 was conducted. Surface superheats of 1 to 50{degrees}C, mass flow rates of 1.7 to 5.6 Kg/min, sphere diameters of 1.59 and 2.54 cm, quality (i.e., mass fraction of vapor) of the inlet flow of 0.02 to 1.0, and two surface conditions were considered. Instrumented smooth and rough aluminum spheres were used to measure the heat transfer coefficients under steady state conditions. Heat transfer coefficients were independently determined for each sphere at three values three values of surface superheat. The quantitative results of this extensive experimental study are successfully correlated. The correlation equation for the boiling heat transfer coefficients is presented in terms of a homogeneous model. The correlation may be used in the development of numerical models to simulate the transient thermal performance of packed bed thermal energy storage unit while operating as an evaporator. The boiling of the liquid-vapor flow around the spheres in the packed bed was visually observed with a fiber-optic baroscope and recorded on a videotape. The visualization results showed qualitatively the presence of four distinct flow regimes. One of these occurs under saturated inlet conditions and are referred to as the Low-quality, Medium-quality, and High-quality Regimes. The regimes are discussed in detail in this paper.
Li, Zhaoguo; Lyu, Shihua; Wen, Lijuan; Zhao, Lin; Meng, Xianhong; Ao, Yinhuan
2017-08-01
The special climate environment creates a distinctive air-lake interaction characteristic in the Tibetan Plateau (TP) lakes, where the variations of surface roughness lengths also differ somewhat from those of other regions. However, how different categories of roughness lengths affect the lake surface energy exchange and the planetary boundary layer height (PBLH) remains unclear in the TP lakes. In this study, we used a tuned Weather Research and Forecasting (WRF) model version 3.6.1 to investigate the responses of the freeze-up date, turbulent fluxes, meteorological variables, and PBLH to surface roughness length variations in Ngoring Lake. Of all meteorological variables, the lake surface temperature responded to roughness length variations most sensitively; increasing roughness lengths can put the lake freeze-up date forward. The effect of momentum roughness length on wind speed was significantly affected by the fetch length. The increase in the roughness length for heat can induce the increment of the nightly PBLH in most months, especially for the central lake area in autumn. The primary factors that contribute to sensible heat flux (H) and latent heat flux (LE) were the roughness lengths for heat and momentum during the ice-free period, respectively. Increasing roughness length for heat can increase the nightly PBLH, and decreasing roughness length for moisture can also promote growth of the PBLH, but there was no obvious correlation between the momentum roughness length and the PBLH.
Brancaccio, R; Bettuzzi, M; Morigi, M P; Casali, F; Levi, G; Baldazzi, G; Inferrera, P
2016-09-01
Dynamic AngioThermography (DATG) is a contact-plate technique capable of producing a digital representation of breast vascularity. The inception and growth of a tumor are associated with neoangenesis, which may result in a demonstrable alteration in the regional blood flow, while in normal health conditions the vascularity remains unchanged throughout life. DATG, if included in the clinical evaluation for breast cancer, could potentially improve the accuracy of the diagnosis of this disease. Conventional DATG is limited, however, in that it is a projection (i.e. two-dimensional) imaging technique that does not provide any information on the depth and its effect on the pattern of the perfusion revealed by this technique. In fact, the blood pattern is detected by projecting temperature signals on the plate, thus acquiring a digital two-dimensional image. In this article we propose a new approach for extracting information on depth through the inversion of the Fourier heat equation. The idea is to extract the information along the third axis while acquiring and analyzing the temporal sequence during the process of image formation. The method implemented has been tested on a dedicated "electric phantom" and in one in vivo experiment. In spite of the limits of these preliminary tests, the experimental results have shown that this method makes it possible to obtain a 3D representation of the vascularity. Although it appears to be promising, further validation and characterization of our technique are required. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Heat pipe thermosyphon heat performance calculation
Novomestský, Marcel; Kapjor, Andrej; Papučík, Štefan; Siažik, Ján
2016-06-01
In this article the heat performance of the heat pipe thermosiphon is achieved through numerical model. The heat performance is calculated from few simplified equations which depends on the working fluid and geometry. Also the thermal conductivity is good to mentioning, because is really interesting how big differences are between heat pipes and full solid surfaces.
Complete equation of state based on sp ecific heat%基于比热的完全物态方程∗
范小兵; 陈俊祥; 向士凯
2016-01-01
In thermodynamics, the complete equation of state (EOS) for closed system is a functional relation defined by two independent state variables, and all other thermodynamic relations can be deduced by it. For example, Helmholtz free energy F as a function of specific volume v and temperature T of the system is a complete EOS. Unfortunately, the concrete expressions of these complete EOSs are unavailable. Here we establish a practical form of the complete EOS based on the pressure function pT (v) and constant-volume specific heat function Cv(v, T ) This complete EOS is mathematically equivalent to the Helmholtz free energy F . Here pT (v) is determined by the measurement and Cv(v, T ) can be expressed by two parts. One part is the lattice contribution based on the Debye model and the other part is electronic contribution obtained from the free electron model. Using this complete EOS we calculate the isothermal equation for six metals from the Hugoniot data. Good agreement between the isothermal equation and the experimental data verifies the reliability of the complete EOS. Through this complete EOS we can derive the concrete expression of physical parameters, and these physical parameters including the volume expansion coeﬃcient, the volume speed of sound, the adiabatic modulus, and W-J coeﬃcient are calculated by using the experimental data of Cu. Analyzing their variation trends we can timely adjust parameter in the calculation of the EOS. This kind of complete EOS is useful in the field of high temperature and high pressure physics.%在热力学中,一个封闭体系的完全物态方程指由两个状态量为自变量所确定的一种函数关系,由这个关系能够导出所有其他热力学量之间的关系。比如亥姆霍兹自由能F表示为体系的比体积v和温度T的函数F (v, T )时,就是这种完全物态方程。但是这种完全物态方程至今没有实际计算的表达式。我们以等温压强函数pT (v)和建立在德拜模
Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems
LIANG Ji-ye; QU Kai-she
2001-01-01
In this paper we address information measures of roughness of knowledge and rough sets for incomplete information systems. The definition of rough entropy of knowledge and its important properties are given. In particular, the relationship between rough entropy of knowledge and the Hartley measure of uncertainty is established. We show that rough entropy of knowledge decreases monotonously as granularity of information become smaller. This gives an information interpretation for roughness of knowledge. Based on rough entropy of knowledge and roughness of rough set. a definition of rough entropy of rough set is proposed, and we show that rough entropy of rough set decreases monotonously as granularity of information become smaller. This gives more accurate measure for roughness of rough set.
Sensing roughness and polish direction
Jakobsen, Michael Linde; Olesen, Anders Sig; Larsen, Henning Engelbrecht;
2016-01-01
needs information about the RMS-value of the surface roughness and the current direction of the scratches introduced by the polishing process. The RMS-value indicates to the operator how far he is from the final finish, and the scratch orientation is often specified by the customer in order to avoid...... complications during the casting process. In this work we present a method for measuring the RMS-values of the surface roughness while simultaneously determining the polishing direction. We are mainly interested in the RMS-values in the range from 0 – 100 nm, which corresponds to the finish categories of A1, A2...... and A3 (Finishing guide, Bales). Based on simple intensity measurements, we estimate the RMS-value of the surface roughness, and by using a sectioned annually shaped photo-detector to collect the scattered light, we can determine the direction of polishing and distinguish light scattered from random...
Surface roughness length dynamic over several different surfaces and its effects on modeling fluxes
2006-01-01
parameter chosen by the model, the effects of roughness length dynamic on flux calculation is analyzed. The maximum effect of roughness length dynamic on sensible heat flux is 2.726%, 33.802% and 18.105%, in Yucheng, Qianyanzhou, and Changbai Mountains experimental stations, respectively.
Topology theory on rough sets.
Wu, QingE; Wang, Tuo; Huang, YongXuan; Li, JiSheng
2008-02-01
For further studying the theories and applications of rough sets (RS), this paper proposes a new theory on RS, which mainly includes topological space, topological properties, homeomorphism, and its properties on RS by some new definitions and theorems given. The relationship between partition and countable open covering is discussed, and some applications based on the topological rough space and its topological properties are introduced. Moreover, some perspectives for future research are given. Throughout this paper, the advancements of the new theory on RS and topological algebra not only represent an important theoretical value but also exhibit significant applications of RS and topology.
Azevedo, Fabio Souto de, E-mail: fabio.azevedo@ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Inst. de Matematica; Sauter, Esequia, E-mail: esequia.sauter@canoas.ifrs.edu.b [Instituto Federal do Rio Grande do Sul (IFRS), Canoas, RS (Brazil); Thompson, Mark; Vilhena, Marco Tulio B., E-mail: mark.thompson@mat.ufrgs.b, E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2011-07-01
In this work we apply the Green Function Decomposition Method the radiative transport equation in a slab. The method consists in converting the radiative transport equation into a integral equation and projecting the integral operators involved into a finite dimensional space. This methodology does not involve an a priori discretization on the angular variable {mu}, requiring only that the kernel is numerically integrated on {mu}. Numerical results are provided for isotropic, linearly anisotropic, and Rayleigh scattering near the unitary albedo. (author)
Homomorphic Properties of Fuzzy Rough Groups
QIN Ke-yun; ZHANG Xiao-hua
2012-01-01
This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.
Fuzzy Rough Ring and Its Prop erties
REN Bi-jun; FU Yan-ling
2013-01-01
This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binary operation of ring was discussed.
A New Minimal Rough Set Axiom Group
DAI Jian-hua
2004-01-01
Rough set axiomatization is one aspect of rough set study, and the purpose is to characterize rough set theory using independable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. To characterize rough set theory, an axiom group named H consisting of 4 axioms, is proposed. That validity of the axiom group in characterizing rough set theory is reasonable, is proved. Simultaneously, the minimization of the axiom group, which requires that each axiom is an inequality and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.
Plant Communities of Rough Rock.
Jacobs, Linda
A unit of study on plants grown in the Navajo community of Rough Rock, Arizona, is presented in sketches providing the common Navajo name for the plant, a literal English translation, the English name of the plant, and the Latin name. A brief description of each plant includes where the plant grows, how the Navajos use the plant, and the color and…
Calibration of surface roughness standards
Thalmann, R.; Nicolet, A.; Meli, F.
2016-01-01
The key comparison EURAMET.L-K8.2013 on roughness was carried out in the framework of a EURAMET project starting in 2013 and ending in 2015. It involved the participation of 17 National Metrology Institutes from Europe, Asia, South America and Africa representing four regional metrology organisat...
Effective boundary condition at a rough surface starting from a slip condition
Dalibard, Anne-Laure
2010-01-01
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength $\\epsilon$. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit $\\epsilon = 0$ is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in previous works, in which the special case of a Dirichlet condition at the rough boundary was examined.
Rough Set Theory over Fuzzy Lattices
Guilong Liu
2006-01-01
Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of roug h sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set, and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices, respectively, based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak's rough sets and fuzzy rough sets.
Human roughness perception and possible factors effecting roughness sensation.
Aktar, Tugba; Chen, Jianshe; Ettelaie, Rammile; Holmes, Melvin; Henson, Brian
2017-06-01
Surface texture sensation is significant for business success, in particular for solid surfaces for most of the materials; including foods. Mechanisms of roughness perception are still unknown, especially under different conditions such as lubricants with varying viscosities, different temperatures, or under different force loads during the observation of the surface. This work aims to determine the effect of those unknown factors, with applied sensory tests on 62 healthy participants. Roughness sensation of fingertip was tested under different lubricants including water and diluted syrup solutions at room temperature (25C) and body temperature (37C) by using simple pair-wise comparison to observe the just noticeable difference threshold and perception levels. Additionally, in this research applied force load during roughness observation was tested with pair-wise ranking method to illustrate its possible effect on human sensation. Obtained results showed that human's capability of roughness discrimination reduces with increased viscosity of the lubricant, where the influence of the temperature was not found to be significant. Moreover, the increase in the applied force load showed an increase in the sensitivity of roughness discrimination. Observed effects of the applied factors were also used for estimating the oral sensation of texture during eating. These findings are significant for our fundamental understanding to texture perception, and for the development of new food products with controlled textural features. Texture discrimination ability, more specifically roughness discrimination capability, is a significant factor for preference and appreciation for a wide range of materials, including food, furniture, or fabric. To explore the mechanism of sensation capability through tactile senses, it is necessary to identify the relevant factors and define characteristics that dominate the process involved. The results that will be obtained under these principles
Transformation and entropy for fuzzy rough sets
无
2008-01-01
A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given.The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed.This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.
Rough Class on a Completely Distributive Lattice
陈德刚; 张文修; 宋士吉
2003-01-01
This paper generalizes the Pawlak rough set method to a completely distributive lattice. Theconcept of a rough set has many applications in data mining. The approximation operators on a completelydistributive lattice are studied, the rough class on a completely distributive lattice is defined and theexpressional theorems of the rough class are proven. These expressional theorems are used to prove that thecollection of all rough classes is an atomic completely distributive lattice.
李邦河
2006-01-01
It was proved by K.W. Kim, S.Y. Chung and D. Kim that if a C∞-solution u(x,t) of the heat equation in Rn++1 satisfiesfor any ε＞ 0, and some C ＞ 0, then its boundary determines a unique Fourier hyperfunction; and conversely, any Fourier hyperfunction is the boundary of such a u(x. t). Also, S. Y. Chung, D. Kim and K. Kim showed that replacing "any ε＞0" by "some ε＞0", then the above statements are true for extended Fourier hyperfunctions (called Fourier ultra-hyperfunctions also in the literature).We show that replacing solutions of the heat equation by solutions U(x,t) of the Hermite heat equation, andexp(ε(1/t+t+|x|)) by(e-t/√1+e-4t)ne-|x|2/21-e-4t/1+e-4teε(1+e-4t/1-e-4t+e-2t/1+e-4t|x|)then the above results relating Fourier hyperfunctions and extended Fourier hyperfunctions to heat equation become the relations with Hermite heat equations.Furthermore we proved that for fixed t,U(x,t) is an element of the space of test functions for extended Fourier hyperfunctions, thus Fourier hyperfunctions and extended Fourier hyperfunctions are limits of such nice functions. This gives also a new proof of the recent result of K. Kim on denseness of test functions in the space of extended Fourier hyperfunctions. Perhaps, the most interesting thing is that if U(x,t) represents a Fourier hyperfunction or an extended Fourier hyperfunction u, then the Fourier transformation of U(x,t) with respect to x represents the Fourier transformation of u.%证明了傅立叶超函数和扩充傅立叶超函数可用爱米特热方程的解来表示,且用以表示的解有很良好的性质.
Rode, Carsten
1998-01-01
Analytical theory of transient heat conduction.Fourier's law. General heat conducation equation. Thermal diffusivity. Biot and Fourier numbers. Lumped analysis and time constant. Semi-infinite body: fixed surface temperature, convective heat transfer at the surface, or constant surface heat flux...
Roughness effect on squeeze ﬁlm pressure
Manju Shukla
2002-10-01
The Stokes equations for the axial symmetric slow motion generated by a plane, approaching towards a solid surface allowing slippage, have been solved in this paper by using ﬁnite Hankel transform. The squeeze ﬁlm pressure between the two rigid faces is then obtained. It is found that the roughness parameter $\\beta \\sim d/4$, where is the separation between the two surfaces, causes an extremely high pressure on the surface.
Enhanced Backscattering from Rough Surfaces
1992-12-01
under Referee ..................... 12 3.4 Papers Presented at Professional Conferences ................... 12 4.0 LIST OF ALL PARTICIPATING SCIENTIFIC...60 -30 0 30 60 90 Scattering Angle (deg) Figure 2 (b). The DRC for the Perfectly Conducting Surface whose Profile is shown in Figure 2 (a) when the...Randomly Rough Surfaces", accepted for publication in Applied Optics (1993). I 3.3 Papers Submitted to Journal under Referee 19. E.R. Mendez, H.M
Rough Sets in Quotient Semigroups
LanShu; JialiYu
2004-01-01
This article is based on the notions of a congruence of a semigroup and the p-lower and p-upper approximations of a nonempty subset of a semigroup, discussing some properties of the product of these two subsets according to the properties of some especial single subsets such as subsemigroups and ideals, then the rigorous proof was given. Thus the rough theory in semigroups are completed and perfected.
Noise of sliding rough contact
Le Bot, Alain
2017-01-01
This article is a discussion about the origin of friction noise produced when rubbing solids having rough surfaces. We show that noise emerges from numerous impacts into the contact between antagonist asperities of surfaces. Prediction of sound sources reduces to a statistical problem of contact mechanics. On the other hand, contact is also responsible of dissipation of vibration. This leads to the paradoxical result that the noise may not be proportional to the number of sources.
Sensing roughness and polish direction
Jakobsen, M. L.; Olesen, A. S.; Larsen, H. E.; Stubager, J.; Hanson, S. G.; Pedersen, T. F.; Pedersen, H. C.
2016-04-01
As a part of the work carried out on a project supported by the Danish council for technology and innovation, we have investigated the option of smoothing standard CNC machined surfaces. In the process of constructing optical prototypes, involving custom-designed optics, the development cost and time consumption can become relatively large numbers in a research budget. Machining the optical surfaces directly is expensive and time consuming. Alternatively, a more standardized and cheaper machining method can be used, but then the object needs to be manually polished. During the polishing process the operator needs information about the RMS-value of the surface roughness and the current direction of the scratches introduces by the polishing process. The RMS-value indicates to the operator how far he is from the final finish, and the scratch orientation is often specified by the customer in order to avoid complications during the casting process. In this work we present a method for measuring the RMS-values of the surface roughness while simultaneously determining the polishing direction. We are mainly interested in the RMS-values in the range from 0 - 100 nm, which corresponds to the finish categories of A1, A2 and A3. Based on simple intensity measurements we estimates the RMS-value of the surface roughness, and by using a sectioned annual photo-detector to collect the scattered light we can determine the direction of polishing and distinguish light scattered from random structures and light scattered from scratches.
Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel
Masilamani, Kannan; Ganguly, Suvankar; Feichtinger, Christian; Bartuschat, Dominik; Rüde, Ulrich, E-mail: suva_112@yahoo.co.in [Department of Computer Science 10 University of Erlangen-Nuremberg, Cauerstr.11 91058 Erlangen (Germany)
2015-06-15
In this paper, a hybrid lattice-Boltzmann and finite-difference (LB-FD) model is applied to simulate the effects of three-dimensional surface roughness and electrokinetic heterogeneity on electroosmotic flow (EOF) in a microchannel. The lattice-Boltzmann (LB) method has been employed to obtain the flow field and a finite-difference (FD) method is used to solve the Poisson-Boltzmann (PB) equation for the electrostatic potential distribution. Numerical simulation of flow through a square cross-section microchannel with designed roughness is conducted and the results are critically analysed. The effects of surface heterogeneity on the electroosmotic transport are investigated for different roughness height, width, roughness interval spacing, and roughness surface potential. Numerical simulations reveal that the presence of surface roughness changes the nature of electroosmotic transport through the microchannel. It is found that the electroosmotic velocity decreases with the increase in roughness height and the velocity profile becomes asymmetric. For the same height of the roughness elements, the EOF velocity rises with the increase in roughness width. For the heterogeneously charged rough channel, the velocity profile shows a distinct deviation from the conventional plug-like flow pattern. The simulation results also indicate locally induced flow vortices which can be utilized to enhance the flow and mixing within the microchannel. The present study has important implications towards electrokinetic flow control in the microchannel, and can provide an efficient way to design a microfluidic system of practical interest. (paper)
薛占熬; 何华灿
2003-01-01
Rough implication operator is the emphasis and difficulty in the study of rough logic. Due to the shortage of rough implication in [3]～[5], we redefine rough set and rough implication operator by Stone algebra, and introduce new rough operators such as rough intersection, rough union, and rough complement. Moreover the characteristics of the proposed rough implication are investigated ,and we also point out that the proposed implication operation is superior to that of three-valued Lukasiewicz logic.
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
Quantitative roughness measurements with iTIRM
Bijl, R.J.M. van der; Fähnle, O.W.; Brug, H. van; Braat, J.J.M.
2000-01-01
A new method, iTIRM, is used for quantitative surface roughness measurements of ground and polished surfaces and it is shown to be a useful tool for measuring total surface quality instead of individual roughness parameters.
Growth of rough epitaxial surfaces
Abhijit Mookerjee
2002-02-01
We present here a set of coupled continuum equations to describe atomic deposition. We take into account evaporation due to thermal and mechanical disturbances as well as subsequent accretion at favourable grooves.
Yuan Wang
2015-01-01
Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.
Function S-Rough sets and its applications
Cui Yuquan; Shi Kaiquan
2006-01-01
Based on S-rough sets(singular rough sets), this paper presents function S-rough sets (function singular rough sets)and its mathematical structures and features. Function S-rough sets has two forms: function one direction S-rough sets (function one direction singular rough sets) and function two direction S-rough sets (function two direction singular rough sets). This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special case of function Srough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.
Anwar Ilmar Ramadhan
2015-03-01
Full Text Available Safety is a major concern in the design, operation and development of a nuclear reactor. One aspect of nuclear reactor safety factor is thermal-hydraulics aspect. In a PWR-type nuclear power plant has been used lighter fluid coolant is water or H2O. In this research, using nanofluid Al2O3-Water with volume fraction of (1%, (2% and also (3%, used as a cooling fluid in a nuclear reactor core with sub channel PWR fuel element rectangular arrangement. This research was carried out modeling of fuel elements are arranged rectangular, then performed numerical simulations using Computational Fluid Dynamics (CFD code. In order to obtain the characteristic pattern of flow velocity of each fluid, the fluid temperature distribution along the cylinder wall temperature distribution of the fuel element. Then analyzed the heat transfer in a nuclear reactor core with sub channel PWR fuel element rectangular arrangement, including heat transfer coefficient, Nusselt number (Nu, as well as heat transfer correlations. Heat transfer correlation for nanofluid Al2O3-Water (1%, (2% and also (3% proved to core of PWR nuclear reactor fuel element sub channel rectangular arrangement with the Reynolds number (Re is stretched, namely: 404 096
On Wind and Roughness over Land
Verkaik, J.W.
2006-01-01
The relation between wind, momentum flux, roughness and land-use in disturbed, non-homogeneous boundary layers is studied. Key questions are: ``how is the roughness related to land-use?'', ``how are wind and friction related to the upstream land-use and roughness?'', and ``is Monin-Obukhov theory
Diffusion-induced line-edge roughness
Stewart, Michael D.; Schmid, Gerard M.; Goldfarb, Dario L.; Angelopoulos, Marie; Willson, C. Grant
2003-06-01
As feature dimensions shrink, line edge roughness has become an increasing concern in semiconductor fabrication. There are numerous potential contributors to line edge roughness throughout the lithographic process and any measured roughness value on a printed device feature is, like the feature itself, a convolved function of every processing step. When the full lithographic process is used to study line edge roughness, it can be difficult to isolate the contribution to final roughness from any individual processing step or factor. To gain a more fundamental understanding of roughness generation that is specifically related to photoresist chemistry and formulation it is necessary to design experiments that separate out exposure related issues like mask dimension variation or local dose variation ("shot noise"). This can be accomplished using previously reported experimental protocols for bilayer film stack creation. The bilayer experimental approach has been used to study the effect of variations in such factors as post exposure bake time, photoacid generator loading, and developer concentration on roughness generation. Surface roughness of the developed film stacks is measured via atomic force microscopy. Surface roughness of developed bilayer film stacks may be considered analogous to sidewall roughness of printed features. An acrylate-based 193nm photoresist resin and an APEX-type resin are used in these experiments. In addition to experimental results, results from mesoscale lithographic simulations are used to gain further insight into diffusion induced roughness and how roughness in the latent image is modified during the development step.
Effect of deformation on the thermal conductivity of granular porous media with rough grain surface
Askari, Roohollah; Hejazi, S. Hossein; Sahimi, Muhammad
2017-08-01
Heat transfer in granular porous media is an important phenomenon that is relevant to a wide variety of problems, including geothermal reservoirs and enhanced oil recovery by thermal methods. Resistance to flow of heat in the contact area between the grains strongly influences the effective thermal conductivity of such porous media. Extensive experiments have indicated that the roughness of the grains' surface follows self-affine fractal stochastic functions, and thus, the contact resistance cannot be accounted for by models based on smooth surfaces. Despite the significance of rough contact area, the resistance has been accounted for by a fitting parameter in the models of heat transfer. In this Letter we report on a study of conduction in a packing of particles that contains a fluid of a given conductivity, with each grain having a rough self-affine surface, and is under an external compressive pressure. The deformation of the contact area depends on the fractal dimension that characterizes the grains' rough surface, as well as their Young's modulus. Excellent qualitative agreement is obtained with experimental data. Deformation of granular porous media with grains that have rough self-affine fractal surface is simulated. Thermal contact resistance between grains with rough surfaces is incorporated into the numerical simulation of heat conduction under compressive pressure. By increasing compressive pressure, thermal conductivity is enhanced more in the grains with smoother surfaces and lower Young's modulus. Excellent qualitative agreement is obtained with the experimental data.
Roughness-dependent dynamics of a point charge near a conducting plane
Gintautas, Vadas [Los Alamos National Laboratory; Hubler, Alfred [U ILLINOIS
2008-01-01
Nearly any surface in the real world is rough at some scale. Fmthermore, in most experiments there is some limit at which a surface is too rough to approximate by a smooth one. In this work the dynamics of a point charge near a rough surface are studied as the roughness of the surface is allowed to vary. The equation of motion of a charged pendulum near a rough, grounded, conducting plane is derived analytically and then analyzed both analytically and numerically . As the roughness is varied, a phase transition is observed in the fixed points of the pendulum. The consequences of a roughness phase transition on waveguide and electromagnetic scattering applications are considered. Also, the grounded plane may be considered to be a rough mirror and the point charge to be interacting with its image in this mirror. The quality of the image degrades with increasing roughness; the implications of this to interactions between systems in the real world and synthetic models are explored.
Axis Problem of Rough 3-Valued Algebras
Jianhua Dai; Weidong Chen; Yunhe Pan
2006-01-01
The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.
Function S-rough sets and mining-discovery of rough law in systems
Shi Kaiquan; Xia Jiarong
2006-01-01
Function S-rough sets (function singular rough sets) is defined on -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of -function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.
Equilibrium contact angles of liquid droplets on ideal rough solids.
Kang, Hie Chan; Jacobi, Anthony M
2011-12-20
This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Jimit R. Patel
2014-01-01
Full Text Available This paper aims to discuss the effect of slip velocity and surface roughness on the performance of Jenkins model based magnetic squeeze film in curved rough circular plates. The upper plate’s curvature parameter is governed by an exponential expression while a hyperbolic form describes the curvature of lower plates. The stochastic model of Christensen and Tonder has been adopted to study the effect of transverse surface roughness of the bearing surfaces. Beavers and Joseph’s slip model has been employed here. The associated Reynolds type equation is solved to obtain the pressure distribution culminating in the calculation of load carrying capacity. The computed results show that the Jenkins model modifies the performance of the bearing system as compared to Neuringer-Rosensweig model, but this model provides little support to the negatively skewed roughness for overcoming the adverse effect of standard deviation and slip velocity even if curvature parameters are suitably chosen. This study establishes that for any type of improvement in the performance characteristics the slip parameter is required to be reduced even if variance (−ve occurs and suitable magnetic strength is in force.
The Riccati Differential Equation and a Diffusion-Type Equation
Suazo, Erwin; Vega-Guzman, Jose M
2008-01-01
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equation with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.
Electromagnetic Scattering from Randomly Rough Surfaces with Hybrid FEM/BIE
LI Jie; GUO Li-Xin; HE Qiong; WEI Bing
2011-01-01
The hybrid finite element method (FEM) together with the boundary integral equation (BIE) is firstly applied to scattering from a conducting rough surface.The BIE is used as the truncation boundary condition for the special unbounled half space,whereas the FEM is used to solve the governing equation in the region surrounded by a rough surface and artificial boundary.Tapered wave incidence is employed to cancel the so-called “edge effect”.A hybrid FEM/BIE form ulation for generalized one-dimensional conducting rough surface scattering is presented,as well as examples that evaluate its validity compared to the method of moments.The bistatic scattering coefficients of a Gaussian rough surface are calculated for transverse-magnetic wave incidence.Conclusions are reached after analyzing the scattering patterns of rough surfaces with different rms heights and correlation lengths Analysis of electromagnetic scattering from a rough surface[1-3] is a very important issue in various areas of electromagnetic wave theory.Methods used to study rough surface scattering can be categorized into two groups:(1) analytical and approximate methods[4,5] and (2) numerical methods.[6,7] including method of moment (MoM)[8-10] and the finite difference in time domain method (FDTD).%The hybrid finite element, method (FEM) together with the boundary integral equation (BIE) in firstly applied to scattering from a conducting rough surface. The BIE is used an the truncation boundary condition for the special unbounded half space, whereas the FEM is used to solve the governing equation in the region surrounded by a rough surface and artificial boundary. Tapered wave incidence is employed to cancel the so-called "edge effect". A hybrid FEM/BIE formulation for generalized one-dimensional conducting rough surface scattering is presented, as well as examples that evaluate its validity compared to the method of moments, The bistatic scattering coefficients of a Gaussian rough surface are
Numerical Investigation Of Surface Roughness Effects On The Flow Field In A Swirl Flow
Ali SAKİN
2014-12-01
Full Text Available The aim of this study is to investigate axial and tangential velocity profiles, turbulent dissipation rate, turbulent kinetic energy and pressure losses under the influence of surface roughness for the swirling flow in a cyclone separator. The governing equations for this flow were solved by using Fluent CFD code. First, numerical analyses were run to verify numerical solution and domain with experimental results. Velocity profiles, turbulent parameters and pressure drops were calculated by increasing inlet velocity from 10 to 20 m/s and roughness height from 0 to 4 mm. Analyses of results showed that pressure losses are decreased and velocity field is considerably affected by increasing roughness height.
Jacobsen, Torben; Broers, G. H. J.
1977-01-01
SP, of theelectrode reaction. eta is the overvoltage at the electrode. This equation is appliedto a high temperature carbonate fuel cell. It is shown that the Peltier entropyterm by far exceeds the heat production due to the irreversible losses, and thatthe main part of heat evolved at the cathode is reabsorbed......The heat evolution at a single irreversibly working electrode is treated onthe basis of the Brønsted heat principle. The resulting equation is analogous to the expression for the total heat evolution in a galvanic cellwith the exception that –DeltaS is substituted by the Peltier entropy, Delta...
Mathematical Modeling of Surface Roughness of Castings Produced Using ZCast Direct Metal Casting
Chhabra, M.; Singh, R.
2015-04-01
Aim of this investigation is to develop a mathematical model for predicting surface roughness of castings produced using ZCast process by employing Buckingham's π-theorem. A relationship has been proposed between surface roughness of castings and shell wall thickness of the shell moulds fabricated using 3D printer. Based on model, experiments were performed to obtain the surface roughness of aluminium, brass and copper castings produced using ZCast process based on 3D printing technique. Based on experimental data, three best fitted third-degree polynomial equations have been established for predicting the surface roughness of castings. The predicted surface roughness values were then calculated using established best fitted equations. An error analysis was performed to compare the experimental and predicted data. The average prediction errors obtained for aluminium, brass and copper castings are 10.6, 2.43 and 3.12 % respectively. The obtained average surface roughness (experimental and predicted) values of castings produced are acceptable with the sand cast surface roughness values range (6.25-25 µm).
Mathematical model for strip surface roughness of stainless steel in cold rolling process
Chen, Jinshan; Li, Changsheng; Zhu, Tao; Han, Wenlong; Cao, Yong
2013-05-01
Surface roughness control is one of the most important subjects during producing stainless steel strips. In this paper, under the conditions of introducing to the concepts of transferring ratio and genetic factor and through the further theoretical analysis, a set of theoretical models about strip surface roughness were put forward in stainless steel cold tandem rolling. Meanwhile, the lubrication experiment in cold rolling process of SUS430 stainless steel strip was carried out in order to comprehensively study surface roughness. The effect of main factors on transferring ratio and genetic factor was analyzed quantitatively, such as reduction, initial thickness, deformation resistance, emulsion technological parameters and so on. Attenuation function equations used for describing roll surface roughness were set up, and also strip surface roughness at the entry of last mill was solved approximately. Ultimately, mathematical model on strip surface roughness for cold tandem rolling of stainless steel was built, and then it was used into the practical production. A great number of statistical results show that experimental data is in excellent agreement with the given regression equations, and exactly, the relative deviation on roughness between calculated and measured is less than 6.34%.
Propagation of elastic waves in a plate with rough surfaces
DAI Shuwu; ZHANG Hailan
2003-01-01
The characteristics of Lamb wave propagating in a solid plate with rough surfacesare studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequencyequation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation fora rough surface plate is different from that for a smooth surface plate, resulting in a smallperturbation Ak on Lamb wave vector k. The imaginary part of Ak gives the attenuationcaused by wave scattering. An experiment is designed to test our theoretical predications.By using wedge-shape pipes, different Lamb wave modes are excited. The signals at differentpositions are received and analyzed to get the dispersion curves and attenuations of differentmodes. The experimental results are compared with the theoretical predications.
Applied partial differential equations
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...
Pool Boiling Heat Transfer on structured Surfaces
Addy, J.; Olbricht, M.; Müller, B.; Luke, A.
2016-09-01
The development in the process and energy sector shows the importance of efficient utilization of available resources to improve thermal devices. To achieve this goal, all thermal components have to be optimized continuously. Various applications of multi-phase heat and mass transfer have to be improved. Therefore, the heat transfer and the influence of surface roughness in nucleate boiling with the working fluid propane is experimentally investigated on structured mild steel tubes, because only few data are available in the literature. The mild steel tube is sandblasted to obtain different surface roughness. The measurements are carried out over wide ranges of heat flux and pressure. The experimental results are compared with correlations from literature and the effect of surface roughness on the heat transfer is discussed. It is shown that the heat transfer coefficient increases with increasing surface roughness, heat flux and reduced pressure at nucleate pool boiling.
1976-01-01
'Air-O-Space' heater, based on spacecraft heat, requires no fuel other than electricity to run fan. Installed in chimney flue, heat pipes transfer heat from waste hot gases (but not the gases themselves) to fresh air blown across the other end of the pipes. It can transport roughly 500 times the heat flux of the best solid conductors with a temperature drop of less than 3 degrees per foot. This instrument has also been used by Kin-Tek Laboratories Inc. to produce an instrument to calibrate gas analyzers for air-pollution monitoring.
Air flow through smooth and rough cracks
Kula, H.-G.; Sharples, S. [Sheffield Univ. (United Kingdom). Dept. of Building Science
1994-12-31
A series of laboratory experiments are described which investigated the effect of surface roughness on the air flow characteristics of simple, straight-through, no-bend cracks with smooth and rough internal surfaces. The crack thicknesses used in the study were 1.0, 1.5 and 2.0mm. The crack lengths, in the direction of flow, were 50.8mm and 76.2mm. For the rough cracks the roughness was simulated with two different grades of commercially available energy-cloth (grade 60 and 100). The experimental results were satisfactorily fitted to a quadratic relationship between {Delta}p and Q of the form {Delta}p = AQ + BQ{sup 2} for both the smooth and rough crack data. The effect of roughness on the reduction of air flowing through a crack is also discussed. (author)
Hot-rolling nanowire transparent electrodes for surface roughness minimization.
Hosseinzadeh Khaligh, Hadi; Goldthorpe, Irene A
2014-01-01
Silver nanowire transparent electrodes are a promising alternative to transparent conductive oxides. However, their surface roughness presents a problem for their integration into devices with thin layers such as organic electronic devices. In this paper, hot rollers are used to soften plastic substrates with heat and mechanically press the nanowires into the substrate surface. By doing so, the root-mean-square surface roughness is reduced to 7 nm and the maximum peak-to-valley value is 30 nm, making the electrodes suitable for typical organic devices. This simple process requires no additional materials, which results in a higher transparency, and is compatible with roll-to-roll fabrication processes. In addition, the adhesion of the nanowires to the substrate significantly increases.
Studies on argon collisions with smooth and rough tungsten surfaces.
Ozhgibesov, M S; Leu, T S; Cheng, C H; Utkin, A V
2013-09-01
The aim of this work is to investigate argon scattering behaviors on the smooth and rough tungsten surfaces. Current work deals with numerical simulation of nanoscale heat transfer process accompanying with rarefied gas-solid substrate interactions using molecular dynamics (MD) method. Taking into account that this method is very time consuming, MD simulation using CUDA capable Graphic Cards is implemented. The results found that imperfection of the surface significantly influences on gas atom's momentum change upon collision. However, the energy exchange rate remains unchanged regardless to the surface roughness. This finding is in contrast with the results in extant literatures. We believed the results found in this paper are important for both numerical and theoretical analyses of rarefied gas flow in micro- and nano-systems where the choice of boundary conditions significantly influences flow.
Rough set models of Physarum machines
Pancerz, Krzysztof; Schumann, Andrew
2015-04-01
In this paper, we consider transition system models of behaviour of Physarum machines in terms of rough set theory. A Physarum machine, a biological computing device implemented in the plasmodium of Physarum polycephalum (true slime mould), is a natural transition system. In the behaviour of Physarum machines, one can notice some ambiguity in Physarum motions that influences exact anticipation of states of machines in time. To model this ambiguity, we propose to use rough set models created over transition systems. Rough sets are an appropriate tool to deal with rough (ambiguous, imprecise) concepts in the universe of discourse.
Estimation of human heat loss in five Mediterranean regions.
Bilgili, M; Simsek, E; Sahin, B; Yasar, A; Ozbek, A
2015-10-01
This study investigates the effects of seasonal weather differences on the human body's heat losses in the Mediterranean region of Turkey. The provinces of Adana, Antakya, Osmaniye, Mersin and Antalya were chosen for the research, and monthly atmospheric temperatures, relative humidity, wind speed and atmospheric pressure data from 2007 were used. In all these provinces, radiative, convective and evaporative heat losses from the human body based on skin surface and respiration were analyzed from meteorological data by using the heat balance equation. According to the results, the rate of radiative, convective and evaporative heat losses from the human body varies considerably from season to season. In all the provinces, 90% of heat loss was caused by heat transfer from the skin, with the remaining 10% taking place through respiration. Furthermore, radiative and convective heat loss through the skin reached the highest values in the winter months at approximately between 110 and 140W/m(2), with the lowest values coming in the summer months at roughly 30-50W/m(2).
The boundary layer over turbine blade models with realistic rough surfaces
McIlroy, Hugh M., Jr.
The impact of turbine blade surface roughness on aerodynamic performance and heat loads is well known. Over time, as the turbine blades are exposed to heat loads, the external surfaces of the blades become rough. Also, for film-cooled blades, surface degradation can have a significant impact on film-cooling effectiveness. Many studies have been conducted on the effects of surface degradation/roughness on engine performance but most investigations have modeled the rough surfaces with uniform or two-dimensional roughness patterns. The objective of the present investigation is to conduct measurements that will reveal the influence of realistic surface roughness on the near-wall behavior of the boundary layer. Measurements have been conducted at the Matched-Index-of-Refraction (MIR) Facility at the Idaho National Engineering and Environmental Laboratory with a laser Doppler velocimeter. A flat plate model of a turbine blade has been developed that produces a transitional boundary layer, elevated freestream turbulence and an accelerating freestream in order to simulate conditions on the suction side of a high-pressure turbine blade. Boundary layer measurements have been completed over a smooth plate model and over a model with a strip of realistic rough surface. The realistic rough surface was developed by scaling actual turbine blade surface data that was provided by U.S. Air Force Research Laboratory. The results indicate that bypass transition occurred very early in the flow over the model and that the boundary layer remained unstable throughout the entire length of the test plate; the boundary layer thickness and momentum thickness Reynolds numbers increased over the rough patch; and the shape factor increased over the rough patch but then decreased downstream of the patch relative to the smooth plate case; in the rough patch case the flow experienced two transition reversals with laminar-like behavior achieved by the end of the test plate; streamwise turbulence
Rock discontinuity surface roughness variation with scale
Bitenc, Maja; Kieffer, D. Scott; Khoshelham, Kourosh
2017-04-01
ABSTRACT: Rock discontinuity surface roughness refers to local departures of the discontinuity surface from planarity and is an important factor influencing the shear resistance. In practice, the Joint Roughness Coefficient (JRC) roughness parameter is commonly relied upon and input to a shear strength criterion such as developed by Barton and Choubey [1977]. The estimation of roughness by JRC is hindered firstly by the subjective nature of visually comparing the joint profile to the ten standard profiles. Secondly, when correlating the standard JRC values and other objective measures of roughness, the roughness idealization is limited to a 2D profile of 10 cm length. With the advance of measuring technologies that provide accurate and high resolution 3D data of surface topography on different scales, new 3D roughness parameters have been developed. A desirable parameter is one that describes rock surface geometry as well as the direction and scale dependency of roughness. In this research a 3D roughness parameter developed by Grasselli [2001] and adapted by Tatone and Grasselli [2009] is adopted. It characterizes surface topography as the cumulative distribution of local apparent inclination of asperities with respect to the shear strength (analysis) direction. Thus, the 3D roughness parameter describes the roughness amplitude and anisotropy (direction dependency), but does not capture the scale properties. In different studies the roughness scale-dependency has been attributed to data resolution or size of the surface joint (see a summary of researches in [Tatone and Grasselli, 2012]). Clearly, the lower resolution results in lower roughness. On the other hand, have the investigations of surface size effect produced conflicting results. While some studies have shown a decrease in roughness with increasing discontinuity size (negative scale effect), others have shown the existence of positive scale effects, or both positive and negative scale effects. We
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Effect of roughness on imaging and characterizing rough crack-like defect using ultrasonic arrays
Zhang, J.; Drinkwater, B. W.; Wilcox, P. D.
2012-05-01
All naturally occurring crack-like defects in solid structures are rough to some degree, which can affect defect inspection and characterization. Based on the simulated array data for various rough cracks and the total focusing method imaging algorithm, the effect of roughness on defect imaging and characterization was discussed. The array data was simulated by using the forward model combining with scattering matrices for various rough cracks. The scattering matrix describes the scattering field of a scatterer from all possible incident and scattering directions. It is shown that roughness can be either beneficial or detrimental to the detectability of a crack-like defect, depending on the defect characteristics such as length, roughness, correlation length, orientation angle, and array inspection configuration. It is also shown that roughness can cause the underestimation of length of rough crack-like defects by using the image-based approach.
Wetting properties of molecularly rough surfaces
Svoboda, Martin; Malijevský, Alexandr; Lísal, Martin
2015-09-01
We employ molecular dynamics simulations to study the wettability of nanoscale rough surfaces in systems governed by Lennard-Jones (LJ) interactions. We consider both smooth and molecularly rough planar surfaces. Solid substrates are modeled as a static collection of LJ particles arranged in a face-centered cubic lattice with the (100) surface exposed to the LJ fluid. Molecularly rough solid surfaces are prepared by removing several strips of LJ atoms from the external layers of the substrate, i.e., forming parallel nanogrooves on the surface. We vary the solid-fluid interactions to investigate strongly and weakly wettable surfaces. We determine the wetting properties by measuring the equilibrium droplet profiles that are in turn used to evaluate the contact angles. Macroscopic arguments, such as those leading to Wenzel's law, suggest that surface roughness always amplifies the wetting properties of a lyophilic surface. However, our results indicate the opposite effect from roughness for microscopically corrugated surfaces, i.e., surface roughness deteriorates the substrate wettability. Adding the roughness to a strongly wettable surface shrinks the surface area wet with the liquid, and it either increases or only marginally affects the contact angle, depending on the degree of liquid adsorption into the nanogrooves. For a weakly wettable surface, the roughness changes the surface character from lyophilic to lyophobic due to a weakening of the solid-fluid interactions by the presence of the nanogrooves and the weaker adsorption of the liquid into the nanogrooves.
Preparation of rough microsomes from rat liver.
Sabatini, David D
2014-08-01
This protocol describes how to prepare rat liver rough microsomes that contain undegraded membrane-bound polysomes and can function very well in an in vitro translation system. It uses endogenous ribonuclease inhibitor in all steps, avoiding pelleting rough microsomes in all steps and sacrificing good recovery.
SOME ROUGH OPERATORS ON PRODUCT SPACES
Chen Jiecheng; Wang Silei
2001-01-01
In this survery report, we shall mainly summarize some recent progress, interesting problems and typi cal methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.
Prediction of Ductile Fracture Surface Roughness Scaling
Needleman, Alan; Tvergaard, Viggo; Bouchaud, Elisabeth
2012-01-01
Experimental observations have shown that the roughness of fracture surfaces exhibit certain characteristic scaling properties. Here, calculations are carried out to explore the extent to which a ductile damage/fracture constitutive relation can be used to model fracture surface roughness scaling....... The scaling properties of the predicted thickness average fracture surfaces are calculated and the results are discussed in light of experimental observations....
Axiomatic Characterizations of IVF Rough Approximation Operators
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Influence of surface roughness on dispersion forces
Svetovoy, V. B.; Palasantzas, G.
Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this
Hydrodynamics and Roughness of Irregular Boundaries
2011-01-01
principle component analysis (PCA) similar to that used by Preston (2009) for ship- mounted multibeam data. Several variables derived from the...complex boundaries as well as characterization of acoustic and optical processes. Turbulent processes at the seabed are at the foundation of littoral...nearshore hydrodynamics, turbulence over rough beds influences optical and acoustic properties. Bed roughness also directly affects acoustic propagation in
Bed roughness experiments in supply limited conditions
Spekkers, Matthieu; Tuijnder, Arjan; Ribberink, Jan S.; Hulscher, Suzanne J.M.H.; Parsons, D.R.; Garlan, T.; Best, J.L.
2008-01-01
Reliable roughness models are of great importance, for example, when predicting water levels in rivers. The currently available roughness models are based on fully mobile bed conditions. However, in rivers where widely graded sediments are present more or less permanent armour layers can develop
Turning rough sleepers into responsible citizens
E. Tonkens; dr Lia van Doorn
2001-01-01
On the eve of the twenty-first century, it is a scandal that there are still people sleeping rough on our streets. This is not a situation we can continue to tolerate in a modern and civil society. These were the words of Tony Blair in his foreword to the policy document Rough Sleeping, The Governme
Roughness on Dutch railway wheels and rails
Dings, P.C.; Dittrich, M.G.
1996-01-01
Surface roughness on 150 railway wheels and on the rails of 30 sites in the Netherlands have been measured. Block braked wheels were found to show higher roughnesses than the rail at any site. The smoothest rail is 8 dB smoother than the smoothest wheel. It was concluded that in reducing railway
Computation of surface roughness using optical correlation
A M hamed; M Saudy
2007-05-01
The laser speckle photography is used to calculate the average surface roughness from the autocorrelation function of the aluminum diffuse objects. The computed results of surface roughness obtained from the proﬁle shapes of the autocorrelation function of the diffuser show good agreement with the results obtained by the stylus proﬁle meter.
Modeling and simulation of surface roughness
Patrikar, Rajendra M
2004-04-30
With the technology advancement, electronic devices are miniaturized at every development node. Physical parameters such as microscopic roughness are affecting these devices because surface to volume ratio is increasing rapidly. On all the real surfaces microscopic roughness appears, which affects many electronic properties of the material, which in turn decides the yield and reliability of the devices. Different type of parameters and simulation methods are used to describe the surface roughness. Classically surface roughness was modeled by methods such as power series and Fast Fourier Transform (FFT). Limitations of this methods lead to use the concept of self-similar fractals to model the rough surface through Mandelbrot-Weierstrass function. It is difficult to express surface roughness as a function of process parameters in the form of analytical functions. Method based on neural networks has been used to model these surfaces to map the process parameters to roughness parameters. Finally, change in electrical parameters such as capacitance, resistance and noise due to surface roughness has been computed by numerical methods.
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
A game-theoretic perspective on rough set analysis
YAO Jing-tao; HERBERT Joseph P
2008-01-01
Determining the correct threshold values for the probabilistic rough set approaches has been a heated issue among the community. Existing techniques offer no way in guaranteeing that the calculated values optimize the classification ability of the decision rules derived from this configuration. This article will formulate a game theoretic approach to calculating these thresholds to ensure correct approximation region size. Using payoff tables created from approximation measures and modified conditional risk strategies, we provide the user with tolerance levels for their loss functions. Using the tolerance values, new thresholds are calculated to provide correct classification regions. This will aid in determining a set of optimal region threshold values for decision making.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Rough sets: the classical and extended views
ZIARKO Wojciech
2008-01-01
The article is a comprehensive review of two major approaches to rough set theory: the classic rough setmodel introduced by Pawlak and the probabilistic approaches. The classic model is presented as a staging ground to the discussion of two varieties of the probabilistic approach, i.e. of the variable precision and Bayesian rough set models. Both of these models extend the classic model to deal with stochastic interactions while preserving the basicideas of the original rough set theory, such as set approximations, data dependencies, reducts etc. The probabilistic models are able to handle weaker data interactions than the classic model, thus extending the applicability of the rough set paradigm. The extended models are presented in considerable detail with some illustrative examples.
MODULAR APPROACH WITH ROUGH DECISION MODELS
Ahmed T. Shawky
2012-09-01
Full Text Available Decision models which adopt rough set theory have been used effectively in many real world applications.However, rough decision models suffer the high computational complexity when dealing with datasets ofhuge size. In this research we propose a new rough decision model that allows making decisions based onmodularity mechanism. According to the proposed approach, large-size datasets can be divided intoarbitrary moderate-size datasets, then a group of rough decision models can be built as separate decisionmodules. The overall model decision is computed as the consensus decision of all decision modulesthrough some aggregation technique. This approach provides a flexible and a quick way for extractingdecision rules of large size information tables using rough decision models.
Modular Approach with Rough Decision Models
Ahmed T. Shawky
2012-10-01
Full Text Available Decision models which adopt rough set theory have been used effectively in many real world applications.However, rough decision models suffer the high computational complexity when dealing with datasets ofhuge size. In this research we propose a new rough decision model that allows making decisions based onmodularity mechanism. According to the proposed approach, large-size datasets can be divided intoarbitrary moderate-size datasets, then a group of rough decision models can be built as separate decisionmodules. The overall model decision is computed as the consensus decision of all decision modulesthrough some aggregation technique. This approach provides a flexible and a quick way for extractingdecision rules of large size information tables using rough decision models.
Electrochemically grown rough-textured nanowires
Tyagi, Pawan; Postetter, David; Saragnese, Daniel [Johns Hopkins University, Department of Chemical and Biomolecular Engineering (United States); Papadakis, Stergios J. [Johns Hopkins University, Applied Physics Laboratory (United States); Gracias, David H., E-mail: dgracias@jhu.ed [Johns Hopkins University, Department of Chemical and Biomolecular Engineering (United States)
2010-03-15
Nanowires with a rough surface texture show unusual electronic, optical, and chemical properties; however, there are only a few existing methods for producing these nanowires. Here, we describe two methods for growing both free standing and lithographically patterned gold (Au) nanowires with a rough surface texture. The first strategy is based on the deposition of nanowires from a silver (Ag)-Au plating solution mixture that precipitates an Ag-Au cyanide complex during electrodeposition at low current densities. This complex disperses in the plating solution, thereby altering the nanowire growth to yield a rough surface texture. These nanowires are mass produced in alumina membranes. The second strategy produces long and rough Au nanowires on lithographically patternable nickel edge templates with corrugations formed by partial etching. These rough nanowires can be easily arrayed and integrated with microscale devices.
Suppression of intrinsic roughness in encapsulated graphene
Thomsen, Joachim Dahl; Gunst, Tue; Gregersen, Søren Schou
2017-01-01
Roughness in graphene is known to contribute to scattering effects which lower carrier mobility. Encapsulating graphene in hexagonal boron nitride (hBN) leads to a significant reduction in roughness and has become the de facto standard method for producing high-quality graphene devices. We have...... fabricated graphene samples encapsulated by hBN that are suspended over apertures in a substrate and used noncontact electron diffraction measurements in a transmission electron microscope to measure the roughness of encapsulated graphene inside such structures. We furthermore compare the roughness...... of these samples to suspended bare graphene and suspended graphene on hBN. The suspended heterostructures display a root mean square (rms) roughness down to 12 pm, considerably less than that previously reported for both suspended graphene and graphene on any substrate and identical within experimental error...
一种基于PETSc的热传导方程大规模并行求解策略%Parallel-computing Strategy for Large-scale Heat Equation Based on PETSc
程汤培; 王群
2009-01-01
提出了一种大规模热传导方程并行求解的策略,采用了分布式内存和压缩矩阵技术解决超大规模稀疏矩阵的存储及其计算,整合了多种Krylov子空间方法和预条件子技术来并行求解大规模线性方程组,基于面向对象设计实现了具体应用与算法的低耦合.在Linux机群系统上进行了性能测试,程序具有良好的加速比和计算性能.%A parallel-computing strategy was presented to solve the large-scale heat equations.The distributed memory and compressed matrices technology was adopted for both the process of storage and evaluation of large-scale sparse matrices.All kinds of Krylov subspace methods and preconditioners were introduced to assemble and solve the linear systems of equations.The code implementation of this strategy was written in high-level abstractions based on object-o-riented technology which promotes code reuse, flexibility and helps to decouple issues of parallelism from algorithm choices.The experiments carried on Linux clusters demonstrate that this strategy has achieved desirable speedup and ef-ficiency.
Ness, H; Stella, L; Lorenz, C D; Kantorovich, L
2017-04-28
We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.
Predicting bed form roughness: the influence of lee side angle
Lefebvre, Alice; Winter, Christian
2016-04-01
Flow transverse bedforms (ripples and dunes) are ubiquitous in rivers and coastal seas. Local hydrodynamics and transport conditions depend on the size and geometry of these bedforms, as they constitute roughness elements at the bed. Bedform influence on flow energy must be considered for the understanding of flow dynamics, and in the development and application of numerical models. Common estimations or predictors of form roughness (friction factors) are based mostly on data of steep bedforms (with angle-of-repose lee slopes), and described by highly simplified bedform dimensions (heights and lengths). However, natural bedforms often are not steep, and differ in form and hydraulic effect relative to idealised bedforms. Based on systematic numerical model experiments, this study shows how the hydraulic effect of bedforms depends on the flow structure behind bedforms, which is determined by the bedform lee side angle, aspect ratio and relative height. Simulations reveal that flow separation behind bedform crests and, thus, a hydraulic effect is induced at lee side angles steeper than 11 to 18° depending on relative height, and that a fully developed flow separation zone exists only over bedforms with a lee side angle steeper than 24°. Furthermore, the hydraulic effect of bedforms with varying lee side angle is evaluated and a reduction function to common friction factors is proposed. A function is also developed for the Nikuradse roughness (k s), and a new equation is proposed which directly relates k s to bedform relative height, aspect ratio and lee side angle.
The apparent state of droplets on a rough surface
CHEN XiaoLing; LU Tian
2009-01-01
The factors influencing the state and wetting transition of droplets on a rough surface are both complex and obscure. The change in wetting is directly reflected by changes under the contact condition of the droplets with the surface. The recent study about the wettability of the superhydrophobic surface under the condensing condition arouses the new understanding about the apparent state of droplets on a rough surface, in this work, to validate the existence of droplets in an intermediate state, a microscale pillar topological polydimethylsiloxane (PDMS) surface was manufactured and its wettability under various conditions was studied. According to the experimental data, it is proposed that the wetting state of a rough surface may be embodied using the contact area ratio of a solid/liquid/gas droplet with the projective plane. A general calculation model for the apparent contact angle of droplets is given and expressed diagrammatically. It is found that the measured apparent contact angles of droplets at dif-ferent states on the surface falls within the range predicted by our proposed equation.
Transport properties of the rough hard sphere fluid.
Kravchenko, Olga; Thachuk, Mark
2012-01-28
Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.
The apparent state of droplets on a rough surface
无
2009-01-01
The factors influencing the state and wetting transition of droplets on a rough surface are both complex and obscure. The change in wetting is directly reflected by changes under the contact condition of the droplets with the surface. The recent study about the wettability of the superhydrophobic surface under the condensing condition arouses the new understanding about the apparent state of droplets on a rough surface. In this work, to validate the existence of droplets in an intermediate state, a microscale pillar topological polydimethylsiloxane (PDMS) surface was manufactured and its wettability under various conditions was studied. According to the experimental data, it is proposed that the wetting state of a rough surface may be embodied using the contact area ratio of a solid/liquid/gas droplet with the projective plane. A general calculation model for the apparent contact angle of droplets is given and expressed diagrammatically. It is found that the measured apparent contact angles of droplets at dif- ferent states on the surface falls within the range predicted by our proposed equation.
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Function S-rough sets and law identification
SHI KaiQuan; YAO BingXue
2008-01-01
By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identifica-tion.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Conservation laws and symmetries of the shallow water system above rough bottom
Aksenov, A. V.; Druzhkov, K. P.
2016-06-01
The system of one-dimensional shallow water equations above the rough bottom is considered. All its hydrodynamic conservation laws are found, and a group classification is performed. A new conservation law additional to the two basic conservation laws is found. It is shown that the system of shallow water equations can be linearized by a point change of variables only in cases of constant and linear bottom profiles.
On Characterization of Rough Type-2 Fuzzy Sets
Tao Zhao; Zhenbo Wei
2016-01-01
Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced f...
Sensitive versus Rough Dependence under Initial Conditions in Atmospheric Flow Regimes
Anthony R. Lupo
2016-12-01
Full Text Available In this work, we will identify the existence of “rough dependence on initial conditions” in atmospheric phenomena, a concept which is a problem for weather analysis and forecasting. Typically, two initially similar atmospheric states will diverge slowly over time such that forecasting the weather using the Navier-Stokes equations is useless after some characteristic time scale. With rough dependence, two initial states diverge very quickly, implying forecasting may be impossible. Using previous research in atmospheric science, rough dependence is characterized by using quantities that can be calculated using atmospheric data and quantities. Rough dependence will be tested for and identified in atmospheric phenomena at different time scales using case studies. Data were provided for this project by archives outside the University of Missouri (MU and by using the MU RADAR at the South Farm experiment station.
Understanding EUV mask blank surface roughness induced LWR and associated roughness requirement
Yan, Pei-Yang [Intel Corp., Santa Clara, CA (United States); Zhang, Guojing [Intel Corp., Santa Clara, CA (United States); Gullickson, Eric M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Goldberg, Kenneth A. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Benk, Markus P. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2015-03-01
Extreme ultraviolet lithography (EUVL) mask multi-layer (ML) blank surface roughness specification historically comes from blank defect inspection tool requirement. Later, new concerns on ML surface roughness induced wafer pattern line width roughness (LWR) arise. In this paper, we have studied wafer level pattern LWR as a function of EUVL mask surface roughness via High-NA Actinic Reticle Review Tool. We found that the blank surface roughness induced LWR at current blank roughness level is in the order of 0.5nm 3σ for NA=0.42 at the best focus. At defocus of ±40nm, the corresponding LWR will be 0.2nm higher. Further reducing EUVL mask blank surface roughness will increase the blank cost with limited benefit in improving the pattern LWR, provided that the intrinsic resist LWR is in the order of 1nm and above.
Characterizing developing adverse pressure gradient flows subject to surface roughness
Brzek, Brian; Chao, Donald; Turan, Özden; Castillo, Luciano
2010-04-01
An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and X-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., T ∞, U ref, and C p) were maintained for smooth, k + = 0, and rough, k + = 41-60, surfaces with Reynolds number based on momentum thickness, 3,000 carefully designed such that the x-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91-108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33-79, 1998a) scaling of the mean velocity deficit, U ∞δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Turbulent transfer coefficient and roughness length in a high-altitude lake, Tibetan Plateau
Li, Zhaoguo; Lyu, Shihua; Zhao, Lin; Wen, Lijuan; Ao, Yinhuan; Wang, Shaoying
2016-05-01
A persistent unstable atmospheric boundary layer was observed over Lake Ngoring, caused by higher temperature on the water surface compared with the overlying air. Against this background, the eddy covariance flux data collected from Lake Ngoring were used to analyse the variation of transfer coefficients and roughness lengths for momentum, heat and moisture. Results are discussed and compared with parameterization schemes in a lake model. The drag coefficient and momentum roughness length rapidly decreased with increasing wind velocity, reached a minimum value in the moderate wind velocity and then increased slowly as wind velocity increased further. Under weak wind conditions, the surface tension or small scale capillary wave becomes more important and increases the surface roughness. The scalar roughness length ratio was much larger than unity under weak wind conditions, and it decreased to values near unity as wind velocity exceeded 4.0 m s-1. The lake model could not reproduce well the variation of drag coefficient, or momentum roughness length, versus wind velocity in Lake Ngoring, but it did simulate well the sensible heat and latent heat fluxes, as a result of complementary opposite errors.
Rough Fuzzy Relation on Two Universal Sets
Xuan Thao Nguyen
2014-03-01
Full Text Available Fuzzy set theory was introduced by L.A. Zadeh in 1965. Immediately, it has many applications in practice and in building databases, one of which is the construction of a fuzzy relational database based on similar relationship. The study of cases of fuzzy relations in different environments will help us understand its applications. In this paper, the rough fuzzy relation on Cartesian product of two universe sets is defined, and then the algebraic properties of them, such as the max, min, and composition of two rough fuzzy relations are examined. Finally, reflexive, α-reflexive, symmetric and transitive rough fuzzy relations on two universe sets are also defined.
Rough Sets, Their Extensions and Applications
Qiang Shen; Richard Jensen
2007-01-01
Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological.
Comparison between rough and smooth plates within the same Rayleigh-Benard cell
Rusaouen, Eleonore; Salort, Julien; Seychelles, Fanny; Tisserand, Jean-Christophe; Creyssels, Matthieu; Liot, Olivier; Castaing, Bernard; Chilla, Francesca
2012-11-01
A Rayleigh-Benard cell consist in a tank filled of a fluid on which a temperature difference is imposed thanks to a cold plate at top and a hot at bottom. Movement is induced by the buoyancy force. Considering most of experimental apparatus previously used all around the world, both plates are smooth. Recently, the effect of roughness on thermal transfer had become a subject of interest. The present experiment is an asymetrical rough Rayleigh-Benard cell. Indeed the hot plate is rough whereas the cold plate is still smooth. Previously, tests conducted with 2 mm high roughness showed independence of the two plates and a heat flux enhancement on the rough plate, which appeared to be greater than expected from the surface increase. This regime was caracterized by a Nu ~ Ra 1 / 2 law. New results obtained with a 4mm high roughness also show this flux enhancement and the independent behaviour of the plates. But a transition appears at high Rayleigh from the 1/2 power law regime to a 1/3 one. Former results obtained in the same symetrical smooth/smooth cell also showed a 1/3 law. But the rough 1/3 regime reveals a multiplier coefficient of 1.6 with the smooth one.
Influence of rough and smooth walls on macroscale granular segregation patterns
D'Ortona, Umberto; Thomas, Nathalie; Lueptow, Richard M.
2016-02-01
Size bidisperse granular materials in a spherical tumbler segregate into two different patterns of three bands with either small particles at the equator and large particles at the poles or vice versa, depending upon the fill level in the tumbler. Here we use discrete element method simulations with supporting qualitative experiments to explore the effect of the tumbler wall roughness on the segregation pattern, modeling the tumbler walls as either a closely packed monolayer of fixed particles resulting in a rough wall or a frictional geometrically smooth wall. Even though the tumbler wall is in contact with the flowing layer only at its periphery, the impact of wall roughness is profound. Smooth walls tend toward a small-large-small (SLS) band pattern at the pole-equator-pole at all but the highest fill fractions; rough walls tend toward a large-small-large (LSL) band pattern at all but the lowest fill fractions. This comes about because smooth walls induce poleward axial drift of small particles and an equator-directed drift for large particles, resulting in an SLS band pattern. On the other hand, rough walls result in both sizes of particles moving poleward at the surface of the flow. Due to radial segregation, small particles percolate lower in the flowing layer and when arriving near the pole are caught in the return current drift that carries them back toward the equator incrementally with each passage through the flowing layer, while large particles remain at the surface near the pole, resulting in an LSL band pattern. The tendency toward either of the two segregation patterns depends on the fill level in the tumbler and the roughness of the tumbler's bounding wall.
Thermal radiation heat transfer
Howell, John R; Siegel, Robert
2016-01-01
Further expanding on the changes made to the fifth edition, Thermal Radiation Heat Transfer, 6th Edition continues to highlight the relevance of thermal radiative transfer and focus on concepts that develop the radiative transfer equation (RTE). The book explains the fundamentals of radiative transfer, introduces the energy and radiative transfer equations, covers a variety of approaches used to gauge radiative heat exchange between different surfaces and structures, and provides solution techniques for solving the RTE.
Use of roughness maps in visualisation of surfaces
Seitavuopio, Paulus; Rantanen, Jukka; Yliruusi, Jouko
2005-01-01
In this study we will present a new method to describe surface roughness. This method builds a roughness map of the studied area. The roughness map can give information of localised roughness. The test surfaces used in the evaluation of the method were tablets, which were made of lactose monohydr...... of the heterogeneity of surface roughness of various materials....
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Umatilla - Umatilla Slough Rough Fish Eradication
US Fish and Wildlife Service, Department of the Interior — The purpose of the proposed action is to enhance environmental conditions in the Whitcomb Island Slough by reducing the population of rough fish, including common...
US Fish and Wildlife Service, Department of the Interior — The purpose of the action is to enhance environmental conditions in the McNary Slough by reducing the population of rough fish, including common carp (Cyprinus...
Accurate Topological Measures for Rough Sets
2015-01-01
Data granulation is considered a good tool of decision making in various types of real life applications. The basic ideas of data granulation have appeared in many fields, such as interval analysis, quantization, rough set theory, Dempster-Shafer theory of belief functions, divide and conquer, cluster analysis, machine learning, databases, information retrieval, and many others. Some new topological tools for data granulation using rough set approximations are initiated. Moreover, some topolo...
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
General Regularities of Wood Surface Roughness
MAGOSS, Endre
2008-01-01
Full Text Available The surface roughness of wood products is depending on many factors related both towood properties and wood working operational parameters. Probably this is the reason why there areno generally valid correlation determining surface roughness parameters as a function of influencingfactors. In particular, the account of wood structure in the surface roughness interpretation proved tobe difficult.In the last years an important progress was made in recognizing the role of the anatomicalstructure of wood species in the attainable surface roughness. The introduction of a structure numbermade it possible to express and characterize the different wood species numerically.The aim of these studies was the separation of roughness components due to the anatomicalstructure and the woodworking operation. Using a special finishing technique, the roughnesscomponent due to woodworking operations was not significant and could be separated. The samespecimens were also subjected to different woodworking operations using cutting velocities between10 and 50 m/s. The processing of experimental data resulted in a chart showing the minimumroughness component due to different woodworking operations. Special experimental investigationwas conducted to clear the influence of edge dullness on the surface roughness, especially on itsAbbott-parameters. The measurements showed that the Rk-parameter is a good indicator to predictedge dullness.
Effects of Chairside Polishing and Brushing on Surface Roughness of Acrylic Denture Base Resins
Seung-Kyun Kim; Ju-Mi Park; Min-Ho Lee; Jae-Youn Jung; Shipu Li; Xinyu Wang
2009-01-01
The effects of 3 chairside polishing kits and mechanical brushing on the surface roughness of 3 different acrylic denture base resins were compared. Acrylic denture base resins (auto-polymerizing, heat-polymerizing, injected heat-polymerizing resins) were examined after a tungsten carbide bur, and after chairside polishing using 3 polishing kits and pumice. The specimens were subjected to mechanical brushing using a wear tester to simulate 30 000 strokes of brushing. The surface roughness of the acrylic denture base resin specimens was measured using a contact pro-filometer. After the test, the random polished acrylic resins were evaluated by scanning electron mi-croscopy (SEM) and atomic force microscopy (AFM). Acrylic denture base resins polished using the 3 types of polishing kits had a smoother surface than those finished with the tungsten carbide bur (p ＜0.05). The surface of the resin polished by a TC cutter exceeded the Ra of 0.2 μm (p＜0.05). The auto-polymerizing resin showed a significantly higher surface roughness than the heat-polymerizing resin and injected heat-polymerizing resin (p＞0.05). In the case of polishing step wise, there was almost no change in surface roughness after brushing (p＞0.05).
Zheng, D.; Velde, van der R.; Su, Z.; Booij, M.J.; Hoekstra, A.Y.; Wen, J.
2014-01-01
Current land surface models still have difficulties with producing reliable surface heat fluxes and skin temperature (Tsfc) estimates for high-altitude regions, which may be addressed via adequate parameterization of the roughness lengths for momentum (z0m) and heat (z0h) transfer. In this study, th
Effect of Cigarette Smoke on Surface Roughness of Different Denture Base Materials
Mahross, Hamada Zaki; Mohamed, Mahmoud Darwish; Hassan, Ahmed Mohammed
2015-01-01
Background Surface roughness is an important property of denture bases since denture bases are in contact with oral tissues and a rough surface may affect tissues health due to microorganism accumulation. Therefore, the effect of cigarette smoke on the surface roughness of two commercially available denture base materials was evaluated to emphasize which type has superior properties for clinical use. Materials and Methods A total numbers of 40 specimens were constructed from two commercially available denture base materials; heat-cured PMMA and visible light cured UDMA resins (20 for each). The specimens for each type were randomly divided into: Group I: Heat cured resin control group; Group II: Heat cured acrylic resin specimens exposed to cigarette smoking; Group III: Light cured resin control group; Group IV: Light cured resin specimens exposed to cigarette smoking. The control groups used for immersion in distilled water and the smoke test groups used for exposure to cigarette smoking. The smoke test groups specimens were exposed to smoking in a custom made smoking chamber by using 20 cigarettes for each specimen. The surface roughness was measured by using Pocket SurfPS1 profilometer and the measurements considered as the difference between the initial and final roughness measured before and after smoking. Results The t-test for paired observation of test specimens after exposure to smoking was indicated significant change in surface roughness for Group II (pdentures constructed from heat cured acrylic resin had been increased after exposure to cigarette smoke but had no impact on the dentures constructed from visible light cured resin. PMID:26501010
Apurba Layek
2010-07-01
Full Text Available The use of an artificial roughness on a surface is an effective technique to enhance the rate of heat transfer to fluid flow in the duct of solar air heater. However, the increase in thermal energy gain is always accompanied by increase in pumping power. This paper is concerned with optimization of roughness parameters of solar air heater based on effective efficiency criterion. Effective efficiency of a solar air heater having repeated transverse chamfered rib–groove roughness on one broad wall has been computed using the correlations for heat transfer and friction factor developed within the investigated range of operating and system parameters. Roughness parameters viz. relative roughness pitch P/e, relative groove position g/P, chamfer angle , relative roughness height e/Dh and flow Reynolds number Re, have a combined effect on the heat transfer as well as fluid friction. The thermo-hydraulic performance of an air heater in terms of effective efficiency is determined on the basis of actual thermal energy gain subtracted by the primary energy required to generate power needed for pumping air through the roughened duct. Based on energy transfer mechanism to the absorber plate, a mathematical model is developed to compute effective efficiency. The selection of the optimal values of the roughness parameters involves the comparison of the enhancement of thermal performance and the increase of pumping losses as a result of using roughness in the collector system with that of the system without roughness. The effective efficiency criterion is maximized and reasonably optimized designs of roughness are found.
刘转转
2011-01-01
在概率论中,求解形如E[φ(X)] -1/(√2πσ)∫-∞+∞φ(x)e-(x-μ)2/(2σ2)ds的积分是很重要的.但即使φ(x)是初等函数如xn,ems,sinmx等,用常规的分部积分法也不易处理.而1维热传导方程初值问题有形如前面的积分解和含有微分算子的级数解,由解的唯一性将把这类期望的积分运算转化为含有微分的级数运算.通过举例说明了该方法在求解数字特征、特征函数等方面的简便实用性,并以公式形式给出了xn,ems,sinmx等解析函数的期望.最后作为补充,给出了n维类似的结论.%In probability theory, the integral such asE [ψ(X) ] =1 -Γ2πσ∫+∞-∞ ψ(x)e-(x-n)2-2σ2 dx is very important,but it is not easy to solve it by using integration by parts, though ψ( x) is the elementary function such asxn, emx , smmx,etc. The solution of the Cauchy problem of one-dimension heat equation has two forms: the integral as E[ψ> (X) ] which was mentioned and the progression with differential operator. Because of the unique of the solution, integral oper-ation can be changed into differential operation. The formulas will be easily given in the form of examples about n-umerical characteristic and characteristic function, etc, when ψ( x) is the elementary function such as xn, emx, sinmx, and the product of them. Finally, the theory of re-dimension heat equation will be given.
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
The Heat Is on: An Inquiry-Based Investigation for Specific Heat
Herrington, Deborah G.
2011-01-01
A substantial number of upper-level science students and practicing physical science teachers demonstrate confusion about thermal equilibrium, heat transfer, heat capacity, and specific heat capacity. The traditional method of instruction, which involves learning the related definitions and equations, using equations to solve heat transfer…
The Heat Is on: An Inquiry-Based Investigation for Specific Heat
Herrington, Deborah G.
2011-01-01
A substantial number of upper-level science students and practicing physical science teachers demonstrate confusion about thermal equilibrium, heat transfer, heat capacity, and specific heat capacity. The traditional method of instruction, which involves learning the related definitions and equations, using equations to solve heat transfer…
Porous Squeeze Film Bearing with Rough Surfaces Lubricated by a Bingham Fluid
Walicka A.
2014-11-01
Full Text Available In the paper the effect of both bearing surfaces and the porosity of one bearing surface on the pressure distribution and load-carrying capacity of a squeeze film bearing is discussed. The equations of motion of a Bingham fluid in a bearing clearance and in a porous layer are presented. Using the Morgan-Cameron approximation and Christensen theory of rough lubrication the modified Reynolds equation is obtained. The analytical solutions of this equation for a squeeze film bearing are presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. A thrust radial bearing is considered as a numerical example.
Porous Squeeze Film Bearing with Rough Surfaces Lubricated by a Bingham Fluid
Walicka, A.; Walicki, E.; Jurczak, P.; Falicki, J.
2014-11-01
In the paper the effect of both bearing surfaces and the porosity of one bearing surface on the pressure distribution and load-carrying capacity of a squeeze film bearing is discussed. The equations of motion of a Bingham fluid in a bearing clearance and in a porous layer are presented. Using the Morgan-Cameron approximation and Christensen theory of rough lubrication the modified Reynolds equation is obtained. The analytical solutions of this equation for a squeeze film bearing are presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. A thrust radial bearing is considered as a numerical example.
Serasa, Ailie Sofyiana; Lai, Goh Thian; Rafek, Abdul Ghani; Simon, Norbert; Hussein, Azimah; Ern, Lee Khai; Surip, Noraini; Mohamed, Tuan Rusli
2016-11-01
The significant influence of surface roughness of discontinuity surfaces is a quantity that is fundamental to the understanding of shear strength of geological discontinuities. This is due to reason that the shear strength of geological discontinuities greatly influenced the mechanical behavior of a rock mass especially in stability evaluation of tunnel, foundation, and natural slopes. In evaluating the stability of these structures, the study of peak friction angle (Φpeak) of rough discontinuity surfaces has become more prominent seeing that the shear strength is a pivotal factor causing failures. The measurement of peak friction angle however, requires an extensive series of laboratory tests which are both time and cost demanding. With that in mind, this publication presents an approach in the form of an experimentally determined polynomial equation to estimate peak friction angle of limestone discontinuity surfaces by measuring the Joint Roughness Coefficient (JRC) values from tilt tests, and applying the fore mentioned empirical correlation. A total of 1967 tilt tests and JRC measurements were conducted in the laboratory to determine the peak friction angles of rough limestone discontinuity surfaces. A polynomial equation of ɸpeak = -0.0635JRC2 + 3.95JRC + 25.2 that exhibited 0.99 coefficient of determination (R2) were obtained from the correlation of JRC and peak friction angles. The proposed correlation offers a practical method for estimation of peak friction angles of rough discontinuity surfaces of limestone from measurement of JRC in the field.
Hasager, C.B.; Nielsen, N.,W.; Jensen, N.O.
2003-01-01
In numerical weather prediction, climate and hydrological modelling, the grid cell size is typically larger than the horizontal length scales of variations in aerodynamic roughness, surface temperature and surface humidity. These local land cover variations give rise to sub-grid scale surface flux...... to be well-described in any large-scale model. A method of aggregating the roughness step changes in arbitrary real terrain has been applied in flat terrain (Denmark) where sub-grid scale vegetation-driven roughness variations are a dominant characteristic of the landscape. The aggregation model...... is a physical two-dimensional atmospheric flow model in the horizontal domain based on a linearized version of the Navier Stoke equation. The equations are solved by the Fast Fourier Transformation technique, hence the code is very fast. The new effective roughness maps have been used in the HIgh Resolution...
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th