Heat transfer from rough surfaces
International Nuclear Information System (INIS)
Dalle Donne, M.
1977-01-01
Artificial roughness is often used in nuclear reactors to improve the thermal performance of the fuel elements. Although these are made up of clusters of rods, the experiments to measure the heat transfer and friction coefficients of roughness are performed with single rods contained in smooth tubes. This work illustrated a new transformation method to obtain data applicable to reactor fuel elements from these annulus experiments. New experimental friction data are presented for ten rods, each with a different artificial roughness made up of two-dimensional rectangular ribs. For each rod four tests have been performed, each in a different outer smooth tube. For two of these rods, each for two different outer tubes, heat transfer data are also given. The friction and heat transfer data, transformed with the present method, are correlated by simple equations. In the paper, these equations are applied to a case typical for a Gas Cooled Fast Reactor fuel element. (orig.) [de
Numerical Schemes for Rough Parabolic Equations
Energy Technology Data Exchange (ETDEWEB)
Deya, Aurelien, E-mail: deya@iecn.u-nancy.fr [Universite de Nancy 1, Institut Elie Cartan Nancy (France)
2012-04-15
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3.
Rough horizontal plates: heat transfer and hysteresis
Energy Technology Data Exchange (ETDEWEB)
Tisserand, J-C; Gasteuil, Y; Pabiou, H; Castaing, B; Chilla, F [Universite de Lyon, ENS Lyon, CNRS, 46 Allee d' ltalie, 69364 Lyon Cedex 7 (France); Creyssels, M [LMFA, CNRS, Ecole Centrale Lyon, 69134 Ecully Cedex (France); Gibert, M, E-mail: mathieu.creyssels@ec-lyon.fr [Also at MPI-DS (LFPN) Gottingen (Germany)
2011-12-22
To investigate the influence of a rough-wall boundary layer on turbulent heat transport, an experiment of high-Rayleigh convection in water is carried out in a Rayleigh-Benard cell with a rough lower plate and a smooth upper plate. A transition in the heat transport is observed when the thermal boundary layer thickness becomes comparable to or smaller than the roughness height. Besides, at larger Rayleigh numbers than the threshold value, heat transport is found to be increased up to 60%. This enhancement cannot be explained simply by an increase in the contact area of the rough surface since the contact area is increased only by a factor of 40%. Finally, a simple model is proposed to explain the enhanced heat transport.
Heat transfer and friction on smooth and rough test rods
International Nuclear Information System (INIS)
Franken, W.M.P.; Hoogland, H.; Deijman, P.
1977-06-01
Results are reported on heat transfer and pressure drop tests on one smooth and nine rough test rods in an annular geometry. The wall roughness consisted of transversal ribs with various roughness pitches, rib heights and rib widths. The tests were performed with air as coolant under a wide range of experimental conditions: 10 5 5 , 1.1 2. Special attention has been given to the effect of variation of the physical coolant properties over the flow cross section. This effect could be described by the power function (Tsub(w)/Tsub(b))sup(-0.3l) in additional systematic variation of the heat transfer could be recognized, dependent on the coolant temperature level. The experimental results were correlated by the equation St = C(Tsub(in)) Resup(-0.2) Prsup(-0.6) (Tsub(w)/Tsub(b)sup(-0.31). Values of C(Tsub(in)) are given in tabular form. The thermal entrance effect has been measured on various test rods. A substantial reduction of the heat transfer coefficient was almost constant along the rough test rods
Differential equations driven by rough paths with jumps
Friz, Peter K.; Zhang, Huilin
2018-05-01
We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.
Heat transfer and pressure drop in microchannels with random roughness
Pelevic, N.; van der Meer, Theodorus H.
2016-01-01
The effect of surface roughness on heat transfer and fluid flow phenomena within a microchannel has been investigated by using the lattice Boltzmann method. The surface roughness has been generated by using Gaussian function. Gaussian function is an efficient and convenient method to create surface
Surface roughness effects on heat transfer in Couette flow
International Nuclear Information System (INIS)
Elia, G.G.
1981-01-01
A cell theory for viscous flow with rough surfaces is applied to two basic illustrative heat transfer problems which occur in Couette flow. Couette flow between one adiabatic surface and one isothermal surface exhibits roughness effects on the adiabatic wall temperature. Two types of rough cell adiabatic surfaces are studied: (1) perfectly insulating (the temperature gradient vanishes at the boundary of each cell); (2) average insulating (each cell may gain or lose heat but the total heat flow at the wall is zero). The results for the roughness on a surface in motion are postulated to occur because of fluid entrainment in the asperities on the moving surface. The symmetry of the roughness effects on thermal-viscous dissipation is discussed in detail. Explicit effects of the roughness on each surface, including combinations of roughness values, are presented to enable the case where the two surfaces may be from different materials to be studied. The fluid bulk temperature rise is also calculated for Couette flow with two ideal adiabatic surfaces. The effect of roughness on thermal-viscous dissipation concurs with the viscous hydrodynamic effect. The results are illustrated by an application to lubrication. (Auth.)
The influence of heat accumulation on the surface roughness in powder-bed additive manufacturing
International Nuclear Information System (INIS)
Jamshidinia, Mahdi; Kovacevic, Radovan
2015-01-01
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 (R k ) and peak height (R pk ). 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. (paper)
Improvement of Reactor Fuel Element Heat Transfer by Surface Roughness
International Nuclear Information System (INIS)
Kjellstroem, B.; Larsson, A.E.
1967-04-01
In heat exchangers with a limited surface temperature such as reactor fuel elements, rough heat transfer surfaces may give lower pumping power than smooth. To obtain data for choice of the most advantageous roughness for the superheater elements in the Marviken reactor, measurements were made of heat transfer and pressure drop in an annular channel with a smooth or rough test rod in a smooth adiabatic shroud. 24 different roughness geometries were tested. The results were transformed to rod cluster geometry by the method of W B Hall, and correlated by the friction and heat transfer similarity laws as suggested by D F Dipprey and R H Sabersky with RMS errors of 12.5 % in the friction factor and 8.1 % in the Stanton number. The relation between the Stanton number and the friction factor could be described by a relation of the type suggested by W Nunner, with a mean error of 3.1 % and an RMS error of 11.6 %. Application of the results to fuel element calculations is discussed, and the great gains in economy which can be obtained with rough surfaces are demonstrated by two examples
Improvement of Reactor Fuel Element Heat Transfer by Surface Roughness
Energy Technology Data Exchange (ETDEWEB)
Kjellstroem, B; Larsson, A E
1967-04-15
In heat exchangers with a limited surface temperature such as reactor fuel elements, rough heat transfer surfaces may give lower pumping power than smooth. To obtain data for choice of the most advantageous roughness for the superheater elements in the Marviken reactor, measurements were made of heat transfer and pressure drop in an annular channel with a smooth or rough test rod in a smooth adiabatic shroud. 24 different roughness geometries were tested. The results were transformed to rod cluster geometry by the method of W B Hall, and correlated by the friction and heat transfer similarity laws as suggested by D F Dipprey and R H Sabersky with RMS errors of 12.5 % in the friction factor and 8.1 % in the Stanton number. The relation between the Stanton number and the friction factor could be described by a relation of the type suggested by W Nunner, with a mean error of 3.1 % and an RMS error of 11.6 %. Application of the results to fuel element calculations is discussed, and the great gains in economy which can be obtained with rough surfaces are demonstrated by two examples.
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.
Heat transfer enhancement by finned heat sinks with micro-structured roughness
International Nuclear Information System (INIS)
Ventola, L; Chiavazzo, E; Asinari, P; Calignano, F; Manfredi, D
2014-01-01
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 R a 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.
Random walk and the heat equation
Lawler, Gregory F
2010-01-01
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...
Directory of Open Access Journals (Sweden)
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
Roughness Length of Water Vapor over Land Surfaces and Its Influence on Latent Heat Flux
Directory of Open Access Journals (Sweden)
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.
Flow and heat transfer over a rotating disk with surface roughness
International Nuclear Information System (INIS)
Yoon, Myung Sup; Hyun, Jae Min; Park, Jun Sang
2007-01-01
A numerical study is made of flow and heat transfer near an infinite disk, which rotates steadily about the longitudinal axis. The surface of the disk is characterized by axisymmetric, sinusoidally-shaped roughness. The representative Reynolds number is large. Numerical solutions are acquired to the governing boundary-layer-type equations. The present numerical results reproduce the previous data for a flat disk. For a wavy surface disk, the radial distributions of local skin friction coefficient and local Nusselt number show double periodicity, which is in accord with the previous results. Physical explanations are provided for this finding. The surface-integrated torque coefficient and average Nusselt number increase as the surface roughness parameter increases. The effect of the Rossby number is also demonstrated
Surface roughness of Ti6Al4V after heat treatment evaluated by artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
Ventola, L; Scaltrito, L; Ferrero, S; Chiavazzo, E; Asinari, P; Maccioni, G
2014-01-01
The aim of this work is to improve heat transfer performances of flush mounted heat sinks used in electronic cooling. To do this we patterned 1.23 cm 2 heat sinks surfaces by microstructured roughnesses built by laser etching manufacturing technique, and experimentally measured the convective heat transfer enhancements due to different patterns. Each roughness differs from the others with regards to the number and the size of the micro-fins (e.g. the micro- fin length ranges from 200 to 1100 μm). Experimental tests were carried out in forced air cooling regime. In particular fully turbulent flows (heating edge based Reynolds number ranging from 3000 to 17000) were explored. Convective heat transfer coefficient of the best micro-structured heat sink is found to be roughly two times compared to the smooth heat sinks one. In addition, surface area roughly doubles with regard to smooth heat sinks, due to the presence of micro-fins. Consequently, patterned heat sinks thermal transmittance [W/K] is found to be roughly four times the smooth heat sinks one. We hope this work may open the way for huge boost in the technology of electronic cooling by innovative manufacturing techniques.
Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation
Energy Technology Data Exchange (ETDEWEB)
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr; Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr [University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)
2016-08-15
It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.
Drying characteristics of rough rice by far-infrared radiation heating
International Nuclear Information System (INIS)
Matsuoka, T.
1990-01-01
The relationship between the heat radiation characteristics of a far-infrared radiation heater and the drying characteristics of rough rice was investigated to determine the basic data required for utilization of far-infrared rays for drying rough rice. Results of investigations are discussed in detail
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.
Suction Side Roughness Effects on Film Cooling Heat Transfer on a Turbine Vane
National Research Council Canada - National Science Library
Rutledge, James
2004-01-01
An experimental study was conducted in a simulated three vane linear cascade to determine the effects of surface roughness and film cooling on the heat transfer coefficient distribution in the region...
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.
Xu, Xianmin; Wang, Xiaoping
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.
Heat Transfer and Pressure Drop with Rough Surfaces, a Literature Survey
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, A
1964-05-15
This literature survey deals with changes in heat transfer coefficient and friction factor with varying nature and degree of roughness. Experimental data cover mainly the turbulent flow region for both air and water as flow mediums. Semiempirical analysis about changes in heat transfer coefficient due to roughness has been included. An example of how to use these data to design a heat exchanger surface is also cited. The extreme case of large fins has not been considered. Available literature between 1933 - 1963 has been covered.
Effect of surface roughness on the heating rates of large-angled hypersonic blunt cones
Irimpan, Kiran Joy; Menezes, Viren
2018-03-01
Surface-roughness caused by the residue of an ablative Thermal Protection System (TPS) can alter the turbulence level and surface heating rates on a hypersonic re-entry capsule. Large-scale surface-roughness that could represent an ablated TPS, was introduced over the forebody of a 120° apex angle blunt cone, in order to test for its influence on surface heating rates in a hypersonic freestream of Mach 8.8. The surface heat transfer rates measured on smooth and roughened models under the same freestream conditions were compared. The hypersonic flow-fields of the smooth and rough-surfaced models were visualized to analyse the flow physics. Qualitative numerical simulations and pressure measurements were carried out to have an insight into the high-speed flow physics. Experimental observations under moderate Reynolds numbers indicated a delayed transition and an overall reduction of 17-46% in surface heating rates on the roughened model.
Kareem, Ali Khaleel; Gao, Shian
2018-02-01
The aim of the present numerical investigation is to comprehensively analyse and understand the heat transfer enhancement process using a roughened, heated bottom wall with two artificial rib types (R-s and R-c) due to unsteady mixed convection heat transfer in a 3D moving top wall enclosure that has a central rotating cylinder, and to compare these cases with the smooth bottom wall case. These different cases (roughened and smooth bottom walls) are considered at various clockwise and anticlockwise rotational speeds, -5 ≤ Ω ≤ 5, and Reynolds numbers of 5000 and 10 000. The top and bottom walls of the lid-driven cavity are differentially heated, whilst the remaining cavity walls are assumed to be stationary and adiabatic. A standard k-ɛ model for the Unsteady Reynolds-Averaged Navier-Stokes equations is used to deal with the turbulent flow. The heat transfer improvement is carefully considered and analysed through the detailed examinations of the flow and thermal fields, the turbulent kinetic energy, the mean velocity profiles, the wall shear stresses, and the local and average Nusselt numbers. It has been concluded that artificial roughness can strongly affect the thermal fields and fluid flow patterns. Ultimately, the heat transfer rate has been dramatically increased by involving the introduced artificial rips. Increasing the cylinder rotational speed or Reynolds number can enhance the heat transfer process, especially when the wall roughness exists.
Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data
Directory of Open Access Journals (Sweden)
Hartmut Pecher
2012-10-01
Full Text Available We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform decays sufficiently rapidly the problem is shown to be globally well-posed for large rough data which not necessarily have finite energy and also in a situation where the energy functional is not positive definite. The proof uses a suitable modification of the I-method.
Analysis of turbulent heat and momentum transfer in a transitionally rough turbulent boundary layer
Doosttalab, Ali; Dharmarathne, Suranga; Tutkun, Murat; Adrian, Ronald; Castillo, Luciano
2016-11-01
A zero-pressure-gradient (ZPG) turbulent boundary layer over a transitionally rough surface is studied using direct numerical simulation (DNS). The rough surface is modeled as 24-grit sandpaper which corresponds to k+ 11 , where k+ is roughness height. Reynolds number based on momentum thickness is approximately 2400. The walls are isothermal and turbulent flow Prandtl number is 0.71. We simulate temperature as passive scalar. We compute the inner product of net turbulent force (d (u1ui) / dxi) and net turbulent heat flux (d (ui θ / dxi)) in order to investigate (i) the correlation between these vectorial quantities, (II) size of the projection of these fields on each other and (IIi) alignment of momentum and hear flux. The inner product in rough case results in larger projection and better alignment. In addition, our study on the vortices shows that surface roughness promotes production of vortical structures which affects the thermal transport near the wall.
Master equation and two heat reservoirs.
Trimper, Steffen
2006-11-01
A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma-sigma and TT'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.
Effect of surface roughness on heat transfer from horizontal immersed tubes in a fluidized bed
International Nuclear Information System (INIS)
Grewal, N.S.; Saxena, S.C.
1979-01-01
Experimental results of the total heat transfer coefficient between 12.7 mm dia copper tubes with four different rough surfaces and glass beads of three different sizes as taken in a 0.305 m x 0.305 m square fluidized bed as a function of fluidizing velocity are reported. The comparison of results for the rough and technically smooth tubes suggests that the heat transfer coefficient strongly depends on the ratio of pitch (P/sub f/) to the average particle diameter (d/sub p/), where P/sub f/ is the distance between the two corresponding points on consecutive threads or knurls. By the proper choice of (P/sub f//d/sub p/) ratio, the maximum total heat transfer coefficient for V-thread tubes (h/sub w/fb) can be increased by as much as 40 percent over the value for a smooth tube with the same outside diameter. However, for values of (P/sub f//d/sub p/) less than 0.95, the maximum heat transfer coefficient for the V-thread rough tubes is smaller than the smooth tube having the same outside diameter. The qualitative variation of the heat transfer coefficient for rough tubes with (P/sub f//d) is explained on the basis of the combined effect of contact geometry between the solid particles and the heat transfer surface, and the solids renewal rate at the surface. The present findings are critically compared with somewhat similar investigations from the literature on the heat transfer from horizontal or vertical rough tubes and tubes with small fins
About application of the 'rough' net method for decision of the neutron transfer transient equation
International Nuclear Information System (INIS)
Seleznev, E.F.; Tarasenko, V.V.
1995-01-01
Method of the decision of a transient equation of the neutrons transfer is developed, which at preservation of necessary accuracy permits considerably to speed up a finding of the decision up to modeling of processes in reactor in real time. The transient equation of neutrons transfer in one-group diffusion approximation is decided by the finite-difference method. The calculating model of reactor is divided into rather large zones, where the currents on internal borders are away, and on external borders ones are a sum of currents on the borders of small-sized zones. For the decision of an equation in finite-difference kind the numerical scheme 'Time - integrate' is used, which permits to search the decision in a half-explicit kind with rather large temporary step. The decision for density of neutrons flux is determine by the SOR method. Under the conducted preliminary analysis of an algorithm efficiency it is possible to conclude, that the time of the decision on a computer can be reduced in 3 and more times, in depending on 'roughness' of a calculated net in comparison with computation on a complete net. The realized algorithm can be used as for scientific researches, and as neutron-physical block of the simulator. 6 refs., 1 fig
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.
The effect of surface roughness on the heat exchange and pressure-drop coefficients
International Nuclear Information System (INIS)
Malherbe, J.M.
1963-02-01
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 3 and 5 x 10 4 and wall temperatures of under 250 deg C. (author) [fr
Turbulent flow and heat transfer in channels with combined rough and smooth surfaces
International Nuclear Information System (INIS)
Aytekin, A.
1978-01-01
A two-part experimental investigation is reported on the effects of transverse square rib roughening on fluid flow and heat transfer in channels with uniform and non-uniform boundary conditions. The first part of the experimental programme consisted of providing detailed measurements of mean and basic turbulent characteristics of fully developed flow in two rectangular ducts of aspect ratios 1.63 and 3.0. In each duct only one wall was roughened. In channels having low aspect ratios secondary flows play an important part in momentum transfer, and an interpretation of their effect on the measured Reynolds shear stress distribution has been attempted. In the second part of the experimental programme mean velocity and temperature profiles, friction factors and Stanton numbers were measured in an internally roughened pipe and annuli composed of a rough inner rod and either a smooth or a rough outer pipe. Heating was always applied on the outer surface. In all the geometries the mean velocities near the rough walls were found to be represented by logarithmic straight lines. The gradients of these lines were independent of Reynolds number but differed for various geometries. The mean temperature profiles, measured in the rough pipe and the fully rough annulus, showed that these could also be represented by logarithmic straight lines, but the slopes of these profiles were markedly different from those of the velocity profiles. (author)
An analytical wall-function for turbulent flows and heat transfer over rough walls
International Nuclear Information System (INIS)
Suga, K.; Craft, T.J.; Iacovides, H.
2006-01-01
This paper reports the development of a refined wall-function strategy for the modelling of turbulent forced convection heat transfer over smooth and rough surfaces. In order to include the effects of fine-grain surface roughness, the present study extends a more fundamental work by Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002. Progress in the generalisation of wall-function treatment. Int. J. Heat Fluid Flow 23, 148-160] on the development of advanced wall-functions of general applicability. The presently proposed model is validated through comparisons with data available for internal flows through channels and for external flows over flat and curved plates with both smooth and rough surfaces. Then, its further validation in separating flows over a sand dune and a sand-roughened ramp is discussed. The validation results suggest that the presently proposed form can be successfully applied to a wide range of attached and separated turbulent flows with heat transfer over smooth and fine-grain rough surfaces
International Nuclear Information System (INIS)
Akhenbakh, Eh.
1976-01-01
The investigation is presented into heat transfer in the boundary layer and in the tear-away region of a rough round cylinder. The data obtained must aid in improving nuclear reactor heat exchangers. The experiments were carried out in the Re range between 2 x 10 4 and 4 x 10 6 . The roughness parameter k 5 /d (where ksub(S) is the equivalent roughness, and d is the cylinder diameter) varied in the range 0 -5 . The degree of turbulence of the incident flow Tu = 0.45%. Heat transfer values are given in relation to Re and the roughness parameter in subcritical, critical, supercritical, and transcritical flows
Directory of Open Access Journals (Sweden)
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
Probabilistic Representations of Solutions to the Heat Equation
Indian Academy of Sciences (India)
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 ...
International Nuclear Information System (INIS)
Takekura, K.; Kawamura, S.; Itoh, K.
2003-01-01
An on-farm experiment in which 361 metric tons of rough rice was stored in a silo from November until July was conducted at a country elevator in Hokkaido to develop new techniques for storing rough rice in cold regions. The temperature of the rough rice near the inner silo wall decreased to below ice point (-5°C) due to natural heat radiation in winter, which the temperature of the rough rice in the center of the silo was maintained at almost the same temperature as that at the beginning of storage (5°C). Ventilation in the upper vacant space of the silo prevented moisture condensation on the inside surface of the silo during storage. When the cold rough rice was unloaded from the silo in summer, an unheated forced-air drier was used to increase the temperature of rough rice to above the dew point temperature of surrounding air. During the unloading and rewarming process, the moisture content of the rough rice increased due to moisture condensation on the grain from the air. However, the husks first absorbed the condensation and then the moisture slowly permeated into the brown rice kernel. Thus the rewarming process didn't cause any fissures in the brown rice. The results of the experiment indicate that condensation on rough rice doesn't give rise to any problems
Analysis of surface roughness effects on heat transfer in micro-conduits
Energy Technology Data Exchange (ETDEWEB)
Koo, J.; Kleinstreuer, C. [North Carolina State University, Raleigh, NC (United States). Dept. of Mechanical and Aerospace Engineering
2005-06-01
Modern heat rejection systems, such as micro-heat sinks, are attractive because of their potential for high performance at small size and low weight. However, the impact of microscale effects on heat transfer have to be considered and quantitatively analyzed in order to gain physical insight and accurate Nusselt number data. The relative surface roughness (SR) was selected as a key microscale parameter, represented by a porous medium layer (PML) model. Assuming steady laminar fully developed liquid flow in microchannels and microtubes, the SR effects in terms of PML thermal conductivity ratio and Darcy number on the dimensionless temperature profile and Nusselt number were analyzed. In summary, the PML characteristics, especially the SR-number and conductivity ratio k{sub m}/k{sub f}, greatly affect the heat transfer performance where the Nusselt number can be either higher or lower than the conventional value. The PML influence is less pronounced in microtubes than in parallel-plate microchannels. (author)
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.
Directory of Open Access Journals (Sweden)
Yunlu Pan
2018-05-01
Full Text Available As a significant interfacial property for micro/nano fluidic system, the effective boundary slip can be induced by the surface roughness. However, the effect of surface roughness on the effective slip is still not clear, both increased and decreased effective boundary slip were found with increased roughness. The present work develops a simplified model to study the effect of surface roughness on the effective boundary slip. In the created rough models, the reference position of the rough surfaces to determinate effective boundary slip was set based on ISO/ASME standard and the surface roughness parameters including Ra (arithmetical mean deviation of the assessed profile, Rsm (mean width of the assessed profile elements and shape of the texture varied to form different surface roughness. Then, the effective boundary slip of fluid flow through the rough surface was analyzed by using COMSOL 5.3. The results show that the effective boundary slip induced by surface roughness of fully wetted rough surface keeps negative and further decreases with increasing Ra or decreasing Rsm. Different shape of roughness texture also results in different effective slip. A simplified corrected method for the measured effective boundary slip was developed and proved to be efficient when the Rsm is no larger than 200 nm. Another important finding in the present work is that the convective heat transfer firstly increases followed by an unobvious change with increasing Ra, while the effective boundary slip keeps decreasing. It is believed that the increasing Ra enlarges the area of solid-liquid interface for convective heat transfer, however, when Ra is large enough, the decreasing roughness-induced effective boundary slip counteracts the enhancement effect of roughness itself on the convective heat transfer.
Gradient estimates on the weighted p-Laplace heat equation
Wang, Lin Feng
2018-01-01
In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
Solution of heat equation with variable coefficient using derive
CSIR Research Space (South Africa)
Lebelo, RS
2008-09-01
Full Text Available In this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases...
Stable solutions of nonlocal electron heat transport equations
International Nuclear Information System (INIS)
Prasad, M.K.; Kershaw, D.S.
1991-01-01
Electron heat transport equations with a nonlocal heat flux are in general ill-posed and intrinsically unstable, as proved by the present authors [Phys. Fluids B 1, 2430 (1989)]. A straightforward numerical solution of these equations will therefore lead to absurd results. It is shown here that by imposing a minimal set of constraints on the problem it is possible to arrive at a globally stable, consistent, and energy conserving numerical solution
International Nuclear Information System (INIS)
Dalle Donne, M.; Meyer, L.
1978-01-01
Measurements of friction factor and heat transfer coefficients for two rods of 18.9 mm 0.D. with two-dimensional roughness, each in two different outer smooth tubes have been performed in turbulent and laminar flow. The turbulent flow results indicate that the flow was not thermally fully established, the isothermal data however agree reasonably well with our previously obtained general correlation. Laminar flow results can be correlated best when the Reynolds and Greatz numbers are evaluated at the temperature average between the temperature of the inner rod surface and of the outer smooth surface of the annulus, the average being weighted over the two surfaces. (orig.) [de
Studies on Microwave Heated Drying-rate Equations of Foods
呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右
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...
Numerical resolution of Navier-Stokes equations coupled to the heat equation
International Nuclear Information System (INIS)
Zenouda, Jean-Claude
1970-08-01
The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr
Reducing deuterium-tritium ice roughness by electrical heating of the saturated vapor
International Nuclear Information System (INIS)
Mapoles, E.R.; Sater, J.D.; Monsler, E.; Pipes, J.
1996-01-01
High gain targets for inertial confinement fusion (ICF) contain a layer of deuterium-tritium (DT) ice which surrounds a volume of DT gas in thermal equilibrium with the solid. The roughness of the cryogenic fuel layer inside of ICF targets is one of the sources of imperfections which cause implosions to deviate from perfect one dimensional performance. Experiments at Lawrence Livermore National Laboratory have shown that applying a heat flux across the inner surface of a hydrogen layer such as that inside an ICF target reduces the intrinsic roughness of the surface. We have developed a technique to generate this heat flux by applying and electric field to the DT vapor in the center of these shells. This vapor has a small but significant conductivity due to ionization caused by beta decay of tritium in the vapor and the solid. We describe here experiments using a 1.15 GHz cavity to apply an electric field to frozen DT inside of a sapphire test cell. The cell and cavity geometry allows visual observation of the frozen layers
International Nuclear Information System (INIS)
Fong, R.W.L.; McRae, G.A.; Coleman, C.E.; Nitheanandan, T.; Sanderson, D.B.
1999-10-01
In CANDU fuel channels, Zircaloy calandria tubes isolate the hot pressure tubes from the cool heavy water moderator. The heavy-water moderator provides a backup heat sink during some postulated loss-of-coolant accidents. The decay heat from the fuel is transferred to the moderator to ensure fuel channel integrity during emergencies. Moderator temperature requirements are specified to ensure that the transfer of decay heat does not exceed the critical heat flux (CHF) on the outside surface of the calandria tube. An enhanced CHF provides increases in safety margin. Pool boiling experiments indicate the CHF is enhanced with glass-peening of the outside surface of the calandria tubes. The objective of this study was to evaluate the surface characteristics of glass-peened tubes and relate these characteristics to CHF. The micro-topologies of the tube surfaces were analysed using stereo-pair micrographs obtained from scanning electron microscopy (SEM) and photogrammetry techniques. A linear relationship correlated the CHF as a function of the 'fractal' surface roughness of the tubes. (author)
Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force
Energy Technology Data Exchange (ETDEWEB)
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)
Bayesian recovery of the initial condition for the heat equation
Knapik, B.T.; Vaart, van der A.W.; Zanten, van 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
Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong
2010-01-01
We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...
June, Tania; Meijide, Ana; Stiegler, Christian; Purba Kusuma, Alan; Knohl, Alexander
2018-05-01
Oil palm plantations are expanding vastly in Jambi, resulted in altered surface roughness and turbulence characteristics, which may influence exchange of heat and mass. Micrometeorological measurements above oil palm canopy were conducted for the period 2013–2015. The oil palms were 12.5 years old, canopy height 13 meters and 1.5 years old canopy height 2.5 m. We analyzed the influence of surface roughness and turbulence strenght on heat (sensible and latent) fluxes by investigating the profiles and gradient of wind speed, and temperature, surface roughness (roughness length, zo, and zero plane displacement, d), and friction velocity u*. Fluxes of heat were calculated using profile similarity methods taking into account atmospheric stability calculated using Richardson number Ri and the generalized stability factor ζ. We found that roughness parameters (zo, d, and u*) directly affect turbulence in oil palm canopy and hence heat fluxes; they are affected by canopy height, wind speed and atmospheric stability. There is a negative trend of d towards air temperature above the oil palm canopy, indicating the effect of plant volume and height in lowering air temperature. We propose studying the relation between zero plane displacement d with a remote sensing vegetation index for scaling up this point based analysis.
Directory of Open Access Journals (Sweden)
Tor eNordam
2013-09-01
Full Text Available A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p- or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.
Rekola, J; Lassila, L V J; Nganga, S; Ylä-Soininmäki, A; Fleming, G J P; Grenman, R; Aho, A J; Vallittu, P K
2014-01-01
Wood has been used as a model material for the development of novel fiber-reinforced composite bone substitute biomaterials. In previous studies heat treatment of wood was perceived to significantly increase the osteoconductivity of implanted wood material. The objective of this study was to examine some of the changing attributes of wood materials that may contribute to improved biological responses gained with heat treatment. Untreated and 140°C and 200°C heat-treated downy birch (Betula pubescens Ehrh.) were used as the wood materials. Surface roughness and the effect of pre-measurement grinding were measured with contact and non-contact profilometry. Liquid interaction was assessed with a dipping test using two manufactured liquids (simulated blood) as well as human blood. SEM was used to visualize possible heat treatment-induced changes in the hierarchical structure of wood. The surface roughness was observed to significantly decrease with heat treatment. Grinding methods had more influence on the surface contour and roughness than heat treatment. The penetration of the human blood in the 200°C heat-treated exceeded that in the untreated and 140°C heat-treated materials. SEM showed no significant change due to heat treatment in the dry-state morphology of the wood. The results of the liquid penetration test support previous findings in literature concerning the effects of heat treatment on the biological response to implanted wood. Heat-treatment has only a marginal effect on the surface contour of wood. The highly specialized liquid conveyance system of wood may serve as a biomimetic model for the further development of tailored fiber-composite materials.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem
2018-01-01
In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Directory of Open Access Journals (Sweden)
Azmat Ullah
Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
An appraisal of computational techniques for transient heat conduction equation
International Nuclear Information System (INIS)
Kant, T.
1983-01-01
A semi-discretization procedure in which the ''space'' dimension is discretized by the finite element method is emphasized for transient problems. This standard methodology transforms the space-time partial differential equation (PDE) system into a set of ordinary differential equations (ODE) in time. Existing methods for transient heat conduction calculations are then reviewed. Existence of two general classes of time integration schemes- implicit and explicit is noted. Numerical stability characteristics of these two methods are elucidated. Implicit methods are noted to be numerically stable, permitting large time steps, but the cost per step is high. On the otherhand, explicit schemes are noted to be inexpensive per step, but small step size is required. Low computational cost of the explicit schemes make it very attractive for nonlinear problems. However, numerical stability considerations requiring use of very small time steps come in the way of its general adoption. Effectiveness of the fourth-order Runge-Kutta-Gill explicit integrator is then numerically evaluated. Finally we discuss some very recent works on development of computational algorithms which not only achieve unconditional stability, high accuracy and convergence but involve computations on matrix equations of elements only. This development is considered to be very significant in the light of our experience gained for simple heat conduction calculations. We conclude that such algorithms have the potential for further developments leading to development of economical methods for general transient analysis of complex physical systems. (orig.)
Quantum group and symmetry of the heat equation
International Nuclear Information System (INIS)
Jha, P.K.; Tripathy, K.C.
1992-07-01
The symmetry associated with the heat equation is re-examined using Lie's method. Under suitable choice of the arbitrary parameters in the Lie field, it is shown that the system exhibits SL(2,R) symmetry. On inspection of the q-analogue of the principal solution, we find broadening of the Gaussian-flow curve when q is varied from 1 to 0.002. The q-analogue of the general solution predicts the existence of additional degeneracy. (author). 8 refs, 1 fig
Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation
International Nuclear Information System (INIS)
Dou, Nicholas G.; Minnich, Austin J.
2016-01-01
Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials
Fast numerical upscaling of heat equation for fibrous materials
Iliev, Oleg; Lazarov, Raytcho; Willems, Joerg
2010-01-01
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.
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.
Sams, E. W.
1952-01-01
An investigation of forced-convection heat transfer and associated pressure drops was conducted with air flowing through electrically heated Inconel tubes having various degrees of square-thread-type roughness, an inside diameter of 1/2 inch, and a length of 24 inches. were obtained for tubes having conventional roughness ratios (height of thread/radius of tube) of 0 (smooth tube), 0.016, 0.025, and 0.037 over ranges of bulk Reynolds numbers up to 350,000, average inside-tube-wall temperatures up to 1950deg R, and heat-flux densities up to 115,000 Btu per hour per square foot. Data The experimental data showed that both heat transfer and friction increased with increase in surface roughness, becoming more pronounced with increase in Reynolds number; for a given roughness, both heat transfer and friction were also influenced by the tube wall-to-bulk temperature ratio. Good correlation of the heat-transfer data for all the tubes investigated was obtained by use of a modification of the conventional Nusselt correlation parameters wherein the mass velocity in the Reynolds number was replaced by the product of air density evaluated at the average film temperature and the so-called friction velocity; in addition, the physical properties of air were evaluated at the average film temperature. The isothermal friction data for the rough tubes, when plotted in the conventional manner, resulted in curves similar to those obtained by other investigators; that is, the curve for a given roughness breaks away from the Blasius line (representing turbulent flow in smooth tubes) at some value of Reynolds number, which decreases with increase in surface roughness, and then becomes a horizontal line (friction coefficient independent of Reynolds number). A comparison of the friction data for the rough tubes used herein indicated that the conventional roughness ratio is not an adequate measure of relative roughness for tubes having a square-thread-type element. The present data, as well
Integration of the time-dependent heat equation in the fuel rod performance program IAMBUS
International Nuclear Information System (INIS)
West, G.
1982-01-01
An iterative numerical method for integration of the time-dependent heat equation is described. No presuppositions are made for the dependency of the thermal conductivity and heat capacity on space, time and temperature. (orig.) [de
Želi, Velibor; Zorica, Dušan
2018-02-01
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.
International Nuclear Information System (INIS)
Kinoshita, Hidetaka; Terada, Atsuhiko; Kaminaga, Masanori; Hino, Ryutaro
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)
International Nuclear Information System (INIS)
Obot, N.T.; Tessier, J.H.; Pedersen, D.R.
1988-01-01
A numerical study was carried out to determine the effects of roughness on the thermal performance of Liquid Metal Reactor (LMR) decay heat removal systems for a range of possible design configurations and operating conditions. The ranges covered for relative rib height (e/D/sub h/), relative pitch (p/e) and flow attack angle were 0.026--0.103, 5--20 and 0--90 degrees, successively. The heat flux was varied between 1.1 and 21.5 kW/m 2 (0.1 and 2.0 kW/ft 2 ). Calculations were made for three cases: smooth duct with no ribs, ribs on both the guard vessel and collector wall, and ribs on the collector wall only. The results indicate that significant benefits, amounting to nearly two-fold reductions in guard vessel and collector wall temperatures, can be realized by placing repeated ribs on both the guard vessel and the collector wall. The magnitudes of the reduction in the reactor vessel temperature are considerably smaller. In general, the level of improvement, be it with respect to temperature or heat flux, is only mildly affected by changes in rib height or pitch but exhibits greater sensitivity to the assumed value for the system form loss. When the ribs are placed only on the collector wall, the heat removal capability is substantially reduced
Directory of Open Access Journals (Sweden)
Chen Jie-Dong
2016-01-01
Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.
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...
Geometry, heat equation and path integrals on the Poincare upper half-plane
International Nuclear Information System (INIS)
Kubo, Reijiro.
1987-08-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)
Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane
Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University
1988-01-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.
A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
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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.
A heat equation for freezing processes with phase change
DEFF Research Database (Denmark)
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 that...
International Nuclear Information System (INIS)
Hatala, Michal; Chep, Robert; Pandilov, Zoran
2010-01-01
This paper deals with thermal cutting technology of materials with plasma arc. In the first part of this paper the theoretical knowledge of the principles of plasma arc cutting and current use of this technology in industry are presented. The cut of products with this technology is perpendicular and accurate, but the use of this technology affects micro-structural changes and depth of the heat affected zone (HAZ). This article deals with the experimental evaluation of plasma arc cutting technological process. The influence of technological factors on the roughness parameter Ra of the steel surface EN S355J0 has been evaluated by using planned experiments. By using the factor experiment, the significance of the four process factors such as plasma burner feed speed, plasma gas pressure, nozzle diameter, distance between nozzle mouth and material has been analyzed. Regression models obtained by multiple linear regression indicate the quality level of observed factors function. The heat from plasma arc cutting affects the micro-structural changes of the material, too.
Directory of Open Access Journals (Sweden)
Dewi Puspitasari
2016-08-01
Full Text Available Acrylic resin denture base has the properties absorbing that affecting physical and mechanical properties. One of the physical properties of acrylic resin is surface roughness. The aim of the study was to find out the roughness effect on heat cured acrylic that was immersed in alkaline peroxide and 75% celery (Apium graveoens L extract as a disinfectant solution. The study was a true experimental and posttest with control group designed with a rectangular shape size 65 x 10 x 3.3 mm based on the ISO standard 1567, six samples were used for alkaline peroxide, celery extract 75% and aquadest group for 5 and 15 days. A Surface Roughness Tester was used for the surface roughness changes observation. The statistical test used One-way ANOVA and post hoc Bonferroni. The results of this study showed the value of roughness on 5 days for alkaline peroxide (1.51 µm is greater than celery extract (0.36µm and aquadest (0.30 µm. The soaking for 15 days in alkaline peroxide (1.52 µm is greater than 75% celery extracts (0.38 µm and aquadest (0.34 µm. Alkaline peroxide caused higher roughness value of heat cured acrylic resin than 75% celery extract.
Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux
International Nuclear Information System (INIS)
Kawamura, Hiroshi
1978-01-01
Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)
Ghannam, Khaled
The atmospheric boundary-layer is the lowest 500-2000 m of the Earth's atmosphere where much of human life and ecosystem services reside. This layer responds to land surface (e.g. buoyancy and roughness elements) and slowly evolving free tropospheric (e.g. temperature and humidity lapse rates) conditions that arguably mediate and modulate biosphere-atmosphere interactions. Such response often results in spatially- and temporally-rich turbulence scales that continue to be the subject of inquiry given their significance to a plethora of applications in environmental sciences and engineering. The work here addresses key aspects of boundary layer turbulence with a focus on the role of roughness elements (vegetation canopies) and buoyancy (surface heating) in modifying the well-studied picture of shear-dominated wall-bounded turbulence. A combination of laboratory channel experiments, field experiments, and numerical simulations are used to explore three distinct aspects of boundary layer turbulence. These are: • The concept of ergodicity in turbulence statistics within canopies: It has been long-recognized that homogeneous and stationary turbulence is ergodic, but less is known about the effects of inhomogeneity introduced by the presence of canopies on the turbulence statistics. A high resolution (temporal and spatial) flume experiment is used here to test the convergence of the time statistics of turbulent scalar concentrations to their ensemble (spatio-temporal) counterpart. The findings indicate that within-canopy scalar statistics have a tendency to be ergodic, mostly in shallow layers (close to canopy top) where the sweeping flow events appear to randomize the statistics. Deeper layers within the canopy are dominated by low-dimensional (quasi-deterministic) von Karman vortices that tend to break ergodicity. • Scaling laws of turbulent velocity spectra and structure functions in near-surface atmospheric turbulence: the existence of a logarithmic scaling in the
Stochastic modeling of stock price process induced from the conjugate heat equation
Paeng, Seong-Hun
2015-02-01
Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.
International Nuclear Information System (INIS)
Hinestroza Gutierrez, D.
2006-08-01
In this work a new and promising algorithm based on the minimization of especial functional that depends on two regularization parameters is considered for the identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)
International Nuclear Information System (INIS)
Hinestroza Gutierrez, D.
2006-12-01
In this work a new and promising algorithm based in the minimization of especial functional that depends on two regularization parameters is considered for identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)
Solution of the two- dimensional heat equation for a rectangular plate
Directory of Open Access Journals (Sweden)
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.
On the controllability of the semilinear heat equation with hysteresis
International Nuclear Information System (INIS)
Bagagiolo, Fabio
2012-01-01
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 bioheat equation and its application to peripheral tissue and whole limb heat transfer
International Nuclear Information System (INIS)
Weinbaum, S.
1987-01-01
Much of the mathematical modeling of heat transfer in perfused tissue over the past three decades has been based on the Pennes bioheat equation. This equation assumes that blood at the local arterial supply temperature reaches the capillaries where the primary thermal equilibration occurs because of the large surface area available for heat exchange. While this argument is correct for gas, water and solute transport, recent theoretical and experimental studies have shown that virtually no heat exchange occurs in vessels under 100 μm and that the primary mechanism for microvascular heat exchange is the imperfect heat exchange between the larger paired countercurrent microvessels that occur 3 to 6 generations prior to the capillaries. A new fundamental bioheat equations has been derived to describe this heat transfer mechanism. This equation contains a basic new expression for the thermal conductivity of perfused tissue which depends on the geometry and flow in the largest microvessels of the local tissue element and the direction of the vessels relative to the local tissue temperature gradient. Although the new equation appears to be complicated, it is shown that it can be applied with relative ease to a host of problems previously treated by the Pennes equation
One-dimensional heat conduction equation of the polar bear hair
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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.
Zhang, Chuang; Guo, Zhaoli; Chen, Songze
2017-12-01
An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2012-01-01
Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.
Dyakonova, Tatyana; Khoperskov, Alexander
2018-03-01
The correct description of the surface water dynamics in the model of shallow water requires accounting for friction. To simulate a channel flow in the Chezy model the constant Manning roughness coefficient is frequently used. The Manning coefficient nM is an integral parameter which accounts for a large number of physical factors determining the flow braking. We used computational simulations in a shallow water model to determine the relationship between the Manning coefficient and the parameters of small-scale perturbations of a bottom in a long channel. Comparing the transverse water velocity profiles in the channel obtained in the models with a perturbed bottom without bottom friction and with bottom friction on a smooth bottom, we constructed the dependence of nM on the amplitude and spatial scale of perturbation of the bottom relief.
Integral transform method for solving time fractional systems and fractional heat equation
Directory of Open Access Journals (Sweden)
Arman Aghili
2014-01-01
Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.
Coupled equations for transient water flow, heat flow, and ...
Indian Academy of Sciences (India)
interacting processes, including flow of fluids, deformation of porous materials, chemical reactions, and transport of ... systems involving the flow of water, heat, and deformation. Such systems are ..... Defined thus, αI is independent of boundary con- ditions in an ... perature change with free deformation at constant total stress ...
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Oyelami, Benjamin Oyediran
2013-09-01
Full Text Available In this paper, criteria for the existence of weak solutions and uniformly weak bounded solution of impulsive heat equation containing maximum temperature are investigated and results obtained. An example is given for heat flow system with impulsive temperature using maximum temperature simulator and criteria for the uniformly weak bounded of solutions of the system are obtained.
Anurose, T. J.; Subrahamanyam, D. Bala
2013-06-01
We discuss the impact of the differential treatment of the roughness lengths for momentum and heat (z_{0m} and z_{0h}) in the flux parametrization scheme of the high-resolution regional model (HRM) for a heterogeneous terrain centred around Thiruvananthapuram, India (8.5°N, 76.9°E). The magnitudes of sensible heat flux ( H) obtained from HRM simulations using the original parametrization scheme differed drastically from the concurrent in situ observations. With a view to improving the performance of this parametrization scheme, two distinct modifications are incorporated: (1) In the first method, a constant value of 100 is assigned to the z_{0m}/z_{0h} ratio; (2) and in the second approach, this ratio is treated as a function of time. Both these modifications in the HRM model showed significant improvements in the H simulations for Thiruvananthapuram and its adjoining regions. Results obtained from the present study provide a first-ever comparison of H simulations using the modified parametrization scheme in the HRM model with in situ observations for the Indian coastal region, and suggest a differential treatment of z_{0m} and z_{0h} in the flux parametrization scheme.
Brownian motion and the heat equation on superspace and anyspace
International Nuclear Information System (INIS)
Majid, S.; Rodriguez-Plaza, M.J.
1993-01-01
We use random walks to study diffusion on anyspace. Anyspace is characterized by co-ordinate ξ with ξ N =0 and statistics ξξ'=e 2πi/N ξ'ξ between independent copies. Anyonic integration and anyonic Dirac δ-functions are introduced, and reduce to familiar results for supersymmetry when N=2. These ingredients are then used to formulate and solve the resulting anyonic diffusion equation. (oirg.)
Energy Technology Data Exchange (ETDEWEB)
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.
Rao, Duggineni Chalapathi; Kalavathy, N; Mohammad, H S; Hariprasad, A; Kumar, C Ravi
2015-01-01
Surface roughness promotes adhesion and colonization of denture plaque. Therefore, it is important to know the effects of polishing and finishing on the surface roughness of various acrylic resin materials. To evaluate and compare the effects of different conventional lathe polishing techniques on heat cured acrylic resins in producing surface roughness. Three different commercially available heat-cured acrylic resin materials namely DPI, Meliodent and Trevalon Hi were selected. 30 Specimens of each acrylic material (30 x 3 = 90, 10 x 60 x 2mm) were prepared and divided into 5 groups, each group consisted of 6 Nos. of specimens per material(6x3=18) and were grouped as Group A(unfinished), Group B (finished), Group C (Polishing Paste), Group D (Polishing Cake) and Group E (Pumice and Gold rouge). The resulted surface roughness (μm) was measured using Perthometer and observed under Scanning Electron Microscope. The values obtained were subjected statistical analyses. Among the materials tested, better results were obtained with Trevalon Hi followed by Meliodent and DPI. Among the polishing methods used, superior results were obtained with universal polishing paste followed by polishing cake; Pumice and Gold rouge. Although Pumice and Gold rouge values produced greater roughness value, they were well within the threshold value of 0.2 mm.
Asymptotic solution for heat convection-radiation equation
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
Goshayeshi, H.R.; Missenden, J.F.
1998-01-01
This paper presents the results of an experimental investigation of the performance of a cooling tower with PVC packing. The following were examined; the effect of surface roughness, the effect of the angle of roughness and the effect of packing spacing. The investigation was divided into two parts: comparison of film heat transfer with air pressure drop, without water circulation and comparison of enthalpy change and pressure drop in the model cooling tower, with circulation of water. Seven commercial packing were investigated, covering a size range of 1.1< P/D<1.70 and 1≤p/e≤5 and a discussion of the dimensionless correlation resulting is given
Global well-posedness for the radial defocusing cubic wave equation on $R^3$ and for rough data
Directory of Open Access Journals (Sweden)
Tristan Roy
2007-11-01
Full Text Available We prove global well-posedness for the radial defocusing cubic wave equation $$displaylines{ partial_{tt} u - Delta u = -u^{3} cr u(0,x = u_{0}(x cr partial_{t} u(0,x = u_{1}(x }$$ with data $(u_0, u_1 in H^{s} imes H^{s-1}$, $1 > s >7/10$. The proof relies upon a Morawetz-Strauss-type inequality that allows us to control the growth of an almost conserved quantity.
Finite element solution of two dimensional time dependent heat equation
International Nuclear Information System (INIS)
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
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.
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.
International Nuclear Information System (INIS)
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)
The generalized approximation method and nonlinear heat transfer equations
Directory of Open Access Journals (Sweden)
Rahmat Khan
2009-01-01
Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.
Sczepanski, Felipe; Sczepanski, Claudia Roberta Brunnquell; Berger, Sandrine Bittencourt; Consani, Rafael Leonardo Xediek; Gonini-Júnior, Alcides; Guiraldo, Ricardo Danil
2014-10-01
To evaluate the surface roughness of acrylic resin submitted to chemical disinfection via 1% sodium hypochlorite (NaClO) or 1% peracetic acid (C2H4O3). The disc-shaped resin specimens (30 mm diameter ×4 mm height) were polymerized by heated water using two cycles (short cycle: 1 h at 74°C and 30 min at 100°C; conventional long cycle: 9 h at 74°C). The release of substances by these specimens in water solution was also quantified. Specimens were fabricated, divided into four groups (n = 10) depending on the polymerization time and disinfectant. After polishing, the specimens were stored in distilled deionized water. Specimens were immersed in 1% NaClO or 1% C2H4O3 for 30 min, and then were immersed in distilled deionized water for 20 min. The release of C2H4O3 and NaClO was measured via visual colorimetric analysis. Roughness was measured before and after disinfection. Roughness data were subjected to two-way ANOVA and Tukey's test. There was no interaction between polymerization time and disinfectant in influencing the average surface roughness (Ra, P = 0.957). Considering these factors independently, there were significant differences between short and conventional long cycles (P = 0.012), but no significant difference between the disinfectants hypochlorite and C2H4O3 (P = 0.366). Visual colorimetric analysis did not detect release of substances. It was concluded that there was the difference in surface roughness between short and conventional long cycles, and disinfection at acrylic resins polymerized by heated water using a short cycle modified the properties of roughness.
Sczepanski, Felipe; Sczepanski, Claudia Roberta Brunnquell; Berger, Sandrine Bittencourt; Consani, Rafael Leonardo Xediek; Gonini-Júnior, Alcides; Guiraldo, Ricardo Danil
2014-01-01
Objective: To evaluate the surface roughness of acrylic resin submitted to chemical disinfection via 1% sodium hypochlorite (NaClO) or 1% peracetic acid (C2H4O3). Materials and Methods: The disc-shaped resin specimens (30 mm diameter ×4 mm height) were polymerized by heated water using two cycles (short cycle: 1 h at 74°C and 30 min at 100°C; conventional long cycle: 9 h at 74°C). The release of substances by these specimens in water solution was also quantified. Specimens were fabricated, divided into four groups (n = 10) depending on the polymerization time and disinfectant. After polishing, the specimens were stored in distilled deionized water. Specimens were immersed in 1% NaClO or 1% C2H4O3 for 30 min, and then were immersed in distilled deionized water for 20 min. The release of C2H4O3 and NaClO was measured via visual colorimetric analysis. Roughness was measured before and after disinfection. Roughness data were subjected to two-way ANOVA and Tukey's test. Results: There was no interaction between polymerization time and disinfectant in influencing the average surface roughness (Ra, P = 0.957). Considering these factors independently, there were significant differences between short and conventional long cycles (P = 0.012), but no significant difference between the disinfectants hypochlorite and C2H4O3 (P = 0.366). Visual colorimetric analysis did not detect release of substances. Conclusion: It was concluded that there was the difference in surface roughness between short and conventional long cycles, and disinfection at acrylic resins polymerized by heated water using a short cycle modified the properties of roughness. PMID:25512737
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.
About Navier-Stokes Equation in the Theory of Convective Heat Transfer
Davidzon, M. Y.
2017-10-01
A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).
Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations
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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.
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.
National Research Council Canada - National Science Library
Gibou, Frederic; Fedkiw, Ronald
2004-01-01
In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains...
Directory of Open Access Journals (Sweden)
Cieśliński Janusz T.
2016-09-01
Full Text Available This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx. The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
International Nuclear Information System (INIS)
An Hengbin; Mo Zeyao; Xu Xiaowen; Liu Xu
2009-01-01
The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.
Exact traveling wave solutions for a new nonlinear heat transfer equation
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Gao Feng
2017-01-01
Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.
Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity
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Hee Chul Pak
2012-01-01
Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.
Numerical method of identification of an unknown source term in a heat equation
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Fatullayev Afet Golayo?lu
2002-01-01
Full Text Available A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.
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
The Hardy inequality and the heat equation with magnetic field in any dimension
Czech Academy of Sciences Publication Activity Database
Cazacu, C.; Krejčiřík, David
2016-01-01
Roč. 41, č. 7 (2016), s. 1056-1088 ISSN 0360-5302 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Aharonov-Bohm magnetic field * Hardy inequality * heat equation * large time behaviour of solutions * magnetic Schrodinger operator Subject RIV: BE - Theoretical Physics Impact factor: 1.608, year: 2016
Projection scheme for a reflected stochastic heat equation with additive noise
Higa, Arturo Kohatsu; Pettersson, Roger
2005-02-01
We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.
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.
Local Equation of State for Protons, and Implications for Proton Heating in the Solar Wind.
Zaslavsky, A.; Maksimovic, M.; Kasper, J. C.
2017-12-01
The solar wind protons temperature is observed to decrease with distance to the Sun at a slower rate than expected from an adiabatic expansion law: the protons are therefore said to be heated. This observation raises the question of the evaluation of the heating rate, and the question of the heat source.These questions have been investigated by previous authors by gathering proton data on various distances to the Sun, using spacecraft as Helios or Ulysses, and then computing the radial derivative of the proton temperature in order to obtain a heating rate from the internal energy equation. The problem of such an approach is the computation of the radial derivative of the temperature profile, for which uncertainties are very large, given the dispersion of the temperatures measured at a given distance.An alternative approach, that we develop in this paper, consists in looking for an equation of state that links locally the pressure (or temperature) to the mass density. If such a relation exists then one can evaluate the proton heating rate on a local basis, without having any space derivative to compute.Here we use several years of STEREO and WIND proton data to search for polytropic equation of state. We show that such relationships are indeed a good approximation in given solar wind's velocity intervals and deduce the associated protons heating rates as a function of solar wind's speed. The obtained heating rates are shown to scale from around 1 kW/kg in the slow wind to around 10 kW/kg in the fast wind, in remarkable agreement with the rate of energy observed by previous authors to cascade in solar wind's MHD turbulence at 1 AU. These results therefore support the idea of proton turbulent heating in the solar wind.
Kawai, Toshiyuki; Takemoto, Mitsuru; Fujibayashi, Shunsuke; Tanaka, Masashi; Akiyama, Haruhiko; Nakamura, Takashi; Matsuda, Shuichi
2015-07-01
In this study, we investigated the effect of different surface treatments (hydroxyapatite (HA) coating, alkali heat treatment, and no treatment) on the ability of bone to bond to a rough arc-sprayed Ti metal surface, using rabbit models. The bone-to-implant contacts for untreated, HA-coated, and alkali heat-treated implants were 21.2%, 72.1%, and 33.8% at 4 weeks, 21.8%, 70.9%, and 30.0% at 8 weeks, and 16.3%, 70.2%, and 29.9% at 16 weeks, respectively (n = 8). HA -coated implants showed significantly higher bone-to-implant contacts than the untreated and alkali heat-treated implants at all the time point, whereas alkali heat-treated implants showed significantly higher bone-to-implant contacts than untreated implants at 4 and 16 weeks. The failure loads in a mechanical test for untreated, HA coated, alkali heat-treated plates were 65.4 N, 70.7 N, and 90.8 N at 4 weeks, 76.1 N, 64.7 N, and 104.8 N at 8 weeks and 88.7 N, 92.6 N, and 118.5 N at 16 weeks, respectively (n = 8). The alkali heat-treated plates showed significantly higher failure loads than HA-coated plates at 8 and 16 weeks. The difference between HA-coated plates and untreated plates were not statistically significant at any time point. Thus HA coating, although it enables high bone-to-implant contact, may not enhance the bone-bonding properties of thermally-sprayed rough Ti metal surfaces. In contrast, alkali heat treatment can be successfully applied to thermally-sprayed Ti metal to enhance both bone-to-implant contact and bone-bonding strength. © 2014 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Kovac, D.; Otto, G.; Hobler, G.
2005-01-01
In this paper we present a model of amorphous pocket formation that is based on binary collision simulations to generate the distribution of deposited energy, and on numerical solution of the heat transport equation to describe the quenching process. The heat transport equation is modified to consider the heat of melting when the melting temperature is crossed at any point in space. It is discretized with finite differences on grid points that coincide with the crystallographic lattice sites, which allows easy determination of molten atoms. Atoms are considered molten if the average of their energy and the energy of their neighbors meets the melting criterion. The results obtained with this model are in good overall agreement with published experimental data on P, As, Te and Tl implantations in Si and with data on the polyatomic effect at cryogenic temperature
A computational procedure for finding multiple solutions of convective heat transfer equations
International Nuclear Information System (INIS)
Mishra, S; DebRoy, T
2005-01-01
In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations
Dose concept of oncological hyperthermia: Heat-equation considering the cell destruction
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Szasz A
2006-01-01
Full Text Available We shall assume, of course, that the objective of hyperthermia is to destroy the malignant cells. Destruction definitely needs energy. Description and quality assurance of hyperthermia use the Pennes heat equation to describe the processes. However the energy balance of the Pennes-equation does not contain the hyperthermic cell-destruction energy, which is a mandatory factor of the process. We propose a generalization of the Pennes-equation, inducing the entire energy balance. The new paradigm could be a theoretical basis of the till now empirical dose-construction for oncological hyperthermia. The cell destruction is a non-equilibrium thermodynamical process, described by the equations of chemical reactions. The dynamic behavior (time dependence has to be considered in this approach. We are going to define also a dose concept that can be objectively compared with other oncological methods. We show how such empirical dose as CEM43oC could be based theoretically as well.
Simplified equations for transient heat transfer problems at low Fourier numbers
DEFF Research Database (Denmark)
Christensen, Martin Gram; Adler-Nissen, Jens
2015-01-01
and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...
A simple Boltzmann transport equation for ballistic to diffusive transient heat transport
International Nuclear Information System (INIS)
Maassen, Jesse; Lundstrom, Mark
2015-01-01
Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions
Barreneche, C.; Ferrer, G.; Palacios, A.; Solé, A.; Inés Fernández, A.; Cabeza, L. F.
2017-10-01
Phase change materials (PCM) used in thermal energy storage (TES) systems have been presented, over recent years, as one of the most effective options in energy storage. Paraffin and fatty acids are some of the most used PCM in TES systems, as they have high phase change enthalpy and in addition they do not present subcooling nor hysteresis and have proper cycling stability. The simulations and design of TES systems require the knowledge of the thermophysical properties of PCM. Thermal conductivity, viscosity, specific heat capacity (Cp) can be experimentally determined, but these are material and time consuming tasks. To avoid or to reduce them, and to have reliable data without the need of experimentation, thermal properties can be calculated by empirical equations. In this study, five different equations are given to calculate the viscosity and specific heat capacity of fatty acid PCM and paraffin PCM. Two of these equations concern, respectively, the empirical calculation of the viscosity and liquid Cp of the whole paraffin PCM family, while the other three equations presented are for the corresponding calculation of viscosity, solid Cp, liquid Cp of the whole fatty acid family of PCM. Therefore, this study summarize the work performed to obtain the main empirical equations to measure the above mentioned properties for whole fatty acid PCM family and whole paraffin PCM family. Moreover, empirical equations have been obtained to calculate these properties for other materials of these PCM groups and these empirical equations can be extrapolated for PCM with higher or lower phase change temperatures within a lower relative error 4%.
Numerical methods to solve the two-dimensional heat conduction equation
International Nuclear Information System (INIS)
Santos, R.S. dos.
1981-09-01
A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt
On the physical solutions to the heat equation subjected to nonlinear boundary conditions
International Nuclear Information System (INIS)
Gama, R.M.S. da.
1990-01-01
This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)
Governing equations for heat and mass transfer in heat-generating porous beds
International Nuclear Information System (INIS)
Chawla, T.C.; Pedersen, D.R.; Minkowycz, W.J.
1985-01-01
Upon dryout of the bed, the dominant modes of heat transfer are conduction and radiation. Radiation is modeled through the Rosseland approximation. The melting of stainless-steel particulate imbedded in the fuel is modeled by assuming the bed to be a continuum with conduction and radiation as the dominant modes of heat transfer. The molten steel, after it drains to the bottom of the bed, is assumed to disappear into cracks and mortar joints of the MgO bricks. The melting of fuel in the interior of the bed is modeled identically to the steel particulate, except for the bed settling which is more pronounced in the case of fuel melting and is assumed to be instantaneous owing to the significant weight of overlying bed and sodium pool. The molten layer of fuel, as it collects at the bottom of the bed, causes the heatup of the MgO lining to the eutectic temperature (2280 0 C), and the MgO lining begins to dissolve. The density gradient caused by the dissolution of MgO leads to natural convection and mixing in the molten layer. The submerged fuel particulate also begins to dissolve in the molten solution and ultimately leads to the conversion of debris to a molten pool of fuel and MgO. The process of penetration of the MgO lining continues until the mixing process lowers the concentration of fuel in the volume of the pool to the level where the internal heat rate per unit volume is not enough to keep the body of the pool molten and leads to freezing in the cooler part of the pool. As the molten pool reaches a frozen or a quiescent state, the MgO brick lining thickness provided is deemed 'safe' for a given bed loading and the external rate of cooling. (author)
How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.
2006-01-01
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.
Hölder-type approximation for the spatial source term of a backward heat equation
DEFF Research Database (Denmark)
Dang, Duc Trong; Mach, Minh Nguyet; Pham, Ngoc Dinh Alain
2010-01-01
We consider the problem of determining a pair of functions $(u,f)$ satisfying the two-dimensional backward heat equation \\bqq u_t -\\Delta u &=&\\varphi(t)f (x,y), ~~t\\in (0,T), (x,y)\\in (0,1)\\times (0,1),\\hfill\\\\ u(x,y,T)&=&g(x,y), \\eqq together with the homogeneous boundary conditions, where...
On the Operator ⨁Bk Related to Bessel Heat Equation
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.
Numerical approximation of null controls for the heat equation: Ill-posedness and remedies
International Nuclear Information System (INIS)
Münch, Arnaud; Zuazua, Enrique
2010-01-01
The numerical approximation of exact or trajectory controls for the wave equation is known to be a delicate issue, since the pioneering work of Glowinski–Lions in the nineties, because of the anomalous behavior of the high-frequency spurious numerical waves. Various efficient remedies have been developed and analyzed in the last decade to filter out these high-frequency components: Fourier filtering, Tychonoff's regularization, mixed finite-element methods, multi-grid strategies, etc. Recently convergence rate results have also been obtained. This work is devoted to analyzing this issue for the heat equation, which is the opposite paradigm because of its strong dissipativity and smoothing properties. The existing analytical results guarantee that, at least in some simple situations, as in the finite-difference scheme in 1 − d, the null or trajectory controls for numerical approximation schemes converge. This is due to the intrinsic high-frequency damping of the heat equation that is inherited by its numerical approximation schemes. But when developing numerical simulations the topic appears to be much more subtle and difficult. In fact, efficiently computing the null control for a numerical approximation scheme of the heat equation is a difficult problem in itself. The difficulty is strongly related to the regularizing effect of the heat kernel. The controls of minimal L 2 -norm are characterized as minima of quadratic functionals on the solutions of the adjoint heat equation, or its numerical versions. These functionals are shown to be coercive in very large spaces of solutions, sufficient to guarantee the L 2 character of controls, but very far from being identifiable as energy spaces for the adjoint system. The very weak coercivity of the functionals under consideration makes the approximation problem exponentially ill-posed and the functional framework far from being well adapted to standard techniques in numerical analysis. In practice, the controls of the
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
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.
Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation
Litaker, Eric T.
1994-12-01
The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.
Solution of the transient Fourier heat conduction equation in r,phi geometry
International Nuclear Information System (INIS)
Kowa, E.; Ehnis, L.
1978-11-01
The two-dimensional transient Fourier heat conduction equation is solved in r,phi geometry for anisotropic materials with the computer program TERFI. The Alternating-Direction-Implicit method is used for the solution of this equation with specified start- and boundary conditions, temperature dependent material properties and space dependent heat sources. The solution area is devided in a mesh grid by the finite difference method. Slidely non-orthogonaly geometry (displacement of mesh grid) can be regarded. There were some difficulties in the treatment of the boundary conditions for the circularly-closed solution area because of the continuity of temperature and heat flux on the 0 0 /360 0 -line. This problem can be solved by an iterativ method with different starting points for the solution scheme. Emphasis was put on reaching reasonable computer time for the iteration. The computer code TERFI, programed in FORTRAN IV, is a modul of the program system RSYST. As an example the temperature distribution of a PWR fuel rod is calculated. (orig.) [de
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.
Directory of Open Access Journals (Sweden)
Sun Huan
2016-01-01
Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.
International Nuclear Information System (INIS)
Dobrev, V.K.; Doebner, H.D.; Mrugalla, C.
1995-12-01
We give a q-deformation S-perpendicular q of the centrally extended Schroedinger algebra. We construct the lowest weight representations of S-perpendicular q , starting from the Verma modules over S-perpendicular q , finding their singular vectors and factoring the Verma submodules built on the singular vectors. We also give a vector-field realization of S-perpendicular q which provides polynomial realization of the lowest weight representations and an infinite hierarchy of q-difference equations which may be called generalized q-deformed heat equations. We also apply our methods to the on-shell q-Schroedinger algebra proposed by Floreanini and Vinet. (author). 12 refs
Global, decaying solutions of a focusing energy-critical heat equation in R4
Gustafson, Stephen; Roxanas, Dimitrios
2018-05-01
We study solutions of the focusing energy-critical nonlinear heat equation ut = Δu - | u|2 u in R4. We show that solutions emanating from initial data with energy and H˙1-norm below those of the stationary solution W are global and decay to zero, via the "concentration-compactness plus rigidity" strategy of Kenig-Merle [33,34]. First, global such solutions are shown to dissipate to zero, using a refinement of the small data theory and the L2-dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza-Seregin-Sverak [17,18] in an argument similar to that of Kenig-Koch [32] for the Navier-Stokes equations.
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),...
Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change
International Nuclear Information System (INIS)
Spindler, B.
1983-01-01
The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods
Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change
Spindler, B.
1983-08-01
The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods.
Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
Directory of Open Access Journals (Sweden)
Henri Schurz
2010-09-01
Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
Directory of Open Access Journals (Sweden)
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.
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 satisfy an equidistribution type law. This property is used to create non-uniform nite-element grids that are dictated by second-order derivatives of the solution. The proposed procedure could be u...
Energy Technology Data Exchange (ETDEWEB)
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)
Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Brear, D.J.
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 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)
International Nuclear Information System (INIS)
Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.
1991-01-01
The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)
Rough Finite State Automata and Rough Languages
Arulprakasam, R.; Perumal, R.; Radhakrishnan, M.; Dare, V. R.
2018-04-01
Sumita Basu [1, 2] recently introduced the concept of a rough finite state (semi)automaton, rough grammar and rough languages. Motivated by the work of [1, 2], in this paper, we investigate some closure properties of rough regular languages and establish the equivalence between the classes of rough languages generated by rough grammar and the classes of rough regular languages accepted by rough finite automaton.
Modeling ARRM Xenon Tank Pressurization Using 1D Thermodynamic and Heat Transfer Equations
Gilligan, Patrick; Tomsik, Thomas
2016-01-01
As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.
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.
Time-Dependent Heat Conduction Problems Solved by an Integral-Equation Approach
International Nuclear Information System (INIS)
Oberaigner, E.R.; Leindl, M.; Antretter, T.
2010-01-01
Full text: A classical task of mathematical physics is the formulation and solution of a time dependent thermoelastic problem. In this work we develop an algorithm for solving the time-dependent heat conduction equation c p ρ∂ t T-kT, ii =0 in an analytical, exact fashion for a two-component domain. By the Green's function approach the formal solution of the problem is obtained. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. This method is applied to a classical engineering problem, i.e. to a special case of a Stefan-Problem. The Green's function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The initial conditions and the system parameters of the investigated problem give rise to two jumps in the temperature field. Purely numerical solutions are obtained by using the FEM (finite element method) and the FDM (finite difference method) and compared with the analytical approach. At the domain boundary the analytical solution and the FEM-solution are in good agreement, but the FDM results show a signicant smearing effect. (author)
DEFF Research Database (Denmark)
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 of coe...
Directory of Open Access Journals (Sweden)
Xue-Lian Jin
2017-01-01
Full Text Available The exponential stability of the monotubular heat exchanger equation with boundary observation possessing a time delay and inner control was investigated. Firstly, the close-loop system was translated into an abstract Cauchy problem in the suitable state space. A uniformly bounded C0-semigroup generated by the close-loop system, which implies that the unique solution of the system exists, was shown. Secondly, the spectrum configuration of the closed-loop system was analyzed and the eventual differentiability and the eventual compactness of the semigroup were shown by the resolvent estimates on some resolvent sets. This implies that the spectrum-determined growth assumption holds. Finally, a sufficient condition, which is related to the physical parameters in the system and is independent of the time delay, of the exponential stability of the closed-loop system was given.
Simple equation for estimating actual evapotranspiration using heat units for wheat in arid regions
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
Christensen, Martin Gram
The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of food engineering such as equipment manufacture the use of predictive...... calculations, modelling activities and simulations for improved design is employed to a high degree. In food manufacture the use process calculations are seldom applied. Even though, the calculation of thermal processes is not a challenging task in academia; this is not the case for food manufacture. However......; the calculations need fundamental validation and a generality that ensures a wide application, thus also the development of simplified approximations and engineering equations have to be conducted in academia. The focus group for the utilization of the presented work is; food manufacture, authorities ensuring food...
Solid and liquid Equation of state for initially porous aluminum where specific heat is constant
Forbes, Jerry W.; Lemar, E. R.; Brown, Mary
2011-06-01
A porous solid's initial state is off the thermodynamic surface of the non-porous solid to start with but when pressure is high enough to cause total pore collapse or crush up, then the final states are on the condensed matter thermodynamic surfaces. The Hugoniot for the fully compacted solid is above the Principle Hugoniot with pressure, temperature and internal energy increased at a given v. There are a number of ways to define this hotter Hugoniot, which can be referenced to other thermodynamic paths on this thermodynamic surface. The choice here was to use the Vinet isotherm to define a consistent thermodynamic surface for the solid and melt phase of 6061 aluminum where specific heat is constant for the P-v-T space of interest. Analytical equations are developed for PH and TH.
Thiébaut, E.; Goupil, C.; Pesty, F.; D'Angelo, Y.; Guegan, G.; Lecoeur, P.
2017-12-01
Increasing the maximum cooling effect of a Peltier cooler can be achieved through material and device design. The use of inhomogeneous, functionally graded materials may be adopted in order to increase maximum cooling without improvement of the Z T (figure of merit); however, these systems are usually based on the assumption that the local optimization of the Z T is the suitable criterion to increase thermoelectric performance. We solve the heat equation in a graded material and perform both analytical and numerical analysis of a graded Peltier cooler. We find a local criterion that we use to assess the possible improvement of graded materials for thermoelectric cooling. A fair improvement of the cooling effect (up to 36%) is predicted for semiconductor materials, and the best graded system for cooling is described. The influence of the equation of state of the electronic gas of the material is discussed, and the difference in term of entropy production between the graded and the classical system is also described.
The one-parameter-model - a constitutive equation applied to a heat resistant alloy
International Nuclear Information System (INIS)
Schwarze, E.; Schuster, H.; Nickel, H.
1992-01-01
In the present work a constitutive model earlier developed and used to predict experimental results of hot tests and fatigue tests from creep experiments of metallic materials were modified to comply with the properties of a high temperature resistant material. The improved model accounts for the properties of a material developing a density and a structure of dislocation lines which are capable of interactions with particles (carbides) from a second phase. The time and temperature dependent evolution of the carbide structure has been described by an equation which explains the formation of seeds as well as their growths (Ostwald ripening). The extended model was applied to Incoloy 800H which is known to develop a carbide structure. Therefore hot tensile and fatigue tests, creep and relaxation experiments using the heats ADU and BAK (KFA specifications) at temperature between 800deg C and 900deg C were performed including both solution treated specimens and specimens heat treated for 10, 100 and 1000 hours. As compared with the results from tensile tests where the carbide structures play a subordinated role, alternately, these structures have a decisive influence on the creep properties of specimens during the primary creep phase, i.e. low stresses and high temperatures. (orig.) [de
International Nuclear Information System (INIS)
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
International Nuclear Information System (INIS)
Alomari, A. K.; Noorani, M. S. M.; Nazar, R.
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 ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is 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 effective and simple with less error than the Adomian decomposition method and the variational iteration method
Zhang, Jianwen; Zhao, Xiaokui
2015-01-01
In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive lim...
Directory of Open Access Journals (Sweden)
Ziaei Poor Hamed
2016-01-01
Full Text Available This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer, hyperbolic (thermal wave and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.
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.
Stochastic control with rough paths
International Nuclear Information System (INIS)
Diehl, Joscha; Friz, Peter K.; Gassiat, Paul
2017-01-01
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).
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
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).
International Nuclear Information System (INIS)
Leont'ev, K.L.
1981-01-01
Known theoretical and empirical formulae are considered for the difference in specific heats at constant pressure and volume. On the basis of the Grunaiser law on the ratio of specific heat to thermal expansion and on the basis of the correlation proposed by the author, between this ratio and average velocity of elastic waves obtained in a new expression for the difference in specific heats and determined are conditions at which empiric Nernst-Lindeman equation can be considered to be strict. Results of calculations for metals with fcc lattice are presented
Impact of roughness on the instability of a free-cooling granular gas
Garzó, Vicente; Santos, Andrés; Kremer, Gilberto M.
2018-05-01
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014), 10.1103/PhysRevE.90.022205], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly degenerate transversal (shear) mode and a longitudinal ("heat") mode are unstable with respect to long enough wavelength excitations. The instability is driven by the shear mode above a certain inelasticity threshold; at larger inelasticity, however, the instability is driven by the heat mode for an inelasticity-dependent range of medium roughness. Comparison with the case of a granular gas of inelastic smooth spheres confirms previous simulation results about the dual role played by surface friction: while small and large levels of roughness make the system less unstable than the frictionless system, the opposite happens at medium roughness. On the other hand, such an intermediate window of roughness values shrinks as inelasticity increases and eventually disappears at a certain value, beyond which the rough-sphere gas is always less unstable than the smooth-sphere gas. A comparison with some preliminary simulation results shows a very good agreement for conditions of practical interest.
International Nuclear Information System (INIS)
Diaz Sanchidrian, C.
1989-01-01
The present paper applies dimensional analysis with spatial discrimination to transform the differential equations in partial derivatives developed in the theory of heat transmission into ordinary ones. The effectivity of the method is comparable to that methods based in transformations of uni or multiparametric groups, with the advantage of being more direct and simple. (Author)
Directory of Open Access Journals (Sweden)
I. Orazov
2013-01-01
Full Text Available We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument. A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem.
Energy Technology Data Exchange (ETDEWEB)
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.
Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier
2018-01-01
The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-03-01
In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.
Zhukovsky, K.; Oskolkov, D.
2018-03-01
A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Oliveira Barroso, A.C. de; Alvim, A.C.M.; Gebrin, A.N.; Santos, R.S. dos
1981-01-01
Various types and variants of alternating direction methods. (ADM), were applied to the solution of the time-dependent heat conduction equation, with source, in regions with axial simmetry. Among the basic ADM's, the alternating direction explicit was the one which performed better. An exponential transformation coupled to the ADE seems to be the variant with greater potential, especially if used with a variable time step scheme. (Author) [pt
Petrofsky, Jerrold; Paluso, Dominic; Anderson, Devyn; Swan, Kristin; Yim, Jong Eun; Murugesan, Vengatesh; Chindam, Tirupathi; Goraksh, Neha; Alshammari, Faris; Lee, Haneul; Trivedi, Moxi; Hudlikar, Akshay N; Katrak, Vahishta
2011-04-01
As predicted by the Pennes equation, skin blood flow is a major contributor to the removal of heat from an external heat source. This protects the skin from erythema and burns. But, for a person in a thermally neutral room, the skin is normally much cooler than arterial blood. Therefore, if skin blood flow (BF) increases, it should initially warm the skin paradoxically. To examine this phenomenon, 10 young male and female subjects participated in a series of experiments to examine the contribution of skin blood flow in the initial warming the skin after the application of local heat. Heat flow was measured by the use of a thermode above the brachioradialis muscle. The thermode was warmed by constant temperature water at 44°C entering the thermode at a water flow rate of 100 cm(3)/min. Skin temperature was measured by a thermistor and blood flow in the underlying skin was measured by a laser Doppler imager in single point mode. The results of the experiments showed that, when skin temperature is cool (31-32°C), the number of calories being transferred to the skin from the thermode cannot account for the rise in skin temperature alone. A significant portion of the rise in skin temperature is due to the warm arterialized blood traversing the skin from the core areas of the body. However, as skin temperature approaches central core temperature, it becomes less of a heat source and more of a heat sync such that when skin temperature is at or above core temperature, the blood flow to the skin, as predicted by Pennes, becomes a heat sync pulling heat from the thermode. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
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.
DEFF Research Database (Denmark)
Lodi, C.; Bacher, Peder; Cipriano, J.
2012-01-01
reduce the ventilation thermal losses of the building by pre-heating the fresh air. Furthermore, by decreasing PV module temperature, the ventilation air heat extraction can simultaneously increase electrical and thermal energy production of the building. A correct prediction of the PV module temperature...... 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......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...
Energy Technology Data Exchange (ETDEWEB)
Aursand, Eskil, E-mail: eskil.aursand@sintef.no; Gjennestad, Magnus Aa.; Yngve Lervåg, Karl; Lund, Halvor
2016-03-15
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base fluid. The magnetization model is based on statistical mechanics, taking into account non-uniform particle size distributions. An implementation of the proposed model is validated against experiments from the literature, and found to give good predictions for the thermomagnetic pumping performance. However, the results reveal a very large sensitivity to uncertainties in heat transfer coefficient predictions. - Highlights: • A multi-phase flow model for thermomagnetically pumped ferrofluid is proposed. • An implementation is validated against experiments from the literature. • Predicted thermomagnetic pumping effect agrees with experiments. • However, a very large sensitivity to heat transfer coefficient is revealed.
Directory of Open Access Journals (Sweden)
Duggineni Chalapathi Rao
2015-01-01
Results: Among the materials tested, better results were obtained with Trevalon Hi followed by Meliodent and DPI. Among the polishing methods used, superior results were obtained with universal polishing paste followed by polishing cake; Pumice and Gold rouge. Although Pumice and Gold rouge values produced greater roughness value, they were well within the threshold value of 0.2 mm.
International Nuclear Information System (INIS)
Roskosch, Dennis; Atakan, Burak
2015-01-01
Fluid selection for thermodynamic cycles like refrigeration cycles, heat pumps or organic Rankine cycles remains an actual topic. Generally the search for a working fluid is based on experimental approaches or on a not very systematic trial and error approach, far from being elegant. An alternative method may be a theory based reverse engineering approach, proposed and investigated here: The design process should start with an optimal process and with (abstract) properties of the fluid needed to fit into this optimal process, best described by some general equation of state and the corresponding fluid-describing parameters. These should be analyzed and optimized with respect to the defined model process, which also has to be optimized simultaneously. From this information real fluids can be selected or even synthesized which have fluid defining properties in the optimum regime like critical temperature or ideal gas capacities of heat, allowing to find new working fluids, not considered so far. The number and kind of the fluid-defining parameters is mainly based on the choice of the used EOS (equation of state). The property model used in the present work is based on the cubic Peng–Robinson equation, chosen due to its moderate numerical expense, sufficient accuracy as well as a general availability of the fluid-defining parameters for many compounds. The considered model-process works between the temperature levels of 273.15 and 333.15 K and can be used as heat pump for supplying buildings with heat, typically. The objective functions are the COP (coefficient of performance) and the VHC (volumetric heating capacity) as a function of critical pressure, critical temperature, acentric factor and two coefficients for the temperature-dependent isobaric ideal gas heat capacity. Also, the steam quality at the compressor entrance has to be regarded as a problem variable. The results give clear hints regarding optimal fluid parameters of the analyzed process and deepen
Exact solutions of time-fractional heat conduction equation by the fractional complex transform
Directory of Open Access Journals (Sweden)
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 Borel summability of divergent solutions of the heat equation
Lutz, D. A.; Miyake, M.; Schäfke, R.
1999-01-01
In recent years, the theory of Borel summability or multisummability of divergent power series of one variable has been established and it has been proved that every formal solution of an ordinary differential equation with irregular singular point is multisummable. For partial differential equations the summability problem for divergent solutions has not been studied so well, and in this paper we shall try to develop the Borel summability of divergent solutions of the Cauch...
Energy Technology Data Exchange (ETDEWEB)
Diez, R.; Dolz, M. Belda, R.; Herraez, J.V.
1988-01-01
The analytical process follow to obtain the adimensional temperature field of air around a horizontal isothermal cylinder of 1 cm diameter and 10.5 length is presented. The equations defining the adimensional temperature variation with the adimensional distance are given for each semiplane that the total field was divide. Comparison of experimental results with obtained of that equations are also carried out and the validity in each case discussed.
A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media
Salama, Amgad; Sun, Shuyu; El-Amin, M. F.
2013-01-01
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.
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.
Directory of Open Access Journals (Sweden)
Fang En
2017-03-01
Φc′/Φc $\\varPhi_{{\\text c}}'/\\varPhi_{{\\text c}}$ 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.
Wall roughness induces asymptotic ultimate turbulence
Zhu, Xiaojue; Verschoof, Ruben Adriaan; Bakhuis, Dennis; Huisman, Sander Gerard; Verzicco, Roberto; Sun, Chao; Lohse, Detlef
2018-01-01
Turbulence governs the transport of heat, mass and momentum on multiple scales. In real-world applications, wall-bounded turbulence typically involves surfaces that are rough; however, characterizing and understanding the effects of wall roughness on turbulence remains a challenge. Here, by
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear system A X = λ X when λ ≠ 0 . But λ = 0 implies that det A = 0 for X ≠ 0 and then the rank of matrix A is reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.
Energy Technology Data Exchange (ETDEWEB)
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 realisees au cours desquelles les deux parois de l
Application of the heat-balance and refined integral methods to the Korteweg-de Vries equation
Directory of Open Access Journals (Sweden)
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.
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\
DEFF Research Database (Denmark)
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John
2015-01-01
In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show...
Modelling the heat dynamics of a building using stochastic differential equations
DEFF Research Database (Denmark)
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...
Energy Technology Data Exchange (ETDEWEB)
Zou, X.L.; Giruzzi, A.G.; Bouquey, F.; Clary, J.; Darbos, C.; Lennholm, M.; Magne, R.; Segui, J.L. [CEA Cadarache, Dept. de Recherches sur la Fusion Controlee, 13 - Saint-Paul-lez-Durance (France); Clemencon, A. [MIT, Electrochemical Energy Laboratory, Cambridge, MA (United States); Guivarch, C. [Ecole Nationale des Ponts et Chaussees, 77 - Marne-la-Vallee (France)
2004-07-01
An exact analytical solution of the electron heat diffusion equation in a cylinder has been found with a step-like diffusion coefficient, plus a monomial increase in the radial direction and a constant damping term. This model is sufficiently general to describe heat diffusion in the presence of a critical gradient threshold or a transport barrier, superimposed to the usual trend of increasing heat diffusivity from the plasma core to the edge. This type of representation allows us to see some well-known properties of heat transport phenomena in a different light. For instance, it has been shown that the contributions of the Eigenmodes to the time dependent solution grow at speeds that depend on the Eigenmode order i.e. at the beginning of the heating phase all the Eigenmodes are equally involved, whereas at the end only the lower order ones are left. This implies, e.g., that high frequency modulation experiments provide a characterization of transport phenomena that is intrinsically different with respect to power balance analysis of a stationary phase. It is particularly useful to analyse power switch on/off events and whenever high frequency modulations are not technically feasible. Low-frequency (1-2 Hz) ECRH modulation experiments have been performed on Tore Supra. A large jump (a factor of 8) in the heat diffusivity has been clearly identified at the ECRH power deposition layer. The amplitude and phase of several harmonics of the Fourier transform of the modulated temperature, as well as the time evolution of the modulated temperature have been reproduced by the analytical solution. The jump is found to be much weaker at lower ECRH power (one gyrotron)
International Nuclear Information System (INIS)
Kadri, M.
1983-01-01
The time dependent heat conduction equation in the x-y Cartesian geometry is formulated in terms of a nine-point finite difference relation using a Taylor series expansion technique. The accuracy of the nine-point formulation over the five-point formulation has been tested and evaluated for various reactor fuel-cladding plate configurations using a computer program. The results have been checked against analytical solutions for various model problems. The following cases were considered in the steady-state condition: (a) The thermal conductivity and the heat generation were uniform. (b) The thermal conductivity was constant, the heat generation variable. (c) The thermal conductivity varied linearly with the temperature, the heat generation was uniform. (d) Both thermal conductivity and heat generation vary. In case (a), approximately, for the same accuracy, 85% fewer grid points were needed for the nine-point relation which has a 14% higher convergence rate as compared to the five-point relation. In case (b), on the average, 84% fewer grid points were needed for the nine-point relation which has a 65% higher convergence rate as compared to the five-point relation. In case (c) and (d), there is significant accuracy (91% higher than the five-point relation) for the nine-point relation when a worse grid was used. The numerical solution of the nine-point formula in the time dependent case was also more accurate and converges faster than the numerical solution of the five-point formula for all comparative tests related to heat conduction problems in a nuclear fuel element
Energy Technology Data Exchange (ETDEWEB)
Habibi, M.; Oloumi, M.; Hosseinkhani, H.; Magidi, S. [Plasma and Fusion Research School, Nuclear Science and Technology Research Institute, Tehran (Iran, Islamic Republic of)
2015-10-15
A highly nonlinear parabolic partial differential equation that models the electron heat transfer process in laser inertial fusion has been solved numerically. The strong temperature dependence of the electron thermal conductivity and heat loss term (Bremsstrahlung emission) makes this a highly nonlinear process. In this case, an efficient numerical method is developed for the energy transport mechanism from the region of energy deposition into the ablation surface by a combination of the Crank-Nicolson scheme and the Newton-Raphson method. The quantitative behavior of the electron temperature and the comparison between analytic and numerical solutions are also investigated. For more clarification, the accuracy and conservation of energy in the computations are tested. The numerical results can be used to evaluate the nonlinear electron heat conduction, considering the released energy of the laser pulse at the Deuterium-Tritium (DT) targets and preheating by heat conduction ahead of a compression shock in the inertial confinement fusion (ICF) approach. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Nucleate boiling heat transfer
Energy Technology Data Exchange (ETDEWEB)
Saiz Jabardo, J.M. [Universidade da Coruna (Spain). Escola Politecnica Superior], e-mail: mjabardo@cdf.udc.es
2009-07-01
Nucleate boiling heat transfer has been intensely studied during the last 70 years. However boiling remains a science to be understood and equated. In other words, using the definition given by Boulding, it is an 'insecure science'. It would be pretentious of the part of the author to explore all the nuances that the title of the paper suggests in a single conference paper. Instead the paper will focus on one interesting aspect such as the effect of the surface microstructure on nucleate boiling heat transfer. A summary of a chronological literature survey is done followed by an analysis of the results of an experimental investigation of boiling on tubes of different materials and surface roughness. The effect of the surface roughness is performed through data from the boiling of refrigerants R-134a and R-123, medium and low pressure refrigerants, respectively. In order to investigate the extent to which the surface roughness affects boiling heat transfer, very rough surfaces (4.6 {mu}m and 10.5 {mu}m ) have been tested. Though most of the data confirm previous literature trends, the very rough surfaces present a peculiar behaviour with respect to that of the smoother surfaces (Ra<3.0 {mu}m). (author)
Nucleate boiling heat transfer
International Nuclear Information System (INIS)
Saiz Jabardo, J.M.
2009-01-01
Nucleate boiling heat transfer has been intensely studied during the last 70 years. However boiling remains a science to be understood and equated. In other words, using the definition given by Boulding, it is an 'insecure science'. It would be pretentious of the part of the author to explore all the nuances that the title of the paper suggests in a single conference paper. Instead the paper will focus on one interesting aspect such as the effect of the surface microstructure on nucleate boiling heat transfer. A summary of a chronological literature survey is done followed by an analysis of the results of an experimental investigation of boiling on tubes of different materials and surface roughness. The effect of the surface roughness is performed through data from the boiling of refrigerants R-134a and R-123, medium and low pressure refrigerants, respectively. In order to investigate the extent to which the surface roughness affects boiling heat transfer, very rough surfaces (4.6 μm and 10.5 μm ) have been tested. Though most of the data confirm previous literature trends, the very rough surfaces present a peculiar behaviour with respect to that of the smoother surfaces (Ra<3.0 μm). (author)
A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations
Directory of Open Access Journals (Sweden)
Wenhua Zhang
2013-01-01
Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.
Guo, Yangyu; Wang, Moran
2017-10-01
The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.
Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.
2018-04-01
An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.
Global representations of the Heat and Schrodinger equation with singular potential
Directory of Open Access Journals (Sweden)
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.
Rough Electrode Creates Excess Capacitance in Thin-Film Capacitors.
Torabi, Solmaz; Cherry, Megan; Duijnstee, Elisabeth A; Le Corre, Vincent M; Qiu, Li; Hummelen, Jan C; Palasantzas, George; Koster, L Jan Anton
2017-08-16
The parallel-plate capacitor equation is widely used in contemporary material research for nanoscale applications and nanoelectronics. To apply this equation, flat and smooth electrodes are assumed for a capacitor. This essential assumption is often violated for thin-film capacitors because the formation of nanoscale roughness at the electrode interface is very probable for thin films grown via common deposition methods. In this work, we experimentally and theoretically show that the electrical capacitance of thin-film capacitors with realistic interface roughness is significantly larger than the value predicted by the parallel-plate capacitor equation. The degree of the deviation depends on the strength of the roughness, which is described by three roughness parameters for a self-affine fractal surface. By applying an extended parallel-plate capacitor equation that includes the roughness parameters of the electrode, we are able to calculate the excess capacitance of the electrode with weak roughness. Moreover, we introduce the roughness parameter limits for which the simple parallel-plate capacitor equation is sufficiently accurate for capacitors with one rough electrode. Our results imply that the interface roughness beyond the proposed limits cannot be dismissed unless the independence of the capacitance from the interface roughness is experimentally demonstrated. The practical protocols suggested in our work for the reliable use of the parallel-plate capacitor equation can be applied as general guidelines in various fields of interest.
Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation
Energy Technology Data Exchange (ETDEWEB)
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.
Roughness coefficients for stream channels in Arizona
Aldridge, B.N.; Garrett, J.M.
1973-01-01
When water flows in an open channel, energy is lost through friction along the banks and bed of the channel and through turbulence within the channel. The amount of energy lost is governed by channel roughness, which is expressed in terms of a roughness coefficient. An evaluation of the roughness coefficient is necessary in many hydraulic computations that involve flow in an open channel. Owing to the lack of satisfactory quantitative procedure, the ability of evaluate roughness coefficients can be developed only through experience; however, a basic knowledge of the methods used to assign the coefficients and the factors affecting them will be a great help. One of the most commonly used equations in open-channel hydraulics is that of Manning. The Manning equation is 1.486
A new analytical method to solve the heat equation for a multi-dimensional composite slab
International Nuclear Information System (INIS)
Lu, X; Tervola, P; Viljanen, M
2005-01-01
A novel analytical approach has been developed for heat conduction in a multi-dimensional composite slab subject to time-dependent boundary changes of the first kind. Boundary temperatures are represented as Fourier series. Taking advantage of the periodic properties of boundary changes, the analytical solution is obtained and expressed explicitly. Nearly all the published works necessitate searching for associated eigenvalues in solving such a problem even for a one-dimensional composite slab. In this paper, the proposed method involves no iterative computation such as numerically searching for eigenvalues and no residue evaluation. The adopted method is simple which represents an extension of the novel analytical approach derived for the one-dimensional composite slab. Moreover, the method of 'separation of variables' employed in this paper is new. The mathematical formula for solutions is concise and straightforward. The physical parameters are clearly shown in the formula. Further comparison with numerical calculations is presented
Energy Technology Data Exchange (ETDEWEB)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)
2017-04-01
In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.
Modeling surface roughness scattering in metallic nanowires
Energy Technology Data Exchange (ETDEWEB)
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.
Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer
International Nuclear Information System (INIS)
Christen, Thomas; Kassubek, Frank
2009-01-01
In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.
Directory of Open Access Journals (Sweden)
Vasyl Chekurin
2017-01-01
Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, E L; Eisenmann, G; Hahne, E [Stuttgart Univ. (TH) (F.R. Germany). Inst. fuer Thermodynamik und Waermetechnik
1976-04-01
A survey is presented on publications on design, heat transfer, form factors, free convection, evaporation processes, cooling towers, condensation, annular gap, cross-flowed cylinders, axial flow through a bundle of tubes, roughnesses, convective heat transfer, loss of pressure, radiative heat transfer, finned surfaces, spiral heat exchangers, curved pipes, regeneraters, heat pipes, heat carriers, scaling, heat recovery systems, materials selection, strength calculation, control, instabilities, automation of circuits, operational problems and optimization.
A methodology for including wall roughness effects in k-ε low-Reynolds turbulence models
International Nuclear Information System (INIS)
Ambrosini, W.; Pucciarelli, A.; Borroni, I.
2015-01-01
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
Measurement of surface roughness
DEFF Research Database (Denmark)
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...
Liu, L.; Sletten, R. S.; Hallet, B.; Waddington, E. D.; Wood, S. E.
2013-12-01
An ancient massive ice body buried under several decimeters of debris in Beacon Valley, Antarctica is believed to be over one million years old, making it older than any known glacier or ice cap. It is fundamentally important as a reservoir of water, proxy for climatic information, and an expression of the periglacial landscape. It is also one of Earth's closest analog for widespread, near-surface ice found in Martian soils and ice-cored landforms. We are interested in understanding controls on how long this ice may persist since our physical model of sublimation suggests it should not be stable. In these models, the soil temperatures and the gradient are important because it determines the direction and magnitude of the vapor flux, and thus sublimation rates. To better understand the heat transfer processes and constrain the rates of processes governing ground ice stability, a model of the thermal behavior of the permafrost is applied to Beacon Valley, Antarctica. It calculates soil temperatures based on a 1-D thermal diffusion equation using a fully implicit finite volume method (FVM). This model is constrained by soil physical properties and boundary conditions of in-situ ground surface temperature measurements (with an average of -23.6oC, a maximum of 20.5oC and a minimum of -54.3oC) and ice-core temperature record at ~30 m. Model results are compared to in-situ temperature measurements at depths of 0.10 m, 0.20 m, 0.30 m, and 0.45 m to assess the model's ability to reproduce the temperature profile for given thermal properties of the debris cover and ice. The model's sensitivity to the thermal diffusivity of the permafrost and the overlaying debris is also examined. Furthermore, we incorporate the role of ice condensation/sublimation which is calculated using our vapor diffusion model in the 1-D thermal diffusion model to assess potential latent heat effects that in turn affect ground ice sublimation rates. In general, the model simulates the ground thermal
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
Rough multiple objective decision making
Xu, Jiuping
2011-01-01
Rough Set TheoryBasic concepts and properties of rough sets Rough Membership Rough Intervals Rough FunctionApplications of Rough SetsMultiple Objective Rough Decision Making Reverse Logistics Problem with Rough Interval Parameters MODM based Rough Approximation for Feasible RegionEVRMCCRMDCRM Reverse Logistics Network Design Problem of Suji Renewable Resource MarketBilevel Multiple Objective Rough Decision Making Hierarchical Supply Chain Planning Problem with Rough Interval Parameters Bilevel Decision Making ModelBL-EVRM BL-CCRMBL-DCRMApplication to Supply Chain Planning of Mianyang Co., LtdStochastic Multiple Objective Rough Decision Multi-Objective Resource-Constrained Project Scheduling UnderRough Random EnvironmentRandom Variable Stochastic EVRM Stochastic CCRM Stochastic DCRM Multi-Objective rc-PSP/mM/Ro-Ra for Longtan Hydropower StationFuzzy Multiple Objective Rough Decision Making Allocation Problem under Fuzzy Environment Fuzzy Variable Fu-EVRM Fu-CCRM Fu-DCRM Earth-Rock Work Allocation Problem.
Investigation on Surface Roughness in Cylindrical Grinding
Rudrapati, Ramesh; Bandyopadhyay, Asish; Pal, Pradip Kumar
2011-01-01
Cylindrical grinding is a complex machining process. And surface roughness is often a key factor in any machining process while considering the machine tool or machining performance. Further, surface roughness is one of the measures of the technological quality of the product and is a factor that greatly influences cost and quality. The present work is related to some aspects of surface finish in the context of traverse-cut cylindrical grinding. The parameters considered have been: infeed, longitudinal feed and work speed. Taguchi quality design is used to design the experiments and to identify the significantly import parameter(s) affecting the surface roughness. By utilization of Response Surface Methodology (RSM), second order differential equation has been developed and attempts have also been made for optimization of the process in the context of surface roughness by using C- programming.
Rough flows and homogenization in stochastic turbulence
Bailleul, I.; Catellier, R.
2016-01-01
We provide in this work a tool-kit for the study of homogenisation of random ordinary differential equations, under the form of a friendly-user black box based on the tehcnology of rough flows. We illustrate the use of this setting on the example of stochastic turbulence.
Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I
2018-04-16
Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.
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.
Wall roughness induces asymptotic ultimate turbulence
Zhu, Xiaojue; Verschoof, Ruben A.; Bakhuis, Dennis; Huisman, Sander G.; Verzicco, Roberto; Sun, Chao; Lohse, Detlef
2018-04-01
Turbulence governs the transport of heat, mass and momentum on multiple scales. In real-world applications, wall-bounded turbulence typically involves surfaces that are rough; however, characterizing and understanding the effects of wall roughness on turbulence remains a challenge. Here, by combining extensive experiments and numerical simulations, we examine the paradigmatic Taylor-Couette system, which describes the closed flow between two independently rotating coaxial cylinders. We show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents associated with wall-bounded turbulence. We reveal that if only one of the walls is rough, the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is eliminated, giving rise to asymptotic ultimate turbulence—the upper limit of transport—the existence of which was predicted more than 50 years ago. In this limit, the scaling laws can be extrapolated to arbitrarily large Reynolds numbers.
International Nuclear Information System (INIS)
Rady, E.A.; Kozae, A.M.; Abd El-Monsef, M.M.E.
2004-01-01
The process of analyzing data under uncertainty is a main goal for many real life problems. Statistical analysis for such data is an interested area for research. The aim of this paper is to introduce a new method concerning the generalization and modification of the rough set theory introduced early by Pawlak [Int. J. Comput. Inform. Sci. 11 (1982) 314
Factors influencing surface roughness of polyimide film
International Nuclear Information System (INIS)
Yao Hong; Zhang Zhanwen; Huang Yong; Li Bo; Li Sai
2011-01-01
The polyimide (PI) films of pyromellitic dianhydride-oxydiamiline (PMDA-ODA) were fabricated using vapor deposition polymerization (VDP) method under high vacuum pressure of 10-4 Pa level. The influence of equipment, substrate temperature, the process of heating and deposition ratio of monomers on the surface roughness of the PI films was investigated. The surface topography of films was measured by interferometer microscopy and scanning electron microscopy(SEM), and the surface roughness was probed with atomic force microscopy(AFM). The results show that consecutive films can be formed when the distance from steering flow pipe to substrate is 74 cm. The surface roughnesses are 291.2 nm and 61.9 nm respectively for one-step heating process and multi-step heating process, and using fine mesh can effectively avoid the splash of materials. The surface roughness can be 3.3 nm when the deposition rate ratio of PMDA to ODA is 0.9:1, and keeping the temperature of substrate around 30 degree C is advantageous to form a film with planar micro-surface topography. (authors)
How supercontinents and superoceans affect seafloor roughness.
Whittaker, Joanne M; Müller, R Dietmar; Roest, Walter R; Wessel, Paul; Smith, Walter H F
2008-12-18
Seafloor roughness varies considerably across the world's ocean basins and is fundamental to controlling the circulation and mixing of heat in the ocean and dissipating eddy kinetic energy. Models derived from analyses of active mid-ocean ridges suggest that ocean floor roughness depends on seafloor spreading rates, with rougher basement forming below a half-spreading rate threshold of 30-35 mm yr(-1) (refs 4, 5), as well as on the local interaction of mid-ocean ridges with mantle plumes or cold-spots. Here we present a global analysis of marine gravity-derived roughness, sediment thickness, seafloor isochrons and palaeo-spreading rates of Cretaceous to Cenozoic ridge flanks. Our analysis reveals that, after eliminating effects related to spreading rate and sediment thickness, residual roughness anomalies of 5-20 mGal remain over large swaths of ocean floor. We found that the roughness as a function of palaeo-spreading directions and isochron orientations indicates that most of the observed excess roughness is not related to spreading obliquity, as this effect is restricted to relatively rare occurrences of very high obliquity angles (>45 degrees ). Cretaceous Atlantic ocean floor, formed over mantle previously overlain by the Pangaea supercontinent, displays anomalously low roughness away from mantle plumes and is independent of spreading rates. We attribute this observation to a sub-Pangaean supercontinental mantle temperature anomaly leading to slightly thicker than normal Late Jurassic and Cretaceous Atlantic crust, reduced brittle fracturing and smoother basement relief. In contrast, ocean crust formed above Pacific superswells, probably reflecting metasomatized lithosphere underlain by mantle at only slightly elevated temperatures, is not associated with basement roughness anomalies. These results highlight a fundamental difference in the nature of large-scale mantle upwellings below supercontinents and superoceans, and their impact on oceanic crustal
International Nuclear Information System (INIS)
Terzi, A.; Foudhil, W.; Harmand, S.; Ben Jabrallah, S.
2016-01-01
Highlights: • Experimental study of the evaporation of a wet porous layer inside a vertical channel. • Resolution of the heat equation by inverse method. • The use of the porous layer is more efficient for high heating flux and low liquid inlet flow. • To improve the evaporation, the system must operate at low water inlet flow. - Abstract: In this paper, we realize an Experimental study of the evaporation of a wet porous layer inside a vertical channel. To develop this study, an experimental dispositive was realised. We measure the temperature along the plate and the evaporated flow rate using the test bed. From these measurements we note that the profiles of the temperature are divided into two areas: the heating and the evaporation zone. We also note that the use of the porous layer is more efficient for high heating flux and low liquid inlet flow. In addition, we studied different dimensionless numbers by solving the energy equation by inverse method. We note that the latent Nusselt number is more important than the sensible Nusselt Number, which proves that the flow dissipated by evaporation is greater than the one used by the film to increase its temperature.
On the computation of the turbulent flow near rough surface
Matveev, S. K.; Jaychibekov, N. Zh.; Shalabayeva, B. S.
2018-05-01
One of the problems in constructing mathematical models of turbulence is a description of the flows near a rough surface. An experimental study of such flows is also difficult because of the impossibility of measuring "inside" the roughness. The theoretical calculation is difficult because of the lack of equations describing the flow in this zone. In this paper, a new turbulence model based on the differential equation of turbulent viscosity balance was used to describe a turbulent flow near a rough surface. The difference between the new turbulence model and the previously known consists in the choice of constants and functions that determine the generation, dissipation and diffusion of viscosity.
DEFF Research Database (Denmark)
Bollerslev, Tim; Li, Sophia Zhengzi; Todorov, Viktor
-section. An investment strategy that goes long stocks with high jump betas and short stocks with low jump betas produces significant average excess returns. These higher risk premiums for the discontinuous and overnight market betas remain significant after controlling for a long list of other firm characteristics......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 of expected returns. Based on a novel highfrequency dataset of almost one-thousand individual stocks over two decades, we find that the two rough betas associated with intraday discontinuous and overnight returns entail significant risk premiums, while the intraday continuous beta is not priced in the cross...
International Nuclear Information System (INIS)
Malescio, G.
1981-04-01
The two-dimensional Fokker-Planck equation describing the ion motion in a coherent lower hybrid wave above the stochasticity threshold is analytically solved. An expression is given for the steady state power dissipation
Turbulent flow with suction in smooth and rough pipes
International Nuclear Information System (INIS)
Verdier, Andre.
1977-11-01
It concerns an experimental study of turbulent flow inside a pipe with rough and porous wall and suction applied through it. The first part recall the basic knowledge concerning the turbulent flow with roughness. In second part statistical equations of fluid wall stress are written in the case of a permeable rough wall, in order to underline the respective role played by viscosity and pressure terms. In the third part the dynamic equilibrium of the flow is experimentally undertaken in the smooth and rough range with and without wall suction. Some empirical formulae are proposed for the mean velocity profiles in the inertial range and for friction velocity with suction. In the case of the sand roughness used, it does not seem that critical Reynolds number of transition from smooth to rough range is varied [fr
Directory of Open Access Journals (Sweden)
Dhananjay Kumar
2018-03-01
Full Text Available This paper presents the performance analysis of the effect of geometrical parameters having multiple v-shaped rib roughness on the airflow side of the absorber plates. Mathematical approach and solution procedure for the analysis of such a solar air heater has been developed theoretically and MATLAB code generated for the solution of the mathematical equations. The effect of parameters such as flow Reynolds number and Relative roughness height on the thermohydraulic performance have been examined and compared with the conventional flat plate solar air heater. A substantial improvement in thermal efficiency of roughened solar air heater as compared to smooth one due to appreciable enhancement in heat transfer coefficient. The enhancement in heat transfer coefficient is also accompanied by a considerable enhancement in pumping power requirement due to the increase in friction factor.
Kamali, Reza; Soloklou, Mohsen Nasiri; Hadidi, Hooman
2018-05-01
In this study, coupled Lattice Boltzmann method is applied to solve the dynamic model for an electroosmotic flow and investigate the effects of roughness in a 2-D flat microchannel. In the present model, the Poisson equation is solved for the electrical potential, the Nernst- Planck equation is solved for the ion concentration. In the analysis of electroosmotic flows, when the electric double layers fully overlap or the convective effects are not negligible, the Nernst-Planck equation must be used to find the ionic distribution throughout the microchannel. The effects of surface roughness height, roughness interval spacing and roughness surface potential on flow conditions are investigated for two different configurations of the roughness, when the EDL layers fully overlap through the microchannel. The results show that in both arrangements of roughness in homogeneously charged rough channels, the flow rate decreases by increasing the roughness height. A discrepancy in the mass flow rate is observed when the roughness height is about 0.15 of the channel width, which its average is higher for the asymmetric configuration and this difference grows by increasing the roughness height. In the symmetric roughness arrangement, the mass flow rate increases until the roughness interval space is almost 1.5 times the roughness width and it decreases for higher values of the roughness interval space. For the heterogeneously charged rough channel, when the roughness surface potential ψr is less than channel surface potential ψs , the net charge density increases by getting far from the roughness surface, while in the opposite situation, when ψs is more than ψr , the net charge density decreases from roughness surface to the microchannel middle center. Increasing the roughness surface potential induces stronger electric driving force on the fluid which results in larger velocities in the flow.
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.
Multidimensional Heat Conduction
DEFF Research Database (Denmark)
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....
Pretorius, Thea; Lix, Lisa; Giesbrecht, Gordon
2011-03-01
Previous studies showed that core cooling rates are similar when only the head or only the body is cooled. Structural equation modeling was used on data from two cold water studies involving body-only, or whole body (including head) cooling. Exposure of both the body and head increased core cooling, while only body cooling elicited shivering. Body fat attenuates shivering and core cooling. It is postulated that this protection occurs mainly during body cooling where fat acts as insulation against cold. This explains why head cooling increases surface heat loss with only 11% while increasing core cooling by 39%. Copyright © 2011 Elsevier Ltd. All rights reserved.
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
Notions of Rough Neutrosophic Digraphs
Directory of Open Access Journals (Sweden)
Nabeela Ishfaq
2018-01-01
Full Text Available [-3]Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS theory is a hybrid tool for handling uncertain information that exists in real life. In this research paper, we apply the concept of rough NS theory to graphs and present a new kind of graph structure, rough neutrosophic digraphs. We present certain operations, including lexicographic products, strong products, rejection and tensor products on rough neutrosophic digraphs. We investigate some of their properties. We also present an application of a rough neutrosophic digraph in decision-making.
A study on the boundary condition for analysis of bio-heat equation according to light irradiation
Energy Technology Data Exchange (ETDEWEB)
Ko, Dong Guk; Bae, Sung Woo; Im, Ik Tae [Chunbuk Natinal University, Junju (Korea, Republic of)
2015-11-15
In this study, the temperature change in an imitational biological tissue, when its surface is irradiated with bio-light, was measured by experiments. Using the experimental data, an equation for temperature as a function of time was developed in order to use it as a boundary condition in numerical studies for the model. The temperature profile was measured along the depth for several wavelengths and distances of the light source from the tissue. It was found that the temperature of the tissue increased with increasing wavelength and irradiation time; however, the difference in the temperatures with red light and near infrared light was not large. The numerical analysis results obtained by using the developed equation as boundary condition show good agreement with the measured temperatures.
Directory of Open Access Journals (Sweden)
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.
Energy Technology Data Exchange (ETDEWEB)
Chawla, T C; Minkowycz, W J; Pedersen, D R
1985-11-01
Upon dryout of the bed, the dominant modes of heat transfer are conduction and radiation. Radiation is modeled through the Rosseland approximation. The melting of stainless-steel particulate imbedded in the fuel is modeled by assuming the bed to be a continuum with conduction and radiatio as the dominant modes of heat transfer. The molten steel, after it drains to the bottom of the bed, is assumed to disappear into cracks and mortar joints of the MgO bricks. The melting of fuel in the interior of the bed is modeled identically to the steel particulate, except for the bed settling which is more pronounced in the case of fuel melting and is assumed to be instantaneous owing to the significant weight of overlying bed and sodium pool. The molten layer of fuel, as it collects at the bottom of the bed, causes the heatup of the MgO lining to the eutectic temperature (2280/sup 0/C), and the MgO lining begins to dissolve. The density gradient caused by the dissolution of MgO leads to natural convection and mixing in the molten layer. The submerged fuel particulate also begins to dissolve in the molten solution and ultimately leads to the conversion of debris to a molten pool of fuel and MgO. The process of penetration of the MgO lining continues until the mixing process lowers the concentration of fuel in the volume of the pool to the level where the internal heat rate per unit volume is not enough to keep the body of the pool molten and leads to freezing in the cooler part of the pool. A the molten pool reaches a frozen or a quiescent state, the MgO brick lining thickness provided is deemed ''safe'' for a given bed loading and the external rate of cooling.
Directory of Open Access Journals (Sweden)
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.
An intermittency model for predicting roughness induced transition
Ge, Xuan; Durbin, Paul
2014-11-01
An extended model for roughness-induced transition is proposed based on an intermittency transport equation for RANS modeling formulated in local variables. To predict roughness effects in the fully turbulent boundary layer, published boundary conditions for k and ω are used, which depend on the equivalent sand grain roughness height, and account for the effective displacement of wall distance origin. Similarly in our approach, wall distance in the transition model for smooth surfaces is modified by an effective origin, which depends on roughness. Flat plate test cases are computed to show that the proposed model is able to predict the transition onset in agreement with a data correlation of transition location versus roughness height, Reynolds number, and inlet turbulence intensity. Experimental data for a turbine cascade are compared with the predicted results to validate the applicability of the proposed model. Supported by NSF Award Number 1228195.
International Nuclear Information System (INIS)
Manteufel, R.D.; Klein, D.E.; Yoshimura, H.R.
1988-01-01
This paper evaluates a translator for finite element data to resistor/capacitor data (FEM/RC) for the numerical solution of heat diffusion problems. The translator involves the derivation of thermal resistors and capacitors, implicit in the heat balance formulation of the finite difference method. It uses a finite element mesh, which consists of nodes and elements and is implicit in the Galerkin finite element method (GFEM). This hybrid translation method, FEM/RC, has been incorporated in Q/TRAN, a new thermal analysis computer code. This evaluation compares Q/TRAN, HEATING-6, and a research code employing GFEM on a purely mathematical, highly nonlinear steady-state conduction benchmark problem. The evaluation concludes that the FEM/RC technique has numerical characteristics that are consistent with comparable schemes for the benchmark problem. FEM/RC also accurately translates skewed meshes. Because FEM/RC generates resistors and capacitors, it appears to offer a more efficient method than the classical GFEM
The contact sport of rough surfaces
Carpick, Robert W.
2018-01-01
Describing the way two surfaces touch and make contact may seem simple, but it is not. Fully describing the elastic deformation of ideally smooth contacting bodies, under even low applied pressure, involves second-order partial differential equations and fourth-rank elastic constant tensors. For more realistic rough surfaces, the problem becomes a multiscale exercise in surface-height statistics, even before including complex phenomena such as adhesion, plasticity, and fracture. A recent research competition, the “Contact Mechanics Challenge” (1), was designed to test various approximate methods for solving this problem. A hypothetical rough surface was generated, and the community was invited to model contact with this surface with competing theories for the calculation of properties, including contact area and pressure. A supercomputer-generated numerical solution was kept secret until competition entries were received. The comparison of results (2) provides insights into the relative merits of competing models and even experimental approaches to the problem.
Numerical simulation of wall roughness effects in cavitating flow
International Nuclear Information System (INIS)
Echouchene, F.; Belmabrouk, H.; Le Penven, L.; Buffat, M.
2011-01-01
Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model based on a single fluid is adopted and the commercial Fluent software is used to solve the transport equations. The discharge coefficient C d is computed for different cavitation numbers and wall roughness heights. Profiles of density mixture, vapor volume fraction, mean velocity and turbulent kinetic energy are reported. The effects of wall roughness and injection pressure are analyzed.
Roughness Effects on Fretting Fatigue
Yue, Tongyan; Abdel Wahab, Magd
2017-05-01
Fretting is a small oscillatory relative motion between two normal loaded contact surfaces. It may cause fretting fatigue, fretting wear and/or fretting corrosion damage depending on various fretting couples and working conditions. Fretting fatigue usually occurs at partial slip condition, and results in catastrophic failure at the stress levels below the fatigue limit of the material. Many parameters may affect fretting behaviour, including the applied normal load and displacement, material properties, roughness of the contact surfaces, frequency, etc. Since fretting damage is undesirable due to contacting, the effect of rough contact surfaces on fretting damage has been studied by many researchers. Experimental method on this topic is usually focusing on rough surface effects by finishing treatment and random rough surface effects in order to increase fretting fatigue life. However, most of numerical models on roughness are based on random surface. This paper reviewed both experimental and numerical methodology on the rough surface effects on fretting fatigue.
Variations in roughness predictions (flume experiments)
Noordam, Daniëlle; Blom, Astrid; van der Klis, H.; Hulscher, Suzanne J.M.H.; Makaske, A.; Wolfert, H.P.; van Os, A.G.
2005-01-01
Data of flume experiments with bed forms are used to analyze and compare different roughness predictors. In this study, the hydraulic roughness consists of grain roughness and form roughness. We predict the grain roughness by means of the size of the sediment. The form roughness is predicted by
Irmak, A.; Singh, Ramesh 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.
International Nuclear Information System (INIS)
Gebrin, A.N.
1981-10-01
Various types and also some variants of alternating direction methods, (A.D.M.), were applied to the solution of the time-dependent heat conduction equation, with source, in region with axial symetry. The results shown that some of the variants perform consistently better than the Classical Cranck-Nicolson method. Having in mind a combination of accuracy, ability to support larg time steps and computational efficiency, the 'alternating direction explicit', (A.D.E.) method appears as the best choice, being the 'alternating direction checkerboard', (A.D.C), method the second best. Additional operations like the exponential transformation or the truncation pos-correction don't seem to be worth, excect for some special cases. (Author) [pt
Directory of Open Access Journals (Sweden)
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.
Comparison of vegetation roughness descriptions
Augustijn, Dionysius C.M.; Huthoff, Freek; van Velzen, E.H.; Altinakar, M.S.; Kokpinar, M.A.; Aydin, I.; Cokgor, S.; Kirkgoz, S.
2008-01-01
Vegetation roughness is an important parameter in describing flow through river systems. Vegetation impedes the flow, which affects the stage-discharge curve and may increase flood risks. Roughness is often used as a calibration parameter in river models, however when vegetation is allowed to
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
Calculation of Reflectance and Transmittance of Coating With Optically Rough Surfaces
International Nuclear Information System (INIS)
El-Depsy, A.; Shawky, A.M.
2011-01-01
For ideal surfaces, components of the reflected beam are related to the components of the incident beam by Fresnel reflection equation. The surfaces encountered in engineering applications deviate from ideal as a result of roughness, oxidization and contamination; hence the Radiative properties of these real surfaces differ greatly from those predicted by electromagnetic theory. In regard to problems of radiative heat transfer; the roughness of surfaces may be divided into two categories: (1) small surface irregularities such that the incident radiation cannot undergo more than a single reflection, (2) deep cavities in which the incident radiation undergoes multi-reflection. The normally incident radiation from rough surface having small irregularities is reflected partly specularly and partly diffusely [1]. Kubelka-Munk theory (K-M) [2] describes optical characteristics (e.g. reflectance, transmittance and absorbance) by a variety of light scattering media including paints, textiles and papers, and It is widely used in various industrial applications. Moder developments in radiative transfer theory (RTT) enable the derivation of (K-M) parameters from first principles [3]. Kubelka and Munk proposed a theory based on a model of two light fluxes travelling in the forward and backward directions. Subsequently a number of authors refined the theory and compared it with experimental data [4]. Several authors attempted to relate the Kubelka- Munk coefficients to the transport coefficients [5,6
He, Xueqin; Han, Lujia; Ge, Jinyi; Huang, Guangqun
2018-04-01
This study establishes an optimal mathematical modelling to rationally describe the dynamic changes and spatial distribution of temperature and oxygen concentration in the aerobic composting process using coupling mass-heat-momentum transfer based on the microbial mechanism. Two different conditional composting experiments, namely continuous aeration and intermittent aeration, were performed to verify the proposed model. The results show that the model accurately predicted the dynamic changes in temperature (case I: R 2 = 0.93, RMSE = 1.95 K; case II: R 2 = 0.86, RMSE = 4.69 K) and oxygen concentration (case I: R 2 = 0.90, RMSE = 1.26%; case II: R 2 = 0.75, RMSE = 2.93%) in the central point of compost substrates. It also systematically simulated fluctuations in oxygen concentration caused by boundary conditions and the spatial distribution of the actual temperature and oxygen concentration. The proposed model exhibits good applicability in simulating the actual working conditions of aerobic composting process. Copyright © 2018 Elsevier Ltd. All rights reserved.
Generalizing roughness: experiments with flow-oriented roughness
Trevisani, Sebastiano
2015-04-01
Surface texture analysis applied to High Resolution Digital Terrain Models (HRDTMs) improves the capability to characterize fine-scale morphology and permits the derivation of useful morphometric indexes. An important indicator to be taken into account in surface texture analysis is surface roughness, which can have a discriminant role in the detection of different geomorphic processes and factors. The evaluation of surface roughness is generally performed considering it as an isotropic surface parameter (e.g., Cavalli, 2008; Grohmann, 2011). However, surface texture has often an anisotropic character, which means that surface roughness could change according to the considered direction. In some applications, for example involving surface flow processes, the anisotropy of roughness should be taken into account (e.g., Trevisani, 2012; Smith, 2014). Accordingly, we test the application of a flow-oriented directional measure of roughness, computed considering surface gravity-driven flow. For the calculation of flow-oriented roughness we use both classical variogram-based roughness (e.g., Herzfeld,1996; Atkinson, 2000) as well as an ad-hoc developed robust modification of variogram (i.e. MAD, Trevisani, 2014). The presented approach, based on a D8 algorithm, shows the potential impact of considering directionality in the calculation of roughness indexes. The use of flow-oriented roughness could improve the definition of effective proxies of impedance to flow. Preliminary results on the integration of directional roughness operators with morphometric-based models, are promising and can be extended to more complex approaches. Atkinson, P.M., Lewis, P., 2000. Geostatistical classification for remote sensing: an introduction. Computers & Geosciences 26, 361-371. Cavalli, M. & Marchi, L. 2008, "Characterization of the surface morphology of an alpine alluvial fan using airborne LiDAR", Natural Hazards and Earth System Science, vol. 8, no. 2, pp. 323-333. Grohmann, C
Directory of Open Access Journals (Sweden)
N. A. Tahir
2003-02-01
Full Text Available The subject of high-energy density (HED in matter is of considerable interest to many branches of physics. Intense beams of energetic heavy ions are a promising tool for creating large samples of HED matter which can be used to study the equation-of-state properties of such exotic states of matter experimentally. The Gesellschaft für Schwerionenforschung (GSI, Darmstadt, is a unique laboratory worldwide which has a heavy ion synchrotron facility, SIS18 (with a magnetic rigidity of 18 Tm, that delivers intense heavy ion beams. Using the beams generated at this present facility, interesting experimental work has been carried out in the field of HED matter [D. H. H. Hoffmann et al., Nucl. Instrum. Methods Phys. Res., Sect. B 161–162, 9 (2000]. The GSI is planning to significantly expand its accelerator capabilities with construction of a new synchrotron ring, SIS100, which will have a magnetic rigidity of 100 Tm. This new facility will deliver a uranium beam which will have orders of magnitude higher intensity than the existing facility and will also have the possibility of multibeam acceleration. This paper presents two-dimensional hydrodynamic simulations of different target geometries including solid as well as hollow cylinders that are irradiated with beams having different shapes of the focal spot which will be available at the SIS100 facility. These include a circular focal spot, an annular focal spot, and an elliptic focal spot, respectively. The purpose of this study is to determine the region of the physical parameters including density, temperature, and pressure that can be accessed using the SIS100 beam. This information, we hope, will be useful for designing experiments on the studies of thermophysical properties of matter including the designing of appropriate diagnostic tools.
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
Fong, Kahei Danny
stability equation (PSE) are performed to ensure the fidelity of the data and to study the relevant flow physics. All results unanimously confirm the conclusion that the relative location of the synchronization point with respect to the roughness element determines the roughness effect on the second mode. Namely, a roughness placed upstream of the synchronization point amplifies the unstable waves while placing a roughness downstream of the synchronization point damps the second-mode waves. The parametric study also shows that a tall roughness element within the local boundary-layer thickness results in a stronger damping effect, while the effect of the roughness width is relatively insignificant compared with the other roughness parameters. On the other hand, the fact that both LST and PSE successfully predict the damping effect only by analyzing the meanflow suggests the mechanism of the damping is by the meanflow alteration due to the existence of roughness elements, rather than new mode generation. In addition to studying the unstable waves, the drag force and heating with and without roughness have been investigated by comparing the numerical simulation data with experimental correlations. It is shown that the increase in drag force generated by the Mach wave around a roughness element in a hypersonic boundary layer is insignificant compared to the reduction of drag force by suppressing turbulent flow. The study also shows that, for a cold wall flow which is the case for practical flight applications, the Stanton number decreases as roughness elements smooth out the temperature gradient in the wall-normal direction. Based on the knowledge of roughness elements damping the second mode gained from the current study, a novel passive transition control method using judiciously placed roughness elements has been developed, and patented, during the course of this research. The main idea of the control method is that, with a given geometry and flow condition, it is possible
Multi-decadal Arctic sea ice roughness.
Tsamados, M.; Stroeve, J.; Kharbouche, S.; Muller, J. P., , Prof; Nolin, A. W.; Petty, A.; Haas, C.; Girard-Ardhuin, F.; Landy, J.
2017-12-01
The transformation of Arctic sea ice from mainly perennial, multi-year ice to a seasonal, first-year ice is believed to have been accompanied by a reduction of the roughness of the ice cover surface. This smoothening effect has been shown to (i) modify the momentum and heat transfer between the atmosphere and ocean, (ii) to alter the ice thickness distribution which in turn controls the snow and melt pond repartition over the ice cover, and (iii) to bias airborne and satellite remote sensing measurements that depend on the scattering and reflective characteristics over the sea ice surface topography. We will review existing and novel remote sensing methodologies proposed to estimate sea ice roughness, ranging from airborne LIDAR measurement (ie Operation IceBridge), to backscatter coefficients from scatterometers (ASCAT, QUICKSCAT), to multi angle maging spectroradiometer (MISR), and to laser (Icesat) and radar altimeters (Envisat, Cryosat, Altika, Sentinel-3). We will show that by comparing and cross-calibrating these different products we can offer a consistent multi-mission, multi-decadal view of the declining sea ice roughness. Implications for sea ice physics, climate and remote sensing will also be discussed.
ROUGHNESS ANALYSIS OF VARIOUSLY POLISHED NIOBIUM SURFACES
Energy Technology Data Exchange (ETDEWEB)
Ribeill, G.; Reece, C.
2008-01-01
Niobium superconducting radio frequency (SRF) cavities have gained widespread use in accelerator systems. It has been shown that surface roughness is a determining factor in the cavities’ effi ciency and maximum accelerating potential achievable through this technology. Irregularities in the surface can lead to spot heating, undesirable local electrical fi eld enhancement and electron multipacting. Surface quality is typically ensured through the use of acid etching in a Buffered Chemical Polish (BCP) bath and electropolishing (EP). In this study, the effects of these techniques on surface morphology have been investigated in depth. The surface of niobium samples polished using different combinations of these techniques has been characterized through atomic force microscopy (AFM) and stylus profi lometry across a range of length scales. The surface morphology was analyzed using spectral techniques to determine roughness and characteristic dimensions. Experimentation has shown that this method is a valuable tool that provides quantitative information about surface roughness at different length scales. It has demonstrated that light BCP pretreatment and lower electrolyte temperature favors a smoother electropolish. These results will allow for the design of a superior polishing process for niobium SRF cavities and therefore increased accelerator operating effi ciency and power.
Turbulent lubrication theory considering the surface roughness effects, 2
International Nuclear Information System (INIS)
Hashimoto, Hiromu; Wada, Sanae; Kobayashi, Toshinobu.
1990-01-01
This second paper describes an application of the generalized turbulent lubrication theory considering the surface roughness effects, which is developed in the previous paper, to the finite-width journal bearings. In the numerical analysis, the nonlinear equations for the modified turbulence coefficients are simplified to save a computation time within a satisfactory accuracy under the assumption that the shear flow is superior to the pressure flow in the turbulent lubrication films. The numerical results of pressure distribution, Sommerfeld number, attitude angle, friction coefficient and flow rate for the Reynolds number of Re=2000, 5000 and 10000 are indicated in graphic form for various values of relative roughness, and the effects of surface roughness on these static performance characteristics are discussed. Moreover, the eccentricity ratio and attitude angle of the journal bearings with homogeneous rough surface are obtained experimentally for a wide range of Sommerfeld number, and the experimental results are compared with theoretical results. (author)
Squeeze film between porous rough elliptical plates | Deheri ...
African Journals Online (AJOL)
The roughness of the bearing surface is described by a stochastic random variable with non zero mean, variance and skew ness. The associated Reynolds' equation is solved with appropriate boundary conditions. Results for bearing performance characteristics such as load carrying capacity and response time for different ...
Armor Plate Surface Roughness Measurements
National Research Council Canada - National Science Library
Stanton, Brian; Coburn, William; Pizzillo, Thomas J
2005-01-01
...., surface texture and coatings) that could become important at high frequency. We measure waviness and roughness of various plates to know the parameter range for smooth aluminum and rolled homogenous armor (RHA...
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.
Energy Technology Data Exchange (ETDEWEB)
Formery, Ph; Gilles, A [Commissariat a l' Energie Atomique, Dir. des Productions, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1968-07-01
The packing used for the transport of highly radioactive materials such as in-pile irradiated rods; have to comply to fairly strict safety standards. They should in particular resist to fire without the radioactive protection being seriously affected. The heating of a transport cask placed in a fire has been calculated by normal automatic computation methods assuming that only thermal radiation is responsible for the heating and that this obeys STEFAN'S law. Simultaneously, a purely analytical treatment has been attempted as follows. The existence of a simple solution, of the Laguerre function type, to the heat equation has been demonstrated. By superposing an infinite number of simple solutions, it is possible to produce a fairly general solution, depending on parameters, which satisfies the initial state and the limiting conditions. The parameters can be adjusted so that the temperature and the flux produced on the shell by this solution satisfy approximately STEFAN'S relationship. (authors) [French] Les emballages qui servent au transport de produits fortement radioactifs, tels que des barreaux irradies dans les piles, doivent satisfaire a des normes de securite assez strictes. Ils doivent, en particulier, resister au feu sans que la protection contre le rayonnement soit sensiblement entamee. L'echauffement, par seul rayonnement thermique suppose obeir a la loi de STEFAN, d'un chateau de transport plonge dans un feu a ete calcule par les methodes habituelles du calcul automatique. Parallelement a ete tentee l'approche purement analytique que voici: Une solution simple, du type fonction de LAGUERRE, a l'equation de la chaleur est mise en evidence. La superposition, en nombre infini, de solutions simples, permet de fabriquer une solution assez generale dependant de parametres, satisfaisant a l'etat initial et aux conditions aux limites. Les parametres peuvent etre ajustes de facon que la temperature et le flux engendres sur la coque par cette solution
Kinetic theory of a rarefied gas of rough spheres
International Nuclear Information System (INIS)
Kremer, G.M.
1987-01-01
A Kinetic theory for the rarefied gas consisting of rough-spherical molecules is developed, in which a macroscopic state is characterized by the 29 scalar fields of density, velocity, pressure tensor, temperature, translational heat flux, rotational heat flux, spin and spin flux. The relations of Navier-Stokes and Fourier are obtained by the use of an iteration method akin to the Maxwellian procedure. (author) [pt
Influence of Sea Surface Roughness on the Electromagnetic Wave Propagation in the Duct Environment
Zhao, X.; Huang, S.
2010-01-01
This paper deals with a study of the influence of sea surface roughness on the electromagnetic wave propagation in the duct environment. The problem of electromagnetic wave propagation is modeled by using the parabolic equation method. The roughness of the sea surface is computed by modifying the smooth surface Fresnel reflection coefficient to account for the reduction in the specular reflection due to the roughness resulting from sea wind speed. The propagation model is solved by the mixed ...
International Nuclear Information System (INIS)
Majumdar, A.; Makowitz, H.
1987-10-01
With the development of modern vector/parallel supercomputers and their lower performance clones it has become possible to increase computational performance by several orders of magnitude when comparing to the previous generation of scalar computers. These performance gains are not observed when production versions of current thermal-hydraulic codes are implemented on modern supercomputers. It is our belief that this is due in part to the inappropriateness of using old thermal-hydraulic algorithms with these new computer architectures. We believe that a new generation of algorithms needs to be developed for thermal-hydraulics simulation that is optimized for vector/parallel architectures, and not the scalar computers of the previous generation. We have begun a study that will investigate several approaches for designing such optimal algorithms. These approaches are based on the following concepts: minimize recursion; utilize predictor-corrector iterative methods; maximize the convergence rate of iterative methods used; use physical approximations as well as numerical means to accelerate convergence; utilize explicit methods (i.e., marching) where stability will permit. We call this approach the ''EPIC'' methodology (i.e., Explicit Predictor Iterative Corrector methods). Utilizing the above ideas, we have begun our work by investigating the one-dimensional transient heat conduction equation. We have developed several algorithms based on variations of the Hopscotch concept, which we discuss in the body of this report. 14 refs
Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems
Institute of Scientific and Technical Information of China (English)
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.
International Nuclear Information System (INIS)
Guo Li-Xin; Gou Xue-Yin; Zhang Lian-Bo
2014-01-01
In this study, the bidirectional reflectance distribution function (BRDF) of a one-dimensional conducting rough surface and a dielectric rough surface are calculated with different frequencies and roughness values in the microwave band by using the method of moments, and the relationship between the bistatic scattering coefficient and the BRDF of a rough surface is expressed. From the theory of the parameters of the rough surface BRDF, the parameters of the BRDF are obtained using a genetic algorithm. The BRDF of a rough surface is calculated using the obtained parameter values. Further, the fitting values and theoretical calculations of the BRDF are compared, and the optimization results are in agreement with the theoretical calculation results. Finally, a reference for BRDF modeling of a Gaussian rough surface in the microwave band is provided by the proposed method. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
The surface roughness and planetary boundary layer
Telford, James W.
1980-03-01
Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 24_2004_Article_BF00877766_TeX2GIFE1.gif {σ _w }/{u^* } = ( {2/{9Aa}} )^{{1/4}} ( {1 - 3^{{1/2}{ a/k{d_n }/z{σ _w }/{u^* }z/L} )^{{1/4}} = 1.28(1 - 0.945({{σ _w }/{u^* }}}) {{z/L}})^{{1/4 where u^* = ( {{tau/ρ}}^{{1/2}}, σ w is the standard deviation of the vertical velocity, z is the height and L is the Obukhov scale lenght. The constants a, A, k and d n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these, a and A, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements
Does Surface Roughness Amplify Wetting?
Czech Academy of Sciences Publication Activity Database
Malijevský, Alexandr
2014-01-01
Roč. 141, č. 18 (2014), s. 184703 ISSN 0021-9606 R&D Projects: GA ČR GA13-09914S Institutional support: RVO:67985858 Keywords : density functional theory * wetting * roughness Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.952, year: 2014
Calibration of surface roughness standards
DEFF Research Database (Denmark)
Thalmann, R.; Nicolet, A.; Meli, F.
2016-01-01
organisations. Five surface texture standards of different type were circulated and on each of the standards several roughness parameters according to the standard ISO 4287 had to be determined. 32 out of 395 individual results were not consistent with the reference value. After some corrective actions...
Fuzzy Rough Ring and Its Prop erties
Institute of Scientific and Technical Information of China (English)
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.
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
The role of the roughness spectral breadth in elastic contact of rough surfaces
Yastrebov, Vladislav A.; Anciaux, Guillaume; Molinari, Jean-François
2017-10-01
We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface's spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we show the effect of the latter on the true contact area. This effect, undetectable for surfaces with poor spectral content, is quite strong for surfaces with rich spectra. Numerical results are compared with analytical models and other available numerical results. A phenomenological equation for the contact area growth is suggested with coefficients depending on the Nayak parameter. Using this equation, the pressure-dependent friction coefficient is deduced based on the adhesive theory of friction. Some observations on Persson's model of rough contact, whose prediction does not depend on Nayak parameter, are reported. Overall, the paper provides a unifying picture of rough elastic contact and clarifies discrepancies between preceding results.
Numerical simulation of wall roughness effects in cavitating flow
Energy Technology Data Exchange (ETDEWEB)
Echouchene, F. [Laboratoire d' electronique et de microelectronique, Departement de Physique, Faculte des Sciences de Monastir, 5000 (Tunisia); Belmabrouk, H., E-mail: frchouchene@yahoo.fr [Laboratoire d' electronique et de microelectronique, Departement de Physique, Faculte des Sciences de Monastir, 5000 (Tunisia); Le Penven, L.; Buffat, M. [LMFA UMR CNRS 5509, Universite de Claude Bernard Lyon 1, Ecole Centrale de Lyon, INSA de Lyon (France)
2011-10-15
Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model based on a single fluid is adopted and the commercial Fluent software is used to solve the transport equations. The discharge coefficient C{sub d} is computed for different cavitation numbers and wall roughness heights. Profiles of density mixture, vapor volume fraction, mean velocity and turbulent kinetic energy are reported. The effects of wall roughness and injection pressure are analyzed.
Multiscale Analysis of the Roughness Effect on Lubricated Rough Contact
Demirci , Ibrahim; MEZGHANI , Sabeur; YOUSFI , Mohammed; El Mansori , Mohamed
2014-01-01
Determining friction is as equally essential as determining the film thickness in the lubricated contact, and is an important research subject. Indeed, reduction of friction in the automotive industry is important for both the minimization of fuel consumption as well as the decrease in the emissions of greenhouse gases. However, the progress in friction reduction has been limited by the difficulty in understanding the mechanism of roughness effects on friction. It was observed that micro-surf...
Energy Technology Data Exchange (ETDEWEB)
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)
Czech Academy of Sciences Publication Activity Database
Kałamajska, A.; Krbec, Miroslav
2015-01-01
Roč. 28, č. 3 (2015), s. 677-713 ISSN 1139-1138 R&D Projects: GA ČR GAP201/10/1920 Institutional research plan: CEZ:AV0Z1019905 Keywords : evolution problems * heat equation * Orlitz-Slobodetskii spaces * Orlitz-Sobolev spaces Subject RIV: BA - General Mathematics Impact factor: 0.631, year: 2015 http://link.springer.com/article/10.1007%2Fs13163-014-0164-4
Time-dependent behavior of rough discontinuities under shearing conditions
Wang, Zhen; Shen, Mingrong; Ding, Wenqi; Jang, Boan; Zhang, Qingzhao
2018-02-01
The mechanical properties of rocks are generally controlled by their discontinuities. In this study, the time-dependent behavior of rough artificial joints under shearing conditions was investigated. Based on Barton’s standard profile lines, samples with artificial joint surfaces were prepared and used to conduct the shear and creep tests. The test results showed that the shear strength of discontinuity was linearly related to roughness, and subsequently an empirical equation was established. The long-term strength of discontinuity can be identified using the inflection point of the isocreep-rate curve, and it was linearly related to roughness. Furthermore, the ratio of long-term and instantaneous strength decreased with the increase of roughness. The shear-stiffness coefficient increased with the increase of shear rate, and the influence of shear rate on the shear stiffness coefficient decreased with the decrease of roughness. Further study of the mechanism revealed that these results could be attributed to the different time-dependent behavior of intact and joint rocks.
Auad, Guillermo; Miller, Arthur J.; White, Warren B.
1998-11-01
We use a primitive equation isopycnal model of the Pacific Ocean to simulate and diagnose the anomalous heat balance on interdecadal timescales associated with heat storage changes observed from 1970-1988 in the expendable bathythermograph (XBT) data set. Given the smallness of the interdecadal signals compared to the El Niño-Southern Oscillation (ENSO) signal, the agreement between model and observations is remarkably good. The total anomalous heat balance is made up of two parts, the diabatic part (from the model temperature equation) and the adiabatic part (from the model mass conservation equation) due to thermocline heave. We therefore describe our analysis of both the total and diabatic anomalous heat balances in four areas of the tropical and subtropical North Pacific Ocean in the upper 400 m. The interdecadal total (diabatic plus adiabatic) heat balance in the North Pacific Ocean is characterized by a complicated interplay of different physical processes, especially revealed in basin-scale averages of the heat budget components that have comparable amounts of variance. In smaller subregions, simpler balances hold. For example, in the western equatorial Pacific (area 1) the total heat content tendency term is nearly zero, so that a simple balance exists between surface heat flux, vertical heat transport, and horizontal mixing. In the western subtropical Pacific the total heat content tendency balances the three-dimensional divergence of the heat flux. We speculate that this complexity is indicative of multiple physical mechanisms involved in the generation of North Pacific interdecadal variability. The diabatic heat balance north of 24°N, a region of special interest to The World Ocean Circulation Experiment (WOCE), can be simplified to a balance between the tendency term, surface heat flux, and meridional advection, the last term dominated by anomalous advection of mean temperature gradients. For the western equatorial region the diabatic heat content
Explicit presentation of the Colebrook's friction factor equation ...
African Journals Online (AJOL)
Two explicit and very accurate equations for calculating the friction factor of pipes over the entire range of relative roughness and Reynold's Number covered by the Colebrook's Equation have been developed. A rectangular array of relative Roughness and Reynold's Number was used to test the accuracy of the new ...
Linear determining equations for differential constraints
International Nuclear Information System (INIS)
Kaptsov, O V
1998-01-01
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed
Ultrasonic backward radiation on painted rough interface
International Nuclear Information System (INIS)
Kwon, Yong Gyu; Yoon, Seok Soo; Kwon, Sung Duck
2002-01-01
The angular dependence(profile) of backscattered ultrasound was measured for steel and brass specimens with periodical surface roughness (1-71μm). Backward radiations showed more linear dependency than normal profile. Direct amplitude increased and averaging amplitude decreased with surface roughness. Painting treatment improved the linearity in direct backward radiation below roughness of 0.03. Scholte and Rayleigh-like waves were observed in the spectrum of averaging backward radiation on periodically rough surface. Painting on periodically rough surface could be used in removing the interface mode effect by periodic roughness.
Sobhani, M.; Behzadmehr, A.
2018-05-01
This study is a numerical investigation of the effect of improving heat transfer namely, modified rough (dimples and protrusions) surfaces on the mixed convective heat transfer of a turbulent flow in a horizontal tube. The effects of different dimples-protrusions arrangements on the improving the thermal performance of a rough tube are investigated at various Richardson numbers. Three dimensional governing equations are discretized by the finite-volume technique. Based on the obtained results the dimples-protrusions arrangements are modified to find a suitable configuration for which heat transfer coefficient and pressure drop to be balanced. Modified dimples-protrusions arrangements that shows higher performance is presented. Its average thermal performance 18% and 11% is higher than the other arrangements. In addition, the results show that roughening a smooth tube is more effective at the higher Richardson number.
A Priori Regularity of Parabolic Partial Differential Equations
Berkemeier, Francisco
2018-01-01
In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular
Lunar heat flow: Regional prospective of the Apollo landing sites
Siegler, M. A.; Smrekar, S. E.
2014-01-01
reexamine the Apollo Heat Flow Experiment in light of new orbital data. Using three-dimensional thermal conduction models, we examine effects of crustal thickness, density, and radiogenic abundance on measured heat flow values at the Apollo 15 and 17 sites. These models show the importance of regional context on heat flux measurements. We find that measured heat flux can be greatly altered by deep subsurface radiogenic content and crustal density. However, total crustal thickness and the presence of a near-surface radiogenic-rich ejecta provide less leverage, representing only minor (<1.5 mW m-2) perturbations on surface heat flux. Using models of the crust implied by Gravity Recovery and Interior Laboratory results, we found that a roughly 9-13 mW m-2 mantle heat flux best approximate the observed heat flux. This equates to a total mantle heat production of 2.8-4.1 × 1011 W. These heat flow values could imply that the lunar interior is slightly less radiogenic than the Earth's mantle, perhaps implying that a considerable fraction of terrestrial mantle material was incorporated at the time of formation. These results may also imply that heat flux at the crust-mantle boundary beneath the Procellarum potassium, rare earth element, and phosphorus (KREEP) Terrane (PKT) is anomalously elevated compared to the rest of the Moon. These results also suggest that a limited KREEP-rich layer exists beneath the PKT crust. If a subcrustal KREEP-rich layer extends below the Apollo 17 landing site, required mantle heat flux can drop to roughly 7 mW m-2, underlining the need for future heat flux measurements outside of the radiogenic-rich PKT region.
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel
Energy Technology Data Exchange (ETDEWEB)
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)
Towards predictive models for transitionally rough surfaces
Abderrahaman-Elena, Nabil; Garcia-Mayoral, Ricardo
2017-11-01
We analyze and model the previously presented decomposition for flow variables in DNS of turbulence over transitionally rough surfaces. The flow is decomposed into two contributions: one produced by the overlying turbulence, which has no footprint of the surface texture, and one induced by the roughness, which is essentially the time-averaged flow around the surface obstacles, but modulated in amplitude by the first component. The roughness-induced component closely resembles the laminar steady flow around the roughness elements at the same non-dimensional roughness size. For small - yet transitionally rough - textures, the roughness-free component is essentially the same as over a smooth wall. Based on these findings, we propose predictive models for the onset of the transitionally rough regime. Project supported by the Engineering and Physical Sciences Research Council (EPSRC).
Rough set classification based on quantum logic
Hassan, Yasser F.
2017-11-01
By combining the advantages of quantum computing and soft computing, the paper shows that rough sets can be used with quantum logic for classification and recognition systems. We suggest the new definition of rough set theory as quantum logic theory. Rough approximations are essential elements in rough set theory, the quantum rough set model for set-valued data directly construct set approximation based on a kind of quantum similarity relation which is presented here. Theoretical analyses demonstrate that the new model for quantum rough sets has new type of decision rule with less redundancy which can be used to give accurate classification using principles of quantum superposition and non-linear quantum relations. To our knowledge, this is the first attempt aiming to define rough sets in representation of a quantum rather than logic or sets. The experiments on data-sets have demonstrated that the proposed model is more accuracy than the traditional rough sets in terms of finding optimal classifications.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Kumar, K. Ravi; Cheepu, Muralimohan; Srinivas, B.; Venkateswarlu, D.; Pramod Kumar, G.; Shiva, Apireddi
2018-03-01
In solar air heater, artificial roughness on absorber plate become prominent technique to improving heat transfer rate of air flowing passage as a result of laminar sublayer. The selection of rib geometries plays important role on friction characteristics and heat transfer rate. Many researchers studying the roughness shapes over the years to investigate the effect of geometries on the performance of friction factor and heat transfer of the solar air heater. The present study made an attempt to develop the different rib shapes utilised for creating artificial rib roughness and its comparison to investigate higher performance of the geometries. The use of computational fluid dynamics software resulted in correlation of friction factor and heat transfer rate. The simulations studies were performed on 2D computational fluid dynamics model and analysed to identify the most effective parameters of relative roughness of the height, width and pitch on major considerations of friction factor and heat transfer. The Reynolds number is varied in a range from 3000 to 20000, in the current study and modelling has conducted on heat transfer and turbulence phenomena by using Reynolds number. The modelling results showed the formation of strong vortex in the main stream flow due to the right angle triangle roughness over the square, rectangle, improved rectangle and equilateral triangle geometries enhanced the heat transfer extension in the solar air heater. The simulation of the turbulence kinetic energy of the geometry suggests the local turbulence kinetic energy has been influenced strongly by the alignments of the right angle triangle.
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.
Directory of Open Access Journals (Sweden)
A. D. Kliukvin
2014-01-01
Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and
Computer simulations of a rough sphere fluid
International Nuclear Information System (INIS)
Lyklema, J.W.
1978-01-01
A computer simulation is described on rough hard spheres with a continuously variable roughness parameter, including the limits of smooth and completely rough spheres. A system of 500 particles is simulated with a homogeneous mass distribution at 8 different densities and for 5 different values of the roughness parameter. For these 40 physically different situations the intermediate scattering function for 6 values of the wave number, the orientational correlation functions and the velocity autocorrelation functions have been calculated. A comparison has been made with a neutron scattering experiment on neopentane and agreement was good for an intermediate value of the roughness parameter. Some often made approximations in neutron scattering experiments are also checked. The influence of the variable roughness parameter on the correlation functions has been investigated and three simple stochastic models studied to describe the orientational correlation function which shows the most pronounced dependence on the roughness. (Auth.)
Axis Problem of Rough 3-Valued Algebras
Institute of Scientific and Technical Information of China (English)
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.
Hwang, Hyeon Gyu; Lee, Jae Hwa
2017-11-01
Direct numerical simulations of turbulent boundary layers (TBLs) over spanwise heterogeneous surface roughness are performed to investigate the characteristics of secondary flow. The longitudinal surface roughness, which features lateral change in bed elevation, is described by immersed boundary method. The Reynolds number based on the momentum thickness is varied in the range of Reθ = 300-900. As the TBLs over the roughness elements spatially develop in the streamwise direction, a secondary flow emerges in a form of counter-rotating vortex pair. As the spanwise spacing between the roughness elements and roughness width vary, it is shown that the size of the secondary flow is determined by the valley width between the roughness elements. In addition, the strength of the secondary flow is mostly affected by the spanwise distance between the cores of the secondary flow. Analysis of the Reynolds-averaged turbulent kinetic energy transport equation reveals that the energy redistribution terms in the TBLs over-the ridge type roughness play an important role to derive low-momentum pathways with upward motion over the roughness crest, contrary to the previous observation with the strip-type roughness. This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1A09000537) and the Ministry of Science, ICT & Future Planning (NRF-2017R1A5A1015311).
Sensing roughness and polish direction
DEFF Research Database (Denmark)
Jakobsen, Michael Linde; Olesen, Anders Sig; Larsen, Henning Engelbrecht
2016-01-01
As a part of the work carried out in 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 prohibitive 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, calling for the object 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 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...
Software testing in roughness calculation
International Nuclear Information System (INIS)
Chen, Y L; Hsieh, P F; Fu, W E
2005-01-01
A test method to determine the function quality provided by the software for roughness measurement is presented in this study. The function quality of the software requirements should be part of and assessed through the entire life cycle of the software package. The specific function, or output accuracy, is crucial for the analysis of the experimental data. For scientific applications, however, commercial software is usually embedded with specific instrument, which is used for measurement or analysis during the manufacture process. In general, the error ratio caused by the software would be more apparent especially when dealing with relatively small quantities, like the measurements in the nanometer-scale range. The model of 'using a data generator' proposed by NPL of UK was applied in this study. An example of the roughness software is tested and analyzed by the above mentioned process. After selecting the 'reference results', the 'reference data' was generated by a programmable 'data generator'. The filter function of 0.8 mm long cutoff value, defined in ISO 11562 was tested with 66 sinusoid data at different wavelengths. Test results from commercial software and CMS written program were compared to the theoretical data calculated from ISO standards. As for the filter function in this software, the result showed a significant disagreement between the reference and test results. The short cutoff feature for filtering at the high frequencies does not function properly, while the long cutoff feature has the maximum difference in the filtering ratio, which is more than 70% between the wavelength of 300 μm and 500 μm. Conclusively, the commercial software needs to be tested more extensively for specific application by appropriate design of reference dataset to ensure its function quality
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
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...
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.
Dou, Z.
2017-12-01
In this study, the influence of multi-scale roughness on transport behavior of the passive solute through the self-affine fracture was investigated. The single self-affine fracture was constructed by the successive random additions (SRA) and the fracture roughness was decomposed into two different scales (i.e. large-scale primary roughness and small-scale secondary roughness) by the Wavelet analysis technique. The fluid flow in fractures, which was characterized by the Forchheimer's law, showed the non-linear flow behaviors such as eddies and tortuous streamlines. The results indicated that the small-scale secondary roughness was primarily responsible for the non-linear flow behaviors. The direct simulations of asymptotic passive solute transport represented the Non-Fickian transport characteristics (i.e. early arrivals and long tails) in breakthrough curves (BTCs) and residence time distributions (RTDs) with and without consideration of the secondary roughness. Analysis of multiscale BTCs and RTDs showed that the small-scale secondary roughness played a significant role in enhancing the Non-Fickian transport characteristics. We found that removing small-scale secondary roughness led to the lengthening arrival and shortening tail. The peak concentration in BTCs decreased as the secondary roughness was removed, implying that the secondary could also enhance the solute dilution. The estimated BTCs by the Fickian advection-dispersion equation (ADE) yielded errors which decreased with the small-scale secondary roughness being removed. The mobile-immobile model (MIM) was alternatively implemented to characterize the Non-Fickian transport. We found that the MIM was more capable of estimating Non-Fickian BTCs. The small-scale secondary roughness resulted in the decreasing mobile domain fraction and the increasing mass exchange rate between immobile and mobile domains. The estimated parameters from the MIM could provide insight into the inherent mechanism of roughness
International Nuclear Information System (INIS)
Kim, Y. I.; Kim, S. H.; Bae, Y. Y.; Cho, B. H.
2003-12-01
Numerical simulation was performed referring to the Yamagata's experiment on the heat transfer in a vertical tube where water flows upward at supercritical pressure. Numerical simulation was performed for the conditions of tube diameter of 7.5 mm, heated tube length of 2 m, operation pressure at 245 bar, bulk temperatures from 300 to 420 .deg. C, heat fluxes from 465 to 930 kW/m 2 and mass velocity 1,260 kg/m 2 s, by Fluent code and compared with the Yamagata's experiments. At the heat flux 465 kW/m 2 , the maximum difference between calculated results and Yamagata's experiment were less than 20% and the difference between the results using different turbulence models was not so significant. But at the heat flux, 930 kW/m 2 , the difference between the calculations and Yamagata's experiment increased to about 25%, and the difference between the results using different turbulence models increased significantly. The case with RNG κ-ε and enhanced wall treatment predicted the Yamagata's experiment best
Compact terahertz spectrometer based on disordered rough surfaces
Yang, Tao; Jiang, Bing; Ge, Jia-cheng; Zhu, Yong-yuan; Li, Xing-ao; Huang, Wei
2018-01-01
In this paper, a compact spectrometer based on disordered rough surfaces for operation in the terahertz band is presented. The proposed spectrometer consists of three components, which are used for dispersion, modulation and detection respectively. The disordered rough surfaces, which are acted as the dispersion component, are modulated by the modulation component. Different scattering intensities are captured by the detection component with different extent of modulation. With a calibration measurement process, one can reconstruct the spectra of the probe terahertz beam by solving a system of simultaneous linear equations. A Tikhonov regularization approach has been implemented to improve the accuracy of the spectral reconstruction. The reported broadband, compact, high-resolution terahertz spectrometer is well suited for portable terahertz spectroscopy applications.
Persisting roughness when deposition stops.
Schwartz, Moshe; Edwards, S F
2004-12-01
Useful theories for growth of surfaces under random deposition of material have been developed by several authors. The simplest theory is that introduced by Edwards and Wilkinson (EW), which is linear and soluble. Its nonlinear generalization by Kardar, Parisi, and Zhang (KPZ) resulted in many subsequent studies. Yet both EW and KPZ theories contain an unphysical feature. When deposition of material is stopped, both theories predict that as time tends to infinity, the surface becomes flat. In fact, of course, the final surface is not flat, but simply has no gradients larger than the gradient related to the angle of repose. We modify the EW and KPZ theories to accommodate this feature and study the consequences for the simpler system which is a modification of the EW equation. In spite of the fact that the equation describing the evolution of the surface is not linear, we find that the steady state in the presence of noise is not very different in the long-wavelength limit from that of the linear EW equation. The situation is quite different from that of EW when deposition stops. Initially there is still some rearrangement of the surface, but that stops as everywhere on the surface the gradient is less than that related to the angle of repose. The most interesting feature observed after deposition stops is the emergence of history-dependent steady-state distributions.
Radiation properties modeling for plasma-sprayed-alumina-coated rough surfaces for spacecrafts
International Nuclear Information System (INIS)
Li, R.M.; Joshi, Sunil C.; Ng, H.W.
2006-01-01
Spacecraft thermal control materials (TCMs) play a vital role in the entire service life of a spacecraft . Most of the conventional TCMs degrade in the harmful space environment . In the previous study, plasma sprayed alumina (PSA) coating was established as a new and better TCM for spacecrafts, in view of its stability and reliability compared to the traditional TCMs . During the investigation, the surface roughness of PSA was found important, because the roughness affects the radiative heat exchange between the surface and its surroundings. Parameters such as root-mean-square roughness cannot properly evaluate surface roughness effects on radiative properties of opaque surfaces . Some models have been developed earlier to predict the effects, such as Davies' model , Tang and Buckius's statistical geometric optics model . However, they are valid only in their own specific situations. In this paper, an energy absorption geometry model was developed and applied to investigate the roughness effects with the help of 2D surface profile of PSA coated substrate scanned at micron level. This model predicts effective normal solar absorptance (α ne ) and effective hemispherical infrared emittance (ε he ) of a rough PSA surface. These values, if used in the heat transfer analysis of an equivalent, smooth and optically flat surface, lead to the prediction of the same rate of heat exchange and temperature as that of for the rough PSA surface. The model was validated through comparison between a smooth and a rough PSA coated surfaces. Even though not tested for other types of materials, the model formulation is generic and can be used to incorporate the rough surface effects for other types of thermal coatings, provided the baseline values of normal solar absorptance (α n ) and hemispherical infrared emittance (ε h ) are available for a generic surface of the same material
Energy Technology Data Exchange (ETDEWEB)
Campo, Antonio [Idaho State Univ., Nuclear Engineering Dept., Pocatello, ID (United States); Sanchez, Alejo [Universidad de los Andes, Depto. de Ingenieria Mecanica, Merida (Venezuela)
1998-03-01
A semi-analytical analysis was conducted for the prediction of the mean bulk- and interface temperatures of gaseous and liquid fluids moving laminarly at high pressures inside thick-walled metallic tubes. The outer surfaces of the tubes are isothermal. The central goal of this article is to critically examine the thermal response of this kind of in-tube flows utilizing two versions of the 1-D lumped model: one is differential-numerical while the other is differential-algebraic. For the former, the local Nusselt number characterizing an inactive, isothermal tube was taken from correlation equations reported in the heat transfer literature. For the latter, a streamwise-mean Nusselt number associated with an active, isothermal tube was taken from standard correlation equations that appear in text-books on basic heat transfer. For the two different versions of the 1-D lumped model tested, the computed results consistently demonstrate that the differential-algebraic, provides accurate estimates of both the mean bulk- and the interface temperatures when compared with those temperature results computed with formal 2-D differential models. (author)
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...
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear differential equations
International Nuclear Information System (INIS)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
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
Ma, Y.M.; Menenti, M.; Feddes, R.A.; Wang, J.M.
2008-01-01
The land surface heterogeneity has a very significant impact on atmospheric variables (air temperature T-a, wind speed u, and humidity q), the aerodynamic roughness length z(0m), thermodynamic roughness length z(0h), and the excess resistance to heat transfer kB(-1). First, in this study the land
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
Hernlund, J. W.; Matsui, H.
2017-12-01
Ultralow-velocity zones (ULVZ) are increasingly illuminated by seismology, revealing surprising diversity in size, shape, and physical characteristics. The only viable hypotheses are that ULVZs are a compositionally distinct FeO-enriched dense material, which could have formed by fractional crystallization of a basal magma ocean, segregation of subducted banded iron formations, precipitation of solids from the outer core, partial melting and segregation of iron-rich melts from subducted basalts, or most likely a combination of many different processes. But many questions remain: Are ULVZ partially molten in some places, and not in others? Are ULVZ simply the thicker portions of an otherwise global thin layer, covering the entire CMB and thus blocking or moderating chemical interactions between the core and overlying mantle? Is such a layer inter-connected and able to conduct electrical currents that allow electro-magnetic coupling of core and mantle angular momentum? Are they being eroded and shrinking in size due to viscous entrainment, or is more material being added to ULVZ over time? Here we derive an advection-diffusion-like equation that governs the dynamical evolution of a chemically distinct ULVZ. Analysis of this equation shows that ULVZ should become readily swept aside by viscous mantle flows at the CMB, exposing "ordinary mantle" to the top of the core, thus inducing chemical heterogeneity that drives lateral CMB chemical reactions. These reactions are correlated with heat flux, thus maintaining large-scale pressure variations atop the core that induce cyclone-like flows centered around ULVZ and ponded subducted slabs. We suggest that turbulent diffusion across adjacent cyclone streams inside a stratified region atop the core readily accommodates lateral transport and re-distribution of components such as O and Si, in addition to heat. Our model implies that the deeper core is at least partly shielded from the influence of strong heat flux variations at
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
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
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.
Intermittent heating of buildings
Energy Technology Data Exchange (ETDEWEB)
Kohonen, K
1983-02-01
Conditions for intermittent heating of buildings are considered both theoretically and experimentally. Thermal behaviour of buildings adn rooms in intermittent heating is simulated by a program based on the convective heat balance equation and by simplified RC-models. The preheat times and the heating energy savings compared with continuous heating are presented for typical lightweight, mediumweight and heavyweight classroom and office modules. Formulaes for estimating the oversizing of the radiator network, the maximum heat output of heat exchangers in district heating and the efficiency of heating boilers in intermittent heating are presented. The preheat times and heating energy savings with different heating control systems are determined also experimentally in eight existing buildings. In addition some principles for the planning and application of intermittent heating systems are suggested.
Electrochemically grown rough-textured nanowires
International Nuclear Information System (INIS)
Tyagi, Pawan; Postetter, David; Saragnese, Daniel; Papadakis, Stergios J.; Gracias, David H.
2010-01-01
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
DEFF Research Database (Denmark)
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...
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.
Fingerprinting the type of line edge roughness
Fernández Herrero, A.; Pflüger, M.; Scholze, F.; Soltwisch, V.
2017-06-01
Lamellar gratings are widely used diffractive optical elements and are prototypes of structural elements in integrated electronic circuits. EUV scatterometry is very sensitive to structure details and imperfections, which makes it suitable for the characterization of nanostructured surfaces. As compared to X-ray methods, EUV scattering allows for steeper angles of incidence, which is highly preferable for the investigation of small measurement fields on semiconductor wafers. For the control of the lithographic manufacturing process, a rapid in-line characterization of nanostructures is indispensable. Numerous studies on the determination of regular geometry parameters of lamellar gratings from optical and Extreme Ultraviolet (EUV) scattering also investigated the impact of roughness on the respective results. The challenge is to appropriately model the influence of structure roughness on the diffraction intensities used for the reconstruction of the surface profile. The impact of roughness was already studied analytically but for gratings with a periodic pseudoroughness, because of practical restrictions of the computational domain. Our investigation aims at a better understanding of the scattering caused by line roughness. We designed a set of nine lamellar Si-gratings to be studied by EUV scatterometry. It includes one reference grating with no artificial roughness added, four gratings with a periodic roughness distribution, two with a prevailing line edge roughness (LER) and another two with line width roughness (LWR), and four gratings with a stochastic roughness distribution (two with LER and two with LWR). We show that the type of line roughness has a strong impact on the diffuse scatter angular distribution. Our experimental results are not described well by the present modelling approach based on small, periodically repeated domains.
An inverse problem in a parabolic equation
Directory of Open Access Journals (Sweden)
Zhilin Li
1998-11-01
Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.
Non-Darcy Flow Experiments of Water Seepage through Rough-Walled Rock Fractures
Directory of Open Access Journals (Sweden)
Xiao-dong Ni
2018-01-01
Full Text Available The knowledge of flow phenomena in fractured rocks is very important for groundwater-resources management in hydrogeological engineering. The most commonly used tool to approximate the non-Darcy behavior of the flow velocity is the well-known Forchheimer equation, deploying the “inertial” coefficient β that can be estimated experimentally. Unfortunately, the factor of roughness is imperfectly considered in the literature. In order to do this, we designed and manufactured a seepage apparatus that can provide different roughness and aperture in the test; the rough fracture surface is established combining JRC and 3D printing technology. A series of hydraulic tests covering various flows were performed. Experimental data suggest that Forchheimer coefficients are to some extent affected by roughness and aperture. At last, favorable semiempirical Forchheimer equation which can consider fracture aperture and roughness was firstly derived. It is believed that such studies will be quite useful in identifying the limits of applicability of the well-known “cubic law,” in further improving theoretical/numerical models associated with fluid flow through a rough fracture.
Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces
International Nuclear Information System (INIS)
Goray, Leonid I.
2010-01-01
The paper presents a comprehensive numerical analysis of x-ray and neutron scattering from finite-conducting rough surfaces which is performed in the frame of the boundary integral equation method in a rigorous formulation for high ratios of characteristic dimension to wavelength. The single integral equation obtained involves boundary integrals of the single and double layer potentials. A more general treatment of the energy conservation law applicable to absorption gratings and rough mirrors is considered. In order to compute the scattering intensity of rough surfaces using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic diffraction grating efficiency due to individual surfaces over an ensemble of realizations. Some rules appropriate for numerical implementation of the theory at small wavelength-to-period ratios are presented. The difference between the rigorous approach and approximations can be clearly seen in specular reflectances of Au mirrors with different roughness parameters at wavelengths where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are obtained by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics and allows exact computation of diffuse scattering.
Surface roughness effects on turbulent Couette flow
Lee, Young Mo; Lee, Jae Hwa
2017-11-01
Direct numerical simulation of a turbulent Couette flow with two-dimensional (2-D) rod roughness is performed to examine the effects of the surface roughness. The Reynolds number based on the channel centerline laminar velocity (Uco) and channel half height (h) is Re =7200. The 2-D rods are periodically arranged with a streamwise pitch of λ = 8 k on the bottom wall, and the roughness height is k = 0.12 h. It is shown that the wall-normal extent for the logarithmic layer is significantly shortened in the rough-wall turbulent Couette flow, compared to a turbulent Couette flow with smooth wall. Although the Reynolds stresses are increased in a turbulent channel flow with surface roughness in the outer layer due to large-scale ejection motions produced by the 2-D rods, those of the rough-wall Couette flow are decreased. Isosurfaces of the u-structures averaged in time suggest that the decrease of the turbulent activity near the centerline is associated with weakened large-scale counter-rotating roll modes by the surface roughness. This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1A09000537) and the Ministry of Science, ICT & Future Planning (NRF-2017R1A5A1015311).
Barros, Julio; Flack, Karen; Schultz, Michael
2017-11-01
Real-world engineering systems which feature either external or internal wall-bounded turbulent flow are routinely affected by surface roughness. This gives rise to performance degradation in the form of increased drag or head loss. However, at present there is no reliable means to predict these performance losses based upon the roughness topography alone. This work takes a systematic approach by generating random surface roughness in which the surface statistics are closely controlled. Skin friction and roughness function results will be presented for two groups of these rough surfaces. The first group is Gaussian (i.e. zero skewness) in which the root-mean-square roughness height (krms) is varied. The second group has a fixed krms, and the skewness is varied from approximately -1 to +1. The effect of the roughness amplitude and skewness on the skin friction will be discussed. Particular attention will be paid to the effect of these parameters on the roughness function in the transitionally-rough flow regime. For example, the role these parameters play in the monotonic or inflectional nature of the roughness function will be addressed. Future research into the details of the turbulence structure over these rough surfaces will also be outlined. Research funded by U.S. Office of Naval Research (ONR).
International Nuclear Information System (INIS)
Bogacz, Wojciech; Lemanowicz, Marcin; Al-Rashed, Mohsen H.; Nakonieczny, Damian; Piotrowski, Tomasz; Wójcik, Janusz
2017-01-01
Highlights: • Steel plates (X5CrNi18-10) with different roughness and wettability were prepared. • Incrustation of MgSO 4 ·7H 2 O under laminar flow (Re = 59–178) was investigated. • Influence of surface properties and fluid velocity on incrustation was found. • Wettability and surface roughness cannot be considered separately. • Analysis of heat transfer and incrustation time-lapse videos are presented. - Abstract: The goal of this work was to investigate the influence of the stainless steel surface roughness and wettability on incrustation of MgSO 4 ·7H 2 O from aqueous solutions and resulting heat transfer resistance. The experiments were done for laminar flow (Re = 59–178) which is characteristic for regions of apparatus where fouling usually begin. A series of steel plates (X5CrNi18-10) were prepared and used as a heat transfer surfaces. Their properties, i.e. roughness, wettability and elementary composition of surfaces were determined. The experiments were done using specially designed flow cell equipped with Peltier element. Each incrustation measurement lasted for two hours, during which heat transfer resistance was measured as a function of time. After the experiments the mass of crystalline deposit was weighted. It was proved that wettability as well as surface roughness cannot be considered separately in the case of incrustation phenomenon. The knowledge of surface roughness is insufficient due to the fact, that it is possible to obtain surfaces with similar roughness but substantially different wettability for the same material.
DEFF Research Database (Denmark)
Jacobsen, Torben; Broers, G. H. J.
1977-01-01
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......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...
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.
Atmospheric stability analysis over statically and dynamically rough surfaces
Maric, Emina; Metzger, Meredith; Singha, Arindam; Sadr, Reza
2011-11-01
The ratio of buoyancy flux to turbulent kinetic energy production in the atmospheric surface layer is investigated experimentally for air flow over two types of surfaces characterized by static and dynamic roughness. In this study, ``static'' refers to the time-invariant nature of naturally-occurring roughness over a mud/salt playa; while, ``dynamic'' refers to the behavior of water waves along an air-water interface. In both cases, time-resolved measurements of the momentum and heat fluxes were acquired from synchronized 3D sonic anemometers mounted on a vertical tower. Field campaigns were conducted at two sites, representing the ``statically'' and ``dynamically'' rough surfaces, respectively: (1) the SLTEST facility in Utah's western desert, and (2) the new Doha airport in Qatar under construction along the coast of the Persian Gulf. Note, at site 2, anemometers were located directly above the water by extension from a tower secured to the end of a 1 km-long pier. Comparisons of the Monin-Obukhov length, flux Richardson number, and gradient Richardson number are presented, and discussed in the context of the observed evolution of the turbulent spectra in response to diurnal variations of atmospheric stability. Supported by the Qatar National Research Fund.
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
Effect of surface roughness scattering on the transport properties of a 2DEG
International Nuclear Information System (INIS)
Yarar, Z.
2004-01-01
In this work surface roughness scattering of electrons in a two dimensional electron gas (2DEG) formed at heterojunction interfaces is investigated for various auto-correlation functions. Gaussian, exponential and Lorentzian auto-correlation functions are used to represent surface roughness. Poisson and Schrodinger equations are solved self consistently at the hetero interface to find the energy levels, the wave functions corresponding to each level and electron concentrations at each level. Using these wave functions and the auto-correlation functions mentioned above, the scattering rates due to surface roughness are calculated. Scattering rates resulting from acoustic and optical phonons are also calculated. These rates are used to study the transport properties of the two dimensional electrons using ensemble Monte Carlo method at various temperatures. Emphasis is given to the effect of surface roughness scattering on the transport properties of the electrons
International Nuclear Information System (INIS)
Juan, Li; Li-Xin, Guo; Hao, Zeng
2009-01-01
Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm (FDTD). The uniaxial perfectly matched layer (UPML) medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail. (fundamental areas of phenomenology (including applications))
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.
Energy Technology Data Exchange (ETDEWEB)
Kjellstroem, B
1968-12-15
Experiments with rough surface friction and heat transfer are often made in an annulus with rough inner surface and smooth outer surface. Utilization of data from such experiments for calculation of rough rod bundle fuel elements requires a transformation of the data. For this purpose the method of WB Hall is frequently used. The errors introduced by two of the assumptions on which this method is based, namely the assumptions of zero shear at the radius of maximum velocity and the assumption of no turbulence exchange between the subchannels, are discussed, and the magnitude of the errors is estimated on basis of experiments in a partially rough annulus. It is found that the necessary corrections does not amount to more than about + 10 % for the friction factor and + 15 % for the Reynolds number and the equivalent diameter. The correction for the turbulence exchange alone is of the order of 2-3 %. A comparison of friction factors measured in a rough 48-rod bundle and predicted from measurements in a partially rough annulus was also made. The prediction was 5 % high instead of about 10 % low which could have been expected from the considerations earlier in the report. Explanations for this can be found in the effect of the channel shape or inaccuracies in the rod bundle experiment. Annulus experiments which will allow comparisons with other rod bundle experiments will be run to clarify this.
Spin Hall effect by surface roughness
Zhou, Lingjun; Grigoryan, Vahram L.; Maekawa, Sadamichi; Wang, Xuhui; Xiao, Jiang
2015-01-01
induced by surface roughness subscribes only to the side-jump contribution but not the skew scattering. The paradigm proposed in this paper provides the second, not if only, alternative to generate a sizable spin Hall effect.
Surface excitation parameter for rough surfaces
International Nuclear Information System (INIS)
Da, Bo; Salma, Khanam; Ji, Hui; Mao, Shifeng; Zhang, Guanghui; Wang, Xiaoping; Ding, Zejun
2015-01-01
Graphical abstract: - Highlights: • Instead of providing a general mathematical model of roughness, we directly use a finite element triangle mesh method to build a fully 3D rough surface from the practical sample. • The surface plasmon excitation can be introduced to the realistic sample surface by dielectric response theory and finite element method. • We found that SEP calculated based on ideal plane surface model are still reliable for real sample surface with common roughness. - Abstract: In order to assess quantitatively the importance of surface excitation effect in surface electron spectroscopy measurement, surface excitation parameter (SEP) has been introduced to describe the surface excitation probability as an average number of surface excitations that electrons can undergo when they move through solid surface either in incoming or outgoing directions. Meanwhile, surface roughness is an inevitable issue in experiments particularly when the sample surface is cleaned with ion beam bombardment. Surface roughness alters not only the electron elastic peak intensity but also the surface excitation intensity. However, almost all of the popular theoretical models for determining SEP are based on ideal plane surface approximation. In order to figure out whether this approximation is efficient or not for SEP calculation and the scope of this assumption, we proposed a new way to determine the SEP for a rough surface by a Monte Carlo simulation of electron scattering process near to a realistic rough surface, which is modeled by a finite element analysis method according to AFM image. The elastic peak intensity is calculated for different electron incident and emission angles. Assuming surface excitations obey the Poisson distribution the SEPs corrected for surface roughness are then obtained by analyzing the elastic peak intensity for several materials and for different incident and emission angles. It is found that the surface roughness only plays an
Small-Scale Surf Zone Geometric Roughness
2017-12-01
using stereo imagery techniques. A waterproof two- camera system with self-logging and internal power was developed using commercial-off-the-shelf...estimates. 14. SUBJECT TERMS surface roughness, nearshore, aerodynamic roughness, surf zone, structure from motion, 3D imagery 15. NUMBER OF... power was developed using commercial-off-the- shelf components and commercial software for operations 1m above the sea surface within the surf zone
Role of surface roughness in superlubricity
International Nuclear Information System (INIS)
Tartaglino, U; Samoilov, V N; Persson, B N J
2006-01-01
We study the sliding of elastic solids in adhesive contact with flat and rough interfaces. We consider the dependence of the sliding friction on the elastic modulus of the solids. For elastically hard solids with planar surfaces with incommensurate surface structures we observe extremely low friction (superlubricity), which very abruptly increases as the elastic modulus decreases. We show that even a relatively small surface roughness may completely kill the superlubricity state
Reduction of vortex induced forces and motion through surface roughness control
Bernitsas, Michael M; Raghavan, Kamaldev
2014-04-01
Roughness is added to the surface of a bluff body in a relative motion with respect to a fluid. The amount, size, and distribution of roughness on the body surface is controlled passively or actively to modify the flow around the body and subsequently the Vortex Induced Forces and Motion (VIFM). The added roughness, when designed and implemented appropriately, affects in a predetermined way the boundary layer, the separation of the boundary layer, the level of turbulence, the wake, the drag and lift forces, and consequently the Vortex Induced Motion (VIM), and the fluid-structure interaction. The goal of surface roughness control is to decrease/suppress Vortex Induced Forces and Motion. Suppression is required when fluid-structure interaction becomes destructive as in VIM of flexible cylinders or rigid cylinders on elastic support, such as underwater pipelines, marine risers, tubes in heat exchangers, nuclear fuel rods, cooling towers, SPAR offshore platforms.
Dissolution of minerals with rough surfaces
de Assis, Thiago A.; Aarão Reis, Fábio D. A.
2018-05-01
We study dissolution of minerals with initial rough surfaces using kinetic Monte Carlo simulations and a scaling approach. We consider a simple cubic lattice structure, a thermally activated rate of detachment of a molecule (site), and rough surface configurations produced by fractional Brownian motion algorithm. First we revisit the problem of dissolution of initial flat surfaces, in which the dissolution rate rF reaches an approximately constant value at short times and is controlled by detachment of step edge sites. For initial rough surfaces, the dissolution rate r at short times is much larger than rF ; after dissolution of some hundreds of molecular layers, r decreases by some orders of magnitude across several time decades. Meanwhile, the surface evolves through configurations of decreasing energy, beginning with dissolution of isolated sites, then formation of terraces with disordered boundaries, their growth, and final smoothing. A crossover time to a smooth configuration is defined when r = 1.5rF ; the surface retreat at the crossover is approximately 3 times the initial roughness and is temperature-independent, while the crossover time is proportional to the initial roughness and is controlled by step-edge site detachment. The initial dissolution process is described by the so-called rough rates, which are measured for fixed ratios between the surface retreat and the initial roughness. The temperature dependence of the rough rates indicates control by kink site detachment; in general, it suggests that rough rates are controlled by the weakest microscopic bonds during the nucleation and formation of the lowest energy configurations of the crystalline surface. Our results are related to recent laboratory studies which show enhanced dissolution in polished calcite surfaces. In the application to calcite dissolution in alkaline environment, the minimal values of recently measured dissolution rate spectra give rF ∼10-9 mol/(m2 s), and the calculated rate
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.
Rough mill simulator version 3.0: an analysis tool for refining rough mill operations
Edward Thomas; Joel Weiss
2006-01-01
ROMI-3 is a rough mill computer simulation package designed to be used by both rip-first and chop-first rough mill operators and researchers. ROMI-3 allows users to model and examine the complex relationships among cutting bill, lumber grade mix, processing options, and their impact on rough mill yield and efficiency. Integrated into the ROMI-3 software is a new least-...
Khoshechin, Mohsen; Salimi, Farhad; Jahangiri, Alireza
2018-04-01
In this research, the effect of surface roughness and concentration of solution on bubble departing frequency and nucleation site density for pool boiling of water/diethanolamine (DEA) binary solution were investigated experimentally. In this investigation, boiling heat transfer coefficient, bubble departing frequency and nucleation site density have been experimentally investigated in various concentrations and heat fluxes. Microstructured surfaces with a wide range of well-defined surface roughness were fabricated, and a heat flux between 1.5-86 kW/m2 was achieved under atmospheric conditions. The Results indicated that surface roughness and concentration of solution increase the bubble departing frequency and nucleation site density with increasing heat flux. The boiling heat transfer coefficient in mixtures of water/DEA increases with increasing concentration of DEA in water. The experimental results were compared with predictions of several used correlations in the literatures. Results showed that the boiling heat transfer coefficients of this case study are much higher than the predicted values by major existing correlations and models. The excellent agreement for bubble departing frequency found between the models of Jackob and Fritz (1966) and experimental data and also the nucleation site density were in close agreement with the model of Paul (1983) data. f bubble departure frequency, 1/s or Hz N Number of nucleation sites per area per time R c Minimum cavity size, m D c critical diameter, m g gravitational acceleration, m/s2 ρ density, kg/m3 T temperature, °c ΔT temperature difference, °c d d vapor bubble diameter, m h fg enthalpy of vaporization, J/kg R Roughness, μm Ja Jakob number cp specific heat, J/kg °c Pr Prandtl number Ar Archimedes number h Heat transfer coefficient, J/(m2 °c) tg time it takes to grow a bubble, s q/A heat flux (kW/m2) tw time required to heat the layer, s gc Correction coefficient of incompatible units R a Surface
Mitigating mask roughness via pupil filtering
Baylav, B.; Maloney, C.; Levinson, Z.; Bekaert, J.; Vaglio Pret, A.; Smith, B.
2014-03-01
The roughness present on the sidewalls of lithographically defined patterns imposes a very important challenge for advanced technology nodes. It can originate from the aerial image or the photoresist chemistry/processing [1]. The latter remains to be the dominant group in ArF and KrF lithography; however, the roughness originating from the mask transferred to the aerial image is gaining more attention [2-9], especially for the imaging conditions with large mask error enhancement factor (MEEF) values. The mask roughness contribution is usually in the low frequency range, which is particularly detrimental to the device performance by causing variations in electrical device parameters on the same chip [10-12]. This paper explains characteristic differences between pupil plane filtering in amplitude and in phase for the purpose of mitigating mask roughness transfer under interference-like lithography imaging conditions, where onedirectional periodic features are to be printed by partially coherent sources. A white noise edge roughness was used to perturbate the mask features for validating the mitigation.
Development of nano-roughness calibration standards
International Nuclear Information System (INIS)
Baršić, Gorana; Mahović, Sanjin; Zorc, Hrvoje
2012-01-01
At the Laboratory for Precise Measurements of Length, currently the Croatian National Laboratory for Length, unique nano-roughness calibration standards were developed, which have been physically implemented in cooperation with the company MikroMasch Trading OU and the Ruđer Bošković Institute. In this paper, a new design for a calibration standard with two measuring surfaces is presented. One of the surfaces is for the reproduction of roughness parameters, while the other is for the traceability of length units below 50 nm. The nominal values of the groove depths on these measuring surfaces are the same. Thus, a link between the measuring surfaces has been ensured, which makes these standards unique. Furthermore, the calibration standards available on the market are generally designed specifically for individual groups of measuring instrumentation, such as interferometric microscopes, stylus instruments, scanning electron microscopes (SEM) or scanning probe microscopes. In this paper, a new design for nano-roughness standards has been proposed for use in the calibration of optical instruments, as well as for stylus instruments, SEM, atomic force microscopes and scanning tunneling microscopes. Therefore, the development of these new nano-roughness calibration standards greatly contributes to the reproducibility of the results of groove depth measurement as well as the 2D and 3D roughness parameters obtained by various measuring methods. (paper)
A Rough Set Approach for Customer Segmentation
Directory of Open Access Journals (Sweden)
Prabha Dhandayudam
2014-04-01
Full Text Available Customer segmentation is a process that divides a business's total customers into groups according to their diversity of purchasing behavior and characteristics. The data mining clustering technique can be used to accomplish this customer segmentation. This technique clusters the customers in such a way that the customers in one group behave similarly when compared to the customers in other groups. The customer related data are categorical in nature. However, the clustering algorithms for categorical data are few and are unable to handle uncertainty. Rough set theory (RST is a mathematical approach that handles uncertainty and is capable of discovering knowledge from a database. This paper proposes a new clustering technique called MADO (Minimum Average Dissimilarity between Objects for categorical data based on elements of RST. The proposed algorithm is compared with other RST based clustering algorithms, such as MMR (Min-Min Roughness, MMeR (Min Mean Roughness, SDR (Standard Deviation Roughness, SSDR (Standard deviation of Standard Deviation Roughness, and MADE (Maximal Attributes DEpendency. The results show that for the real customer data considered, the MADO algorithm achieves clusters with higher cohesion, lower coupling, and less computational complexity when compared to the above mentioned algorithms. The proposed algorithm has also been tested on a synthetic data set to prove that it is also suitable for high dimensional data.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
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
Thermodynamical Approach for The Determination of The Speed of Heat Propagation in Heat Conduction
International Nuclear Information System (INIS)
Shnaid, I.
1998-01-01
In this work, a thermodynamical approach for the determination of the speed of heat propagation in a heat conductive body is developed. It employs equations of the First and the Second Laws of thermodynamics. The present analyses show that no time delay exists between time moments of heat extraction and heat supply. Therefore, an infinite speed of heat propagation is proven. It is also predicted that there is no time lag between heat flow and temperature difference. A theoretical approach straightforwardly leading from basic equations of the First and the Second Laws of thermodynamics to a kinetic equation describing heat conduction in an isotropic continuum is also developed. It is shown that Fourier's equation is a particular case of the derived kinetic equation. Based on the kinetic equation, the governing heat conduction equation is of tile parabolic type, thus, confirming that speed of heat propagation is infinite
Heat simulation via Scilab programming
Hasan, Mohammad Khatim; Sulaiman, Jumat; Karim, Samsul Arifin Abdul
2014-07-01
This paper discussed the used of an open source sofware called Scilab to develop a heat simulator. In this paper, heat equation was used to simulate heat behavior in an object. The simulator was developed using finite difference method. Numerical experiment output show that Scilab can produce a good heat behavior simulation with marvellous visual output with only developing simple computer code.
Turbulent flow velocity distribution at rough walls
International Nuclear Information System (INIS)
Baumann, W.
1978-08-01
Following extensive measurements of the velocity profile in a plate channel with artificial roughness geometries specific investigations were carried out to verify the results obtained. The wall geometry used was formed by high transverse square ribs having a large pitch. The measuring position relative to the ribs was varied as a parameter thus providing a statement on the local influence of roughness ribs on the values measured. As a fundamental result it was found that the gradient of the logarithmic rough wall velocity profiles, which differs widely from the value 2.5, depends but slightly on the measuring position relative to the ribs. The gradients of the smooth wall velocity profiles deviate from 2.5 near the ribs, only. This fact can be explained by the smooth wall shear stress varying with the pitch of the ribs. (orig.) 891 GL [de
Spin Hall effect by surface roughness
Zhou, Lingjun
2015-01-08
The spin Hall and its inverse effects, driven by the spin orbit interaction, provide an interconversion mechanism between spin and charge currents. Since the spin Hall effect generates and manipulates spin current electrically, to achieve a large effect is becoming an important topic in both academia and industries. So far, materials with heavy elements carrying a strong spin orbit interaction, provide the only option. We propose here a new mechanism, using the surface roughness in ultrathin films, to enhance the spin Hall effect without heavy elements. Our analysis based on Cu and Al thin films suggests that surface roughness is capable of driving a spin Hall angle that is comparable to that in bulk Au. We also demonstrate that the spin Hall effect induced by surface roughness subscribes only to the side-jump contribution but not the skew scattering. The paradigm proposed in this paper provides the second, not if only, alternative to generate a sizable spin Hall effect.
Why do rough surfaces appear glossy?
Qi, Lin; Chantler, Mike J; Siebert, J Paul; Dong, Junyu
2014-05-01
The majority of work on the perception of gloss has been performed using smooth surfaces (e.g., spheres). Previous studies that have employed more complex surfaces reported that increasing mesoscale roughness increases perceived gloss [Psychol. Sci.19, 196 (2008), J. Vis.10(9), 13 (2010), Curr. Biol.22, 1909 (2012)]. We show that the use of realistic rendering conditions is important and that, in contrast to [Psychol. Sci.19, 196 (2008), J. Vis.10(9), 13 (2010)], after a certain point increasing roughness further actually reduces glossiness. We investigate five image statistics of estimated highlights and show that for our stimuli, one in particular, which we term "percentage of highlight area," is highly correlated with perceived gloss. We investigate a simple model that explains the unimodal, nonmonotonic relationship between mesoscale roughness and percentage highlight area.
Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method
Directory of Open Access Journals (Sweden)
Yunfeng Dai
2017-01-01
Full Text Available To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.
The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface
Klass, E. V.
2017-12-01
The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
Fuzzy sets, rough sets, multisets and clustering
Dahlbom, Anders; Narukawa, Yasuo
2017-01-01
This book is dedicated to Prof. Sadaaki Miyamoto and presents cutting-edge papers in some of the areas in which he contributed. Bringing together contributions by leading researchers in the field, it concretely addresses clustering, multisets, rough sets and fuzzy sets, as well as their applications in areas such as decision-making. The book is divided in four parts, the first of which focuses on clustering and classification. The second part puts the spotlight on multisets, bags, fuzzy bags and other fuzzy extensions, while the third deals with rough sets. Rounding out the coverage, the last part explores fuzzy sets and decision-making.
Diffuse neutron scattering signatures of rough films
International Nuclear Information System (INIS)
Pynn, R.; Lujan, M. Jr.
1992-01-01
Patterns of diffuse neutron scattering from thin films are calculated from a perturbation expansion based on the distorted-wave Born approximation. Diffuse fringes can be categorised into three types: those that occur at constant values of the incident or scattered neutron wavevectors, and those for which the neutron wavevector transfer perpendicular to the film is constant. The variation of intensity along these fringes can be used to deduce the spectrum of surface roughness for the film and the degree of correlation between the film's rough surfaces
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
Surface Roughness of the Moon Derived from Multi-frequency Radar Data
Fa, W.
2011-12-01
Surface roughness of the Moon provides important information concerning both significant questions about lunar surface processes and engineering constrains for human outposts and rover trafficabillity. Impact-related phenomena change the morphology and roughness of lunar surface, and therefore surface roughness provides clues to the formation and modification mechanisms of impact craters. Since the Apollo era, lunar surface roughness has been studied using different approaches, such as direct estimation from lunar surface digital topographic relief, and indirect analysis of Earth-based radar echo strengths. Submillimeter scale roughness at Apollo landing sites has been studied by computer stereophotogrammetry analysis of Apollo Lunar Surface Closeup Camera (ALSCC) pictures, whereas roughness at meter to kilometer scale has been studied using laser altimeter data from recent missions. Though these studies shown lunar surface roughness is scale dependent that can be described by fractal statistics, roughness at centimeter scale has not been studied yet. In this study, lunar surface roughnesses at centimeter scale are investigated using Earth-based 70 cm Arecibo radar data and miniature synthetic aperture radar (Mini-SAR) data at S- and X-band (with wavelengths 12.6 cm and 4.12 cm). Both observations and theoretical modeling show that radar echo strengths are mostly dominated by scattering from the surface and shallow buried rocks. Given the different penetration depths of radar waves at these frequencies (< 30 m for 70 cm wavelength, < 3 m at S-band, and < 1 m at X-band), radar echo strengths at S- and X-band will yield surface roughness directly, whereas radar echo at 70-cm will give an upper limit of lunar surface roughness. The integral equation method is used to model radar scattering from the rough lunar surface, and dielectric constant of regolith and surface roughness are two dominate factors. The complex dielectric constant of regolith is first estimated
Directory of Open Access Journals (Sweden)
Yoshikazu Fujii
2013-01-01
Full Text Available X-ray reflectometry is a powerful tool for investigations on rough surface and interface structures of multilayered thin film materials. The X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, in previous studies, the calculations of the X-ray reflectivity often show a strange effect where interference effects would increase at a rough surface. And estimated surface and interface roughnesses from the X-ray reflectivity measurements did not correspond to the TEM image observation results. The strange result had its origin in a used equation due to a serious mistake in which the Fresnel transmission coefficient in the reflectivity equation is increased at a rough interface because of a lack of consideration of diffuse scattering. In this review, a new accurate formalism that corrects this mistake is presented. The new accurate formalism derives an accurate analysis of the X-ray reflectivity from a multilayer surface of thin film materials, taking into account the effect of roughness-induced diffuse scattering. The calculated reflectivity by this accurate reflectivity equation should enable the structure of buried interfaces to be analyzed more accurately.
Some estimates of mirror plasma startup by neutral beam heating of pellet and gas cloud targets
International Nuclear Information System (INIS)
Shearer, J.W.; Willmann, P.A.
1978-01-01
Hot plasma buildup by neutral beam injection into an initially cold solid or gaseous target is found to be conceivable in large mirror machine experiments such as 2XIIB or MFTF. A simple analysis shows that existing neutral beam intensities are sufficient to ablate suitable targets to form a gas or vapor cloud. An approximate rate equation model is used to follow the subsequent processes of ionization, heating, and hot plasma formation. Solutions of these rate equations are obtained by means of the ''GEAR'' techniques for solving ''stiff'' systems of differential equations. These solutions are in rough agreement with the 2XIIB stream plasma buildup experiment. They also predict that buildup on a suitable nitrogen-like target will occur in the MFTF geometry. In 2XIIB the solutions are marginal; buildup may be possible, but is not certain
Zeqiri, F.; Alkan, M.; Kaya, B.; Toros, S.
2018-01-01
In this paper, the effects of cutting parameters on cutting forces and surface roughness based on Taguchi experimental design method are determined. Taguchi L9 orthogonal array is used to investigate the effects of machining parameters. Optimal cutting conditions are determined using the signal/noise (S/N) ratio which is calculated by average surface roughness and cutting force. Using results of analysis, effects of parameters on both average surface roughness and cutting forces are calculated on Minitab 17 using ANOVA method. The material that was investigated is Inconel 625 steel for two cases with heat treatment and without heat treatment. The predicted and calculated values with measurement are very close to each other. Confirmation test of results showed that the Taguchi method was very successful in the optimization of machining parameters for maximum surface roughness and cutting forces in the CNC turning process.
Potential roughness near lithographically fabricated atom chips
DEFF Research Database (Denmark)
Krüger, Peter; Andersson, L. M.; Wildermuth, Stefan
2007-01-01
Potential roughness has been reported to severely impair experiments in magnetic microtraps. We show that these obstacles can be overcome as we measure disorder potentials that are reduced by two orders of magnitude near lithographically patterned high-quality gold layers on semiconductor atom chip...
Reproducibility of surface roughness in reaming
DEFF Research Database (Denmark)
Müller, Pavel; De Chiffre, Leonardo
An investigation on the reproducibility of surface roughness in reaming was performed to document the applicability of this approach for testing cutting fluids. Austenitic stainless steel was used as a workpiece material and HSS reamers as cutting tools. Reproducibility of the results was evaluat...
Optical measurement of surface roughness in manufacturing
Energy Technology Data Exchange (ETDEWEB)
Brodmann, R.
1984-11-01
The measuring system described here is based on the light-scattering method, and was developed by Optische Werke G. Rodenstock, Munich. It is especially useful for rapid non-contact monitoring of surface roughness in production-related areas. This paper outlines the differences between this system and the common stylus instrument, including descriptions of some applications in industry.
Microscopic Holography for flow over rough plate
Talapatra, Siddharth; Hong, Jiarong; Lu, Yuan; Katz, Joseph
2008-11-01
Our objective is to measure the near wall flow structures in a turbulent channel flow over a rough wall. In-line microscopic holographic PIV can resolve the 3-D flow field in a small sample volume, but recording holograms through a rough surface is a challenge. To solve this problem, we match the refractive indices of the fluid with that of the wall. Proof of concept tests involve an acrylic plate containing uniformly distributed, closely packed 0.45mm high pyramids with slope angle of 22^^o located within a concentrated sodium iodide solution. Holograms recorded by a 4864 x 3248 pixel digital camera at 10X magnification provide a field of view of 3.47mm x 2.32mm and pixel resolution of 0.714 μm. Due to index matching, reconstructed seed particles can be clearly seen over the entire volume, with only faint traces with the rough wall that can be removed. Planned experiments will be performed in a 20 x 5 cm rectangular channel with the top and bottom plates having the same roughness as the sample plate.
Roughly isometric minimal immersions into Riemannian manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
of the intrinsic combinatorial discrete Laplacian, and we will show that they share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in $N$. The intrinsic properties thus obtained may hence serve as roughly invariant descriptors for the original metric space $X$....
Three-tier rough superhydrophobic surfaces
International Nuclear Information System (INIS)
Cao, Yuanzhi; Yuan, Longyan; Hu, Bin; Zhou, Jun
2015-01-01
A three-tier rough superhydrophobic surface was fabricated by growing hydrophobic modified (fluorinated silane) zinc oxide (ZnO)/copper oxide (CuO) hetero-hierarchical structures on silicon (Si) micro-pillar arrays. Compared with the other three control samples with a less rough tier, the three-tier surface exhibits the best water repellency with the largest contact angle 161° and the lowest sliding angle 0.5°. It also shows a robust Cassie state which enables the water to flow with a speed over 2 m s"−"1. In addition, it could prevent itself from being wetted by the droplet with low surface tension (mixed water and ethanol 1:1 in volume) which reveals a flow speed of 0.6 m s"−"1 (dropped from the height of 2 cm). All these features prove that adding another rough tier on a two-tier rough surface could futher improve its water-repellent properties. (paper)
Roughness-induced streaming in turbulent wave boundary layers
DEFF Research Database (Denmark)
Fuhrman, David R.; Sumer, B. Mutlu; Fredsøe, Jørgen
2011-01-01
-averaged streaming characteristics induced by bottom roughness variations are systematically assessed. The effects of variable roughness ratio, gradual roughness transitions, as well as changing flow orientation in plan are all considered. As part of the latter, roughness-induced secondary flows are predicted...
Self-affine roughness influence on redox reaction charge admittance
Palasantzas, G
2005-01-01
In this work we investigate the influence of self-affine electrode roughness on the admittance of redox reactions during facile charge transfer kinetics. The self-affine roughness is characterized by the rms roughness amplitude w, the correlation length xi and the roughness exponent H (0
Zafar, Muhammad Sohail; Ahmed, Naseer
2014-01-01
Polymers have a wide range of applications in dentistry. Poly methyl methacrylate (PMMA) is the most popular for making orthodontic retainers, dentures as well as synthetic teeth. Prior to clinical applications, the appliances are polished in the dental laboratory to achieve smooth, polished and comfortable surfaces. The objective of this study was to analyze the surface roughness profiles of PMMA dentures polished using two different approaches. In addition, the effects of ultrasonication and sandblasting were also evaluated on the fitting surface of PMMA dentures. This was an in vitro study using non-contact mode surface roughness profilometer and nano-indenter. Samples were polished using two different techniques (Standard and modified). Both cold cure and heat cure PMMA denture surfaces were evaluated for roughness, nanohardness and elastic modulus. The absolute hardness was recorded 297.72±19.04 MPa and 229.93±18.53 MPa for heat cured PMMA and cold cured PMMA. Manufactured acrylic teeth were harder (319.20±12.58 MPa) with an elastic modulus of (4.34±1.86 GPa). Modified polishing techniques (group 3) produced smoother surface. It was concluded that elastic moduli of acrylic tooth and heat cure PMMA is not very different. Surface treatments such as ultrasonication or sandblasting do not affect the roughness profiles of denture fitting surfaces.
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
More on neutrosophic soft rough sets and its modification
Directory of Open Access Journals (Sweden)
Emad Marei
2015-12-01
Full Text Available This paper aims to introduce and discuss anew mathematical tool for dealing with uncertainties, which is a combination of neutrosophic sets, soft sets and rough sets, namely neutrosophic soft rough set model. Also, its modification is introduced. Some of their properties are studied and supported with proved propositions and many counter examples. Some of rough relations are redefined as a neutrosophic soft rough relations. Comparisons among traditional rough model, suggested neutrosophic soft rough model and its modification, by using their properties and accuracy measures are introduced. Finally, we illustrate that, classical rough set model can be viewed as a special case of suggested models in this paper.
Turbulent boundary layer over roughness transition with variation in spanwise roughness length scale
Westerweel, Jerry; Tomas, Jasper; Eisma, Jerke; Pourquie, Mathieu; Elsinga, Gerrit; Jonker, Harm
2016-11-01
Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic PIV and LIF were done to investigate pollutant dispersion in a region where the surface changes from rural to urban roughness. This consists of rectangular obstacles where we vary the spanwise aspect ratio of the obstacles. A line source of passive tracer was placed upstream of the roughness transition. The objectives of the study are: (i) to determine the influence of the aspect ratio on the roughness-transition flow, and (ii) to determine the dominant mechanisms of pollutant removal from street canyons in the transition region. It is found that for a spanwise aspect ratio of 2 the drag induced by the roughness is largest of all considered cases, which is caused by a large-scale secondary flow. In the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identied that is responsible for exchange of the fluid between the roughness obstacles and the outer part of the boundary layer. Furthermore, it is found that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the roughness region.
Numerical Investigation of Effect of Surface Roughness in a Microchannel
Energy Technology Data Exchange (ETDEWEB)
Shin, Myung Seob; Byun, Sung Jun; Yoon, Joon Yong [Hanyang University, Seoul (Korea, Republic of)
2010-05-15
In this paper, lattice Boltzmann method(LBM) results for a laminar flow in a microchannel with rough surface are presented. The surface roughness is modeled as an array of rectangular modules placed on the top and bottom surface of a parallel-plate channel. The effects of relative surface roughness, roughness distribution, and roughness size are presented in terms of the Poiseuille number. The roughness distribution characterized by the ratio of the roughness height to the spacing between the modules has a negligible effect on the flow and friction factors. Finally, a significant increase in the Poiseuille number is observed when the surface roughness is considered, and the effects of roughness on the microflow field mainly depend on the surface roughness.
Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers
Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan
2015-01-01
Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.
Surface roughness studies with DALLAS-detector array for laser light angular scattering
Vorburger, T. V.; Teague, E. C.; Scire, F. E.; Mclay, M. J.; Gilsinn, D. E.
1984-01-01
An attempt is made to develop a better mathematical description of optical scattering phenomena, in order to construct an optical scattering apparatus for reliable and routine measurements of roughness parameters without resorting to comparator standards. After a brief outline of optical scattering theory, a description is presented of an experimental instrument for measuring surface roughness which incorporates optical scattering principles. The instrument has a He-Ne laser which illuminates the test surface at a variable angle of incidence. Scattered light distribution is detected by an array of 87 fiber-optic sensors positioned in a rotating semicircular yoke. The output from the detector is digitized and analyzed in a laboratory computer. For a comparison with experimental data, theoretical distributions are calculated by substituting the roughness profiles into the operand of and integral equation for electromagnetic scattering developed by Beckmann and Spizzichino (1963). A schematic diagram of the instrument is provided and the general implications of the experimental results are discussed.
Influence of Sea Surface Roughness on the Electromagnetic Wave Propagation in the Duct Environment
Directory of Open Access Journals (Sweden)
X. Zhao
2010-12-01
Full Text Available This paper deals with a study of the influence of sea surface roughness on the electromagnetic wave propagation in the duct environment. The problem of electromagnetic wave propagation is modeled by using the parabolic equation method. The roughness of the sea surface is computed by modifying the smooth surface Fresnel reflection coefficient to account for the reduction in the specular reflection due to the roughness resulting from sea wind speed. The propagation model is solved by the mixed Fourier split-step algorithm. Numerical experiments indicate that wind-driven roughened sea surface has an impact on the electromagnetic wave propagation in the duct environment, and the strength is intensified along with the increment of sea wind speeds and/or the operating frequencies. In a fixed duct environment, however, proper disposition of the transmitter could reduce these impacts.
Models for Surface Roughness Scattering of Electrons in a 2DEG
International Nuclear Information System (INIS)
Yarar, Z.
2004-01-01
In this work surface roughness scattering of electrons in a two dimensional electron gas (2DEG) formed at heterojunction interfaces is investigated for different auto-correlation tions and potential forms. Gaussian, exponentiaI and lorentsian auto-correlation tions are used to represent surface roughness. Both an infinitely deep triangular potential model and the potential that is found from the numerical solution of Poisson Shrodinger equations self consistently are used as the potential that holds 2DEG at the hetero Interface. Using the wave functions appropriate for the potentials just mentioned and the auto-correlation functions indicated above, the scattering rates due to surface roughness are calculated. The calculations were repeated when the effect of screening is also included for the case of triangular potential
Hanumagowda, B. N.; Salma, A.; Nagarajappa, C. S.
2018-04-01
The theoretical discussion is carried out for understanding the combined study of MHD, rough surface and couple-stress in the presence of applied magnetic field between two curved circular plates is present analysis. Modified Reynolds Equations accounting for rough surface using stochastic model of Christensen are mathematically formulated. The close form derivations for pressure, load-supporting capacity and response-film time are obtained. Our results shows that, there is an significant increase (decrease) for pressure, load-supporting capacity and squeeze film time due to the effect of azimuthal (radial) roughness parameter when compared to the Hanumagowda.et.al [14] and numerical data of load supporting capacity and response time are given in Table for engineering applications.
Brownian motion of spins; generalized spin Langevin equation
International Nuclear Information System (INIS)
Jayannavar, A.M.
1990-03-01
We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concomitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature. (author). 16 refs
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…
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Anomalous roughness of turbulent interfaces with system size dependent local roughness exponent
International Nuclear Information System (INIS)
Balankin, Alexander S.; Matamoros, Daniel Morales
2005-01-01
In a system far from equilibrium the system size can play the role of control parameter that governs the spatiotemporal dynamics of the system. Accordingly, the kinetic roughness of interfaces in systems far from equilibrium may depend on the system size. To get an insight into this problem, we performed a detailed study of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λ, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non-universal global roughness exponent α and by the system size dependent spectrum of local roughness exponents, ζ q (λ)=ζ 1 (1)q -ω λ φ q =0.93q -0.15 . The structure factor of turbulent flame fronts also exhibits unconventional scaling dependence on λ. These results are expected to apply to a broad range of far from equilibrium systems when the kinetic energy fluctuations exceed a certain critical value.
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
A contact mechanics model for ankle implants with inclusion of surface roughness effects
International Nuclear Information System (INIS)
Hodaei, M; Farhang, K; Maani, N
2014-01-01
Total ankle replacement is recognized as one of the best procedures to treat painful arthritic ankles. Even though this method can relieve patients from pain and reproduce the physiological functions of the ankle, an improper design can cause an excessive amount of metal debris due to wear, causing toxicity in implant recipient. This paper develops a contact model to treat the interaction of tibia and talus implants in an ankle joint. The contact model describes the interaction of implant rough surfaces including both elastic and plastic deformations. In the model, the tibia and the talus surfaces are viewed as macroscopically conforming cylinders or conforming multi-cylinders containing micrometre-scale roughness. The derived equations relate contact force on the implant and the minimum mean surface separation of the rough surfaces. The force is expressed as a statistical integral function of asperity heights over the possible region of interaction of the roughness of the tibia and the talus implant surfaces. A closed-form approximate equation relating contact force and minimum separation is used to obtain energy loss per cycle in a load–unload sequence applied to the implant. In this way implant surface statistics are related to energy loss in the implant that is responsible for internal void formation and subsequent wear and its harmful toxicity to the implant recipient. (paper)
A contact mechanics model for ankle implants with inclusion of surface roughness effects
Hodaei, M.; Farhang, K.; Maani, N.
2014-02-01
Total ankle replacement is recognized as one of the best procedures to treat painful arthritic ankles. Even though this method can relieve patients from pain and reproduce the physiological functions of the ankle, an improper design can cause an excessive amount of metal debris due to wear, causing toxicity in implant recipient. This paper develops a contact model to treat the interaction of tibia and talus implants in an ankle joint. The contact model describes the interaction of implant rough surfaces including both elastic and plastic deformations. In the model, the tibia and the talus surfaces are viewed as macroscopically conforming cylinders or conforming multi-cylinders containing micrometre-scale roughness. The derived equations relate contact force on the implant and the minimum mean surface separation of the rough surfaces. The force is expressed as a statistical integral function of asperity heights over the possible region of interaction of the roughness of the tibia and the talus implant surfaces. A closed-form approximate equation relating contact force and minimum separation is used to obtain energy loss per cycle in a load-unload sequence applied to the implant. In this way implant surface statistics are related to energy loss in the implant that is responsible for internal void formation and subsequent wear and its harmful toxicity to the implant recipient.
Collisions of ideal gas molecules with a rough/fractal surface. A computational study.
Panczyk, Tomasz
2007-02-01
The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).
Heat transfer in rotating serpentine passages with trips normal to the flow
Wagner, J. H.; Johnson, B. V.; Graziani, R. A.; Yeh, F. C.
1991-01-01
Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.
Generalized rough sets hybrid structure and applications
Mukherjee, Anjan
2015-01-01
The book introduces the concept of “generalized interval valued intuitionistic fuzzy soft sets”. It presents the basic properties of these sets and also, investigates an application of generalized interval valued intuitionistic fuzzy soft sets in decision making with respect to interval of degree of preference. The concept of “interval valued intuitionistic fuzzy soft rough sets” is discussed and interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The book also details concept of interval valued intuitionistic fuzzy sets of type 2. It presents the basic properties of these sets. The book also introduces the concept of “interval valued intuitionistic fuzzy soft topological space (IVIFS topological space)” together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft cl...
Single-layer model for surface roughness.
Carniglia, C K; Jensen, D G
2002-06-01
Random roughness of an optical surface reduces its specular reflectance and transmittance by the scattering of light. The reduction in reflectance can be modeled by a homogeneous layer on the surface if the refractive index of the layer is intermediate to the indices of the media on either side of the surface. Such a layer predicts an increase in the transmittance of the surface and therefore does not provide a valid model for the effects of scatter on the transmittance. Adding a small amount of absorption to the layer provides a model that predicts a reduction in both reflectance and transmittance. The absorbing layer model agrees with the predictions of a scalar scattering theory for a layer with a thickness that is twice the rms roughness of the surface. The extinction coefficient k for the layer is proportional to the thickness of the layer.
Offshore Wind Power at Rough Sea
DEFF Research Database (Denmark)
Petersen, Kristian Rasmus; Madsen, Erik Skov; Bilberg, Arne
2013-01-01
This study compare the current operations and maintenance issues of one offshore wind park at very rough sea conditions and two onshore wind parks. Through a detailed data analysis and case studies this study identifies how improvements have been made in maintenance of large wind turbines. Howeve......, the study has also revealed the need for new maintenance models including a shift from breakdown and preventive maintenances and towards more predictive maintenance to reduce the cost of energy for offshore wind energy installations in the future.......This study compare the current operations and maintenance issues of one offshore wind park at very rough sea conditions and two onshore wind parks. Through a detailed data analysis and case studies this study identifies how improvements have been made in maintenance of large wind turbines. However...
Prediction of Ductile Fracture Surface Roughness Scaling
DEFF Research Database (Denmark)
Needleman, Alan; Tvergaard, Viggo; Bouchaud, Elisabeth
2012-01-01
. Ductile crack growth in a thin strip under mode I, overall plane strain, small scale yielding conditions is analyzed. Although overall plane strain loading conditions are prescribed, full 3D analyses are carried out to permit modeling of the three dimensional material microstructure and of the resulting......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...... three dimensional stress and deformation states that develop in the fracture process region. An elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid is used to model the material. Two populations of second phase particles are represented: large inclusions with low...
Estimation of gloss from rough surface parameters
Simonsen, Ingve; Larsen, Åge G.; Andreassen, Erik; Ommundsen, Espen; Nord-Varhaug, Katrin
2005-12-01
Gloss is a quantity used in the optical industry to quantify and categorize materials according to how well they scatter light specularly. With the aid of phase perturbation theory, we derive an approximate expression for this quantity for a one-dimensional randomly rough surface. It is demonstrated that gloss depends in an exponential way on two dimensionless quantities that are associated with the surface randomness: the root-mean-square roughness times the perpendicular momentum transfer for the specular direction, and a correlation function dependent factor times a lateral momentum variable associated with the collection angle. Rigorous Monte Carlo simulations are used to access the quality of this approximation, and good agreement is observed over large regions of parameter space.
Sparseness and Roughness of Foreign Exchange Rates
Vandewalle, N.; Ausloos, M.
An accurate multiaffine analysis of 23 foreign currency exchange rates has been performed. The roughness exponent H1 which characterizes the excursion of the exchange rate has been numerically measured. The degree of intermittency C1 has been also estimated. In the (H1,C1) phase diagram, the currency exchange rates are dispersed in a wide region around the Brownian motion value (H1=0.5,C1=0) and have a significantly intermittent component (C1≠0).
Rough surface scattering simulations using graphics cards
International Nuclear Information System (INIS)
Klapetek, Petr; Valtr, Miroslav; Poruba, Ales; Necas, David; Ohlidal, Miloslav
2010-01-01
In this article we present results of rough surface scattering calculations using a graphical processing unit implementation of the Finite Difference in Time Domain algorithm. Numerical results are compared to real measurements and computational performance is compared to computer processor implementation of the same algorithm. As a basis for computations, atomic force microscope measurements of surface morphology are used. It is shown that the graphical processing unit capabilities can be used to speedup presented computationally demanding algorithms without loss of precision.
Roughness Length Variability over Heterogeneous Surfaces
2010-03-01
2004), the influence of variable roughness reaches its maximum at the height of local 0z and vanishes at the so- called blending height (Wieringa...the distribution of visibility restrictors such as low clouds, fog, haze, dust, and pollutants . An improved understanding of ABL structure...R. D., B. H. Lynn, A. Boone, W.-K. Tao, and J. Simpson, 2001: The influence of soil moisture, coastline curvature, and land-breeze circulations on
Analysis of accuracy in photogrammetric roughness measurements
Olkowicz, Marcin; Dąbrowski, Marcin; Pluymakers, Anne
2017-04-01
Regarding permeability, one of the most important features of shale gas reservoirs is the effective aperture of cracks opened during hydraulic fracturing, both propped and unpropped. In a propped fracture, the aperture is controlled mostly by proppant size and its embedment, and fracture surface roughness only has a minor influence. In contrast, in an unpropped fracture aperture is controlled by the fracture roughness and the wall displacement. To measure fracture surface roughness, we have used the photogrammetric method since it is time- and cost-efficient. To estimate the accuracy of this method we compare the photogrammetric measurements with reference measurements taken with a White Light Interferometer (WLI). Our photogrammetric setup is based on high resolution 50 Mpx camera combined with a focus stacking technique. The first step for photogrammetric measurements is to determine the optimal camera positions and lighting. We compare multiple scans of one sample, taken with different settings of lighting and camera positions, with the reference WLI measurement. The second step is to perform measurements of all studied fractures with the parameters that produced the best results in the first step. To compare photogrammetric and WLI measurements we regrid both data sets onto a regular 10 μm grid and determined the best fit, followed by a calculation of the difference between the measurements. The first results of the comparison show that for 90 % of measured points the absolute vertical distance between WLI and photogrammetry is less than 10 μm, while the mean absolute vertical distance is 5 μm. This proves that our setup can be used for fracture roughness measurements in shales.
The characteristic function of rough Heston models
Euch, Omar El; Rosenbaum, Mathieu
2016-01-01
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we c...
Directory of Open Access Journals (Sweden)
Prasad Radha K.
2017-09-01
Full Text Available This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.
Radiative transfer model for contaminated rough slabs.
Andrieu, François; Douté, Sylvain; Schmidt, Frédéric; Schmitt, Bernard
2015-11-01
We present a semi-analytical model to simulate the bidirectional reflectance distribution function (BRDF) of a rough slab layer containing impurities. This model has been optimized for fast computation in order to analyze massive hyperspectral data by a Bayesian approach. We designed it for planetary surface ice studies but it could be used for other purposes. It estimates the bidirectional reflectance of a rough slab of material containing inclusions, overlaying an optically thick media (semi-infinite media or stratified media, for instance granular material). The inclusions are assumed to be close to spherical and constituted of any type of material other than the ice matrix. It can be any other type of ice, mineral, or even bubbles defined by their optical constants. We assume a low roughness and we consider the geometrical optics conditions. This model is thus applicable for inclusions larger than the considered wavelength. The scattering on the inclusions is assumed to be isotropic. This model has a fast computation implementation and thus is suitable for high-resolution hyperspectral data analysis.
Modeling superhydrophobic surfaces comprised of random roughness
Samaha, M. A.; Tafreshi, H. Vahedi; Gad-El-Hak, M.
2011-11-01
We model the performance of superhydrophobic surfaces comprised of randomly distributed roughness that resembles natural surfaces, or those produced via random deposition of hydrophobic particles. Such a fabrication method is far less expensive than ordered-microstructured fabrication. The present numerical simulations are aimed at improving our understanding of the drag reduction effect and the stability of the air-water interface in terms of the microstructure parameters. For comparison and validation, we have also simulated the flow over superhydrophobic surfaces made up of aligned or staggered microposts for channel flows as well as streamwise or spanwise ridge configurations for pipe flows. The present results are compared with other theoretical and experimental studies. The numerical simulations indicate that the random distribution of surface roughness has a favorable effect on drag reduction, as long as the gas fraction is kept the same. The stability of the meniscus, however, is strongly influenced by the average spacing between the roughness peaks, which needs to be carefully examined before a surface can be recommended for fabrication. Financial support from DARPA, contract number W91CRB-10-1-0003, is acknowledged.
Rough – Granular Computing knowledge discovery models
Directory of Open Access Journals (Sweden)
Mohammed M. Eissa
2016-11-01
Full Text Available Medical domain has become one of the most important areas of research in order to richness huge amounts of medical information about the symptoms of diseases and how to distinguish between them to diagnose it correctly. Knowledge discovery models play vital role in refinement and mining of medical indicators to help medical experts to settle treatment decisions. This paper introduces four hybrid Rough – Granular Computing knowledge discovery models based on Rough Sets Theory, Artificial Neural Networks, Genetic Algorithm and Rough Mereology Theory. A comparative analysis of various knowledge discovery models that use different knowledge discovery techniques for data pre-processing, reduction, and data mining supports medical experts to extract the main medical indicators, to reduce the misdiagnosis rates and to improve decision-making for medical diagnosis and treatment. The proposed models utilized two medical datasets: Coronary Heart Disease dataset and Hepatitis C Virus dataset. The main purpose of this paper was to explore and evaluate the proposed models based on Granular Computing methodology for knowledge extraction according to different evaluation criteria for classification of medical datasets. Another purpose is to make enhancement in the frame of KDD processes for supervised learning using Granular Computing methodology.
International Nuclear Information System (INIS)
Chae, Byung Gon; Choi, Jung Hae; Ichikawa, Yasuaki; Seo, Yong Seok
2012-01-01
To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the fracture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.
Kakac, Sadik; Pramuanjaroenkij, Anchasa
2014-01-01
Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....
Effects of graphite surface roughness on bypass flow computations for an HTGR
Energy Technology Data Exchange (ETDEWEB)
Tung, Yu-Hsin, E-mail: touushin@gmail.com [Idaho National Laboratory, P.O. Box 1625, M.S. 3855, Idaho Falls, ID (United States); Johnson, Richard W., E-mail: Rich.Johnson@inl.gov [Idaho National Laboratory, P.O. Box 1625, M.S. 3855, Idaho Falls, ID (United States); Sato, Hiroyuki, E-mail: sato.hiroyuki09@jaea.go.jp [Idaho National Laboratory, P.O. Box 1625, M.S. 3855, Idaho Falls, ID (United States)
2012-11-15
Highlights: Black-Right-Pointing-Pointer CFD calculations are made of bypass flow between graphite blocks in HTGR. Black-Right-Pointing-Pointer Several turbulence models are employed to compare to friction and heat transfer correlations. Black-Right-Pointing-Pointer Parameters varied include bypass gap width and surface roughness. Black-Right-Pointing-Pointer Surface roughness causes increases in max fuel and coolant temperatures. Black-Right-Pointing-Pointer Surface roughness does not cause increase in outlet coolant temperature variation. - Abstract: Bypass flow in a prismatic high temperature gas reactor (HTGR) occurs between graphite blocks as they sit side by side in the core. Bypass flow is not intentionally designed to occur in the reactor, but is present because of tolerances in manufacture, imperfect installation and expansion and shrinkage of the blocks from heating and irradiation. It is desired to increase the knowledge of the effects of such flow; it has been suggested that it may be as much as 20% of the total helium coolant flow [INL Report 2007, INL/EXT-07-13289]. Computational fluid dynamic (CFD) simulations can provide estimates of the scale and impacts of bypass flow. Previous CFD calculations have examined the effects of bypass gap width, level and distribution of heat generation and effects of shrinkage. The present contribution examines the effects of graphite surface roughness on the bypass flow for different relative roughness factors for three gap widths. Such calculations should be validated using specific bypass flow measurements. While such experiments are currently underway for the specific reference prismatic HTGR design for the next generation nuclear plant (NGNP) program of the U.S. Dept. of Energy, the data are not yet available. To enhance confidence in the present calculations, wall shear stress and heat transfer results for several turbulence models and their associated wall treatments are first compared for steady flow in a
Lubrication theory analysis of the permeability of rough-walled fractures
International Nuclear Information System (INIS)
Zimmerman, R.W.; Kumar, S.; Bodvarsson, G.S.
1991-01-01
The flow of a fluid between the rough surfaces of a rock fracture is very complex, due to the tortuous paths followed by the fluid particles. Exact analytical modeling of these flows is made difficult by the irregular geometry of rock fracture surfaces, while full three-dimensional numerical simulations of these flows are as yet still impractical. To overcome the difficulties of working with the three-dimensional Navier-Stokes equations, the simpler Reynolds lubrication equation has sometimes been used to model flow in fractures. This paper focuses on two aspects of lubrication theory. First, lubrication theory is applied to two simplified aperture profiles, sinusoidal and sawtooth, and analytical expressions are found for the permeabilities. These results are then compared with numerical results obtained by solving the lubrication equation for fractures with random surfaces. Secondly, the validity of the lubrication equations for modeling flow in rough fractures is studied by examining higher-order perturbation solutions, as well as numerical solutions, to the Navier-Stokes equations for flow in fractures with sinusoidally-varying apertures. 22 refs., 6 figs
Wilder, Michael C.; Reda, Daniel C.; Prabhu, Dinesh K.
2015-01-01
Blunt-body geometries were flown through carbon dioxide in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility to investigate the influence of distributed surface roughness on transition to turbulence in CO2-dominated atmospheres, such as those of Mars and Venus. Tests were also performed in air for direct comparison with archival results. Models of hemispherical and spherically-blunted large-angle conical geometries were flown at speeds between 2.8 km/s and 5.1 km/s and freestream pressures between 50 Torr and 228 Torr. Transition fronts were determined from global surface heat flux distributions measured using thermal imaging techniques. Distributed surface roughness was produced by grit-blasting the model surfaces. Real-gas Navier-Stokes solutions were used to calculate non-dimensional correlating parameters at the measured transition onset locations. Transition-onset locations correlated well with a constant roughness Reynolds number based on the mean roughness element height. The critical roughness Reynolds number for transition onset determined for flight in CO2 was 223 +/- 25%. This mean value is lower than the critical value of 250 +/- 20% previously-established from tests conducted in air, but within the bounds of the expected measurement uncertainty.
Real-time kinetic modeling of YSZ thin film roughness deposited by e-beam evaporation technique
International Nuclear Information System (INIS)
Galdikas, A.; Cerapaite-Trusinskiene, R.; Laukaitis, G.; Dudonis, J.
2008-01-01
In the present study, the process of yttrium-stabilized zirconia (YSZ) thin films deposition on optical quartz (SiO 2 ) substrates using e-beam deposition technique controlling electron gun power is analyzed. It was found that electron gun power influences the non-monotonous kinetics of YSZ film surface roughness. The evolution of YSZ thin film surface roughness was analyzed by a kinetic model. The model is based on the rate equations and includes processes of surface diffusion of the adatoms and the clusters, nucleation, growth and coalescence of islands in the case of thin film growth in Volmer-Weber mode. The analysis of the experimental results done by modeling explains non-monotonous kinetics and dependence of the surface roughness on the electron gun power. A good quantitative agreement with experimental results is obtained taking into account the initial roughness of the substrate surface and the amount of the clusters in the flux of evaporated material.
Pathikonda, Gokul; Clark, Caitlyn; Christensen, Kenneth T.
2017-11-01
Inner-outer interactions over rough-wall boundary layer were investigated using high frame-rate, PIV measurements in a Refractive index-matched (RIM) facility. Flows over canonical smooth-wall and hexagonally-packed hemispherical roughness under transitionally rough flow conditions (and with Reτ 1500) were measured using a dual camera PIV system with different fields of view (FOVs) and operating simultaneously. The large FOV measures the large scales and boundary layer parameters, while the small FOV measures the small scales very close to the wall with high spatial ( 7y*) and temporal ( 2.5t*) resolutions. Conditional metrics were formulated to investigate these scale interactions in a spatio-temporal sense using the PIV data. It was found that the observations complement the interaction structure made via hotwire experiments and DNS in previous studies over both smooth and rough-wall flows, with a strong correlation between the large scales and small scale energies indicative of the amplitude modulation interactions. Additionally, frequency and scale modulations were also investigated with limited success. These experiments highlight the similarities and differences in these interactions between the smooth- and rough-wall flows.
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
Directory of Open Access Journals (Sweden)
JesÃƒÂºs ÃƒÂlvarez-Mozos
2009-01-01
Full Text Available Radar-based surface soil moisture retrieval has been subject of intense research during the last decades. However, several difficulties hamper the operational estimation of soil moisture based on currently available spaceborne sensors. The main difficulty experienced so far results from the strong influence of other surface characteristics, mainly roughness, on the backscattering coefficient, which hinders the soil moisture inversion. This is especially true for single configuration observations where the solution to the surface backscattering problem is ill-posed. Over agricultural areas cultivated with winter cereal crops, roughness can be assumed to remain constant along the growing cycle allowing the use of simplified approaches that facilitate the estimation of the moisture content of soils. However, the field scale spatial variability and temporal variations of roughness can introduce errors in the estimation of soil moisture that are difficult to evaluate. The objective of this study is to assess the impact of roughness spatial variability and roughness temporal variations on the retrieval of soil moisture from radar observations. A series of laser profilometer measurements were performed over several fields in an experimental watershed from September 2004 to March 2005. The influence of the observed roughness variability and its temporal variations on the retrieval of soil moisture is studied using simulations performed with the Integral Equation Model, considering different sensor configurations. Results show that both field scale roughness spatial variability and its temporal variations are aspects that need to be taken into account, since they can introduce large errors on the retrieved soil moisture values.
Demuzere, M.; De Ridder, K.; van Lipzig, N. P. M.
2008-08-01
During the ESCOMPTE campaign (Experience sur Site pour COntraindre les Modeles de Pollution atmospherique et de Transport d'Emissions), a 4-day intensive observation period was selected to evaluate the Advanced Regional Prediction System (ARPS), a nonhydrostatic meteorological mesoscale model that was optimized with a parameterization for thermal roughness length to better represent urban surfaces. The evaluation shows that the ARPS model is able to correctly reproduce temperature, wind speed, and direction for one urban and two rural measurements stations. Furthermore, simulated heat fluxes show good agreement compared to the observations, although simulated sensible heat fluxes were initially too low for the urban stations. In order to improve the latter, different roughness length parameterization schemes were tested, combined with various thermal admittance values. This sensitivity study showed that the Zilitinkevich scheme combined with and intermediate value of thermal admittance performs best.
Dewetting of thin polymer film on rough substrate: II. Experiment
International Nuclear Information System (INIS)
Volodin, Pylyp; Kondyurin, Alexey
2008-01-01
The theory of the dewetting process developed for a model of substrate-film interaction forces was examined by an experimental investigation of the dewetting process of thin polystyrene (PS) films on chemically etched silicon substrates. In the dependence on PS films thickness and silicon roughness, various situations of dewetting were observed as follows: (i) if the wavelength of the substrate roughness is much larger than the critical spinodal wavelength of a film, then spinodal dewetting of the film is observed; (ii) if the wavelength of the substrate roughness is smaller than the critical wavelength of the film and the substrate roughness is larger in comparison with film thickness, then the dewetting due to substrate roughness is observed and the dewetted film patterns repeat the rough substrate structure; (iii) if the wavelength of the substrate roughness is smaller than the critical wavelength of the film and the substrate roughness is small in comparison with the film thickness, then spinodal dewetting proceeds
Sub-Patch Roughness in Earthquake Rupture Investigations
Zielke, Olaf; Mai, Paul Martin
2016-01-01
Fault geometric complexities exhibit fractal characteristics over a wide range of spatial scales (<µm to >km) and strongly affect the rupture process at corresponding scales. Numerical rupture simulations provide a framework to quantitatively investigate the relationship between a fault's roughness and its seismic characteristics. Fault discretization however introduces an artificial lower limit to roughness. Individual fault patches are planar and sub-patch roughness –roughness at spatial scales below fault-patch size– is not incorporated. Does negligence of sub-patch roughness measurably affect the outcome of earthquake rupture simulations? We approach this question with a numerical parameter space investigation and demonstrate that sub-patch roughness significantly modifies the slip-strain relationship –a fundamental aspect of dislocation theory. Faults with sub-patch roughness induce less strain than their planar-fault equivalents at distances beyond the length of a slipping fault. We further provide regression functions that characterize the stochastic effect sub-patch roughness.
Roughness characterization of the galling of metals
Hubert, C.; Marteau, J.; Deltombe, R.; Chen, Y. M.; Bigerelle, M.
2014-09-01
Several kinds of tests exist to characterize the galling of metals, such as that specified in ASTM Standard G98. While the testing procedure is accurate and robust, the analysis of the specimen's surfaces (area=1.2 cm) for the determination of the critical pressure of galling remains subject to operator judgment. Based on the surface's topography analyses, we propose a methodology to express the probability of galling according to the macroscopic pressure load. After performing galling tests on 304L stainless steel, a two-step segmentation of the S q parameter (root mean square of surface amplitude) computed from local roughness maps (100 μ m× 100 μ m) enables us to distinguish two tribological processes. The first step represents the abrasive wear (erosion) and the second one the adhesive wear (galling). The total areas of both regions are highly relevant to quantify galling and erosion processes. Then, a one-parameter phenomenological model is proposed to objectively determine the evolution of non-galled relative area A e versus the pressure load P, with high accuracy ({{A}e}=100/(1+a{{P}2}) with a={{0.54}+/- 0.07}× {{10}-3} M P{{a}-2} and with {{R}2}=0.98). From this model, the critical pressure of galling is found to be equal to 43MPa. The {{S}5 V} roughness parameter (the five deepest valleys in the galled region's surface) is the most relevant roughness parameter for the quantification of damages in the ‘galling region’. The significant valleys’ depths increase from 10 μm-250 μm when the pressure increases from 11-350 MPa, according to a power law ({{S}5 V}=4.2{{P}0.75}, with {{R}2}=0.93).
Robust surface roughness indices and morphological interpretation
Trevisani, Sebastiano; Rocca, Michele
2016-04-01
Geostatistical-based image/surface texture indices based on variogram (Atkison and Lewis, 2000; Herzfeld and Higginson, 1996; Trevisani et al., 2012) and on its robust variant MAD (median absolute differences, Trevisani and Rocca, 2015) offer powerful tools for the analysis and interpretation of surface morphology (potentially not limited to solid earth). In particular, the proposed robust index (Trevisani and Rocca, 2015) with its implementation based on local kernels permits the derivation of a wide set of robust and customizable geomorphometric indices capable to outline specific aspects of surface texture. The stability of MAD in presence of signal noise and abrupt changes in spatial variability is well suited for the analysis of high-resolution digital terrain models. Moreover, the implementation of MAD by means of a pixel-centered perspective based on local kernels, with some analogies to the local binary pattern approach (Lucieer and Stein, 2005; Ojala et al., 2002), permits to create custom roughness indices capable to outline different aspects of surface roughness (Grohmann et al., 2011; Smith, 2015). In the proposed poster, some potentialities of the new indices in the context of geomorphometry and landscape analysis will be presented. At same time, challenges and future developments related to the proposed indices will be outlined. Atkinson, P.M., Lewis, P., 2000. Geostatistical classification for remote sensing: an introduction. Computers & Geosciences 26, 361-371. Grohmann, C.H., Smith, M.J., Riccomini, C., 2011. Multiscale Analysis of Topographic Surface Roughness in the Midland Valley, Scotland. IEEE Transactions on Geoscience and Remote Sensing 49, 1220-1213. Herzfeld, U.C., Higginson, C.A., 1996. Automated geostatistical seafloor classification - Principles, parameters, feature vectors, and discrimination criteria. Computers and Geosciences, 22 (1), pp. 35-52. Lucieer, A., Stein, A., 2005. Texture-based landform segmentation of LiDAR imagery
Traceability of optical roughness measurements on polymers
DEFF Research Database (Denmark)
De Chiffre, Leonardo; Gasparin, Stefania; Carli, Lorenzo
2008-01-01
-focus instrument, and a confocal microscope. Using stylus measurements as reference, parameter settings on the optical instruments were optimised and residual noise reduced by low pass filtering. Traceability of optical measurements could be established with expanded measuring uncertainties (k=2) of 4......An experimental investigation on surface roughness measurements on plastics was carried out with the objective of developing a methodology to achieve traceability of optical instruments. A ground steel surface and its replicas were measured using a stylus instrument, an optical auto......% for the auto-focus instrument and 10% for confocal microscope....
Wave scattering from statistically rough surfaces
Bass, F G; ter Haar, D
2013-01-01
Wave Scattering from Statistically Rough Surfaces discusses the complications in radio physics and hydro-acoustics in relation to wave transmission under settings seen in nature. Some of the topics that are covered include radar and sonar, the effect of variations in topographic relief or ocean waves on the transmission of radio and sound waves, the reproduction of radio waves from the lower layers of the ionosphere, and the oscillations of signals within the earth-ionosphere waveguide. The book begins with some fundamental idea of wave transmission theory and the theory of random processes a
Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces
Thakkar, Manan; Busse, Angela; Sandham, Neil
2017-02-01
Rough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and root-mean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface
Magnetotactic bacteria at the geomagnetic equator
International Nuclear Information System (INIS)
Frankel, R.B.; Blakemore, R.P.; Araujo, F.F.T. de; Esquivel, D.M.S.; Danon, J.
1981-01-01
Magnetotatic bacteria are observed in freshwater and marine sediments of Fortaleza, Brazil, situated close to the geomagnetic equator. Both South-seeking and North-seeking bacteria are present in roughly equal numbers in the same samples. This observation is consistent with the hypothesis that the vertical component of the geomagnetic field selects the predominant polarity type among magnetotactic bacteria in natural environments. (Author) [pt
Urban roughness mapping validation techniques and some first results
Bottema, M; Mestayer, PG
1998-01-01
Because of measuring problems related to evaluation of urban roughness parameters, a new approach using a roughness mapping tool has been tested: evaluation of roughness length z(o) and zero displacement z(d) from cadastral databases. Special attention needs to be given to the validation of the
Procedure and applications of combined wheel/rail roughness measurement
Dittrich, M.G.
2009-01-01
Wheel-rail roughness is known to be the main excitation source of railway rolling noise. Besides the already standardised method for direct roughness measurement, it is also possible to measure combined wheel-rail roughness from vertical railhead vibration during a train pass-by. This is a different
Rough sets applied in sublattices and ideals of lattices
Directory of Open Access Journals (Sweden)
R. Ameri
2015-12-01
Full Text Available The purpose of this paper is the study of rough hyperlattice. In this regards we introduce rough sublattice and rough ideals of lattices. We will proceed by obtaining lower and upper approximations in these lattices.
Use of roughness maps in visualisation of surfaces
DEFF Research Database (Denmark)
Seitavuopio, Paulus; Rantanen, Jukka; Yliruusi, Jouko
2005-01-01
monohydrate, theophylline anhydrate, sodium chloride and potassium chloride. The roughness determinations were made by a laser profilometer. The new matrix method gives detailed roughness maps, which are able to show local variations in surface roughness values and provide an illustrative picture...
ROMI 4.0: Updated Rough Mill Simulator
Timo Grueneberg; R. Edward Thomas; Urs Buehlmann
2012-01-01
In the secondary hardwood industry, rough mills convert hardwood lumber into dimension parts for furniture, cabinets, and other wood products. ROMI 4.0, the US Department of Agriculture Forest Service's ROugh-MIll simulator, is a software package designed to simulate the cut-up of hardwood lumber in rough mills in such a way that a maximum possible component yield...
Rough sets selected methods and applications in management and engineering
Peters, Georg; Ślęzak, Dominik; Yao, Yiyu
2012-01-01
Introduced in the early 1980s, Rough Set Theory has become an important part of soft computing in the last 25 years. This book provides a practical, context-based analysis of rough set theory, with each chapter exploring a real-world application of Rough Sets.
7 CFR 868.201 - Definition of rough rice.
2010-01-01
... 7 Agriculture 7 2010-01-01 2010-01-01 false Definition of rough rice. 868.201 Section 868.201... FOR CERTAIN AGRICULTURAL COMMODITIES United States Standards for Rough Rice Terms Defined § 868.201 Definition of rough rice. Rice (Oryza sativa L.) which consists of 50 percent or more of paddy kernels (see...
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Rough viscoelastic sliding contact: Theory and experiments
Carbone, G.; Putignano, C.
2014-03-01
In this paper, we show how the numerical theory introduced by the authors [Carbone and Putignano, J. Mech. Phys. Solids 61, 1822 (2013), 10.1016/j.jmps.2013.03.005] can be effectively employed to study the contact between viscoelastic rough solids. The huge numerical complexity is successfully faced up by employing the adaptive nonuniform mesh developed by the authors in Putignano et al. [J. Mech. Phys. Solids 60, 973 (2012), 10.1016/j.jmps.2012.01.006]. Results mark the importance of accounting for viscoelastic effects to correctly simulate the sliding rough contact. In detail, attention is, first, paid to evaluate the viscoelastic dissipation, i.e., the viscoelastic friction. Fixed the sliding speed and the normal load, friction is completely determined. Furthermore, since the methodology employed in the work allows to study contact between real materials, a comparison between experimental outcomes and numerical prediction in terms of viscoelastic friction is shown. The good agreement seems to validate—at least partially—the presented methodology. Finally, it is shown that viscoelasticity entails not only the dissipative effects previously outlined, but is also strictly related to the anisotropy of the contact solution. Indeed, a marked anisotropy is present in the contact region, which results stretched in the direction perpendicular to the sliding speed. In the paper, the anisotropy of the deformed surface and of the contact area is investigated and quantified.
Directory of Open Access Journals (Sweden)
Yongmin Yang
2017-01-01
Full Text Available The partitioning of available energy between sensible heat and latent heat is important for precise water resources planning and management in the context of global climate change. Land surface temperature (LST is a key variable in energy balance process and remotely sensed LST is widely used for estimating surface heat fluxes at regional scale. However, the inequality between LST and aerodynamic surface temperature (Taero poses a great challenge for regional heat fluxes estimation in one-source energy balance models. To address this issue, we proposed a One-Source Model for Land (OSML to estimate regional surface heat fluxes without requirements for empirical extra resistance, roughness parameterization and wind velocity. The proposed OSML employs both conceptual VFC/LST trapezoid model and the electrical analog formula of sensible heat flux (H to analytically estimate the radiometric-convective resistance (rae via a quartic equation. To evaluate the performance of OSML, the model was applied to the Soil Moisture-Atmosphere Coupling Experiment (SMACEX in United States and the Multi-Scale Observation Experiment on Evapotranspiration (MUSOEXE in China, using remotely sensed retrievals as auxiliary data sets at regional scale. Validated against tower-based surface fluxes observations, the root mean square deviation (RMSD of H and latent heat flux (LE from OSML are 34.5 W/m2 and 46.5 W/m2 at SMACEX site and 50.1 W/m2 and 67.0 W/m2 at MUSOEXE site. The performance of OSML is very comparable to other published studies. In addition, the proposed OSML model demonstrates similar skills of predicting surface heat fluxes in comparison to SEBS (Surface Energy Balance System. Since OSML does not require specification of aerodynamic surface characteristics, roughness parameterization and meteorological conditions with high spatial variation such as wind speed, this proposed method shows high potential for routinely acquisition of latent heat flux estimation
Percolation characteristics of solvent invasion in rough fractures under miscible conditions
Korfanta, M.; Babadagli, T.; Develi, K.
2017-10-01
Surface roughness and flow rate effects on the solvent transport under miscible conditions in a single fracture are studied. Surface replicas of seven different rocks (marble, granite, and limestone) are used to represent different surface roughness characteristics each described by different mathematical models including three fractal dimensions. Distribution of dyed solvent is investigated at various flow rate conditions to clarify the effect of roughness on convective and diffusive mixing. After a qualitative analysis using comparative images of different rocks, the area covered by solvent with respect to time is determined to conduct a semi-quantitative analysis. In this exercise, two distinct zones are identified, namely the straight lines obtained for convective (early times) and diffusive (late times) flow. The bending point between these two lines is used to point the transition between the two zones. Finally, the slopes of the straight lines and the bending points are correlated to five different roughness parameters and the rate (Peclet number). It is observed that both surface roughness and flow rate have significant effect on solvent spatial distribution. The largest area covered is obtained at moderate flow rates and hence not only the average surface roughness characteristic is important, but coessentially total fracture surface area needs to be considered when evaluating fluid distribution. It is also noted that the rate effect is critically different for the fracture samples of large grain size (marbles and granite) compared to smaller grain sizes (limestones). Variogram fractal dimension exhibits the strongest correlation with the maximum area covered by solvent, and display increasing trend at the moderate flow rates. Equations with variogram surface fractal dimension in combination with any other surface fractal parameter coupled with Peclet number can be used to predict maximum area covered by solvent in a single fracture, which in turn can be
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Roughness as classicality indicator of a quantum state
Lemos, Humberto C. F.; Almeida, Alexandre C. L.; Amaral, Barbara; Oliveira, Adélcio C.
2018-03-01
We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L2 (R2) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [ 0 , 1 ], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness approaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.
Effect of Blade Roughness on Transition and Wind Turbine Performance.
Energy Technology Data Exchange (ETDEWEB)
Ehrmann, Robert S. [Texas A & M Univ., College Station, TX (United States); White, E. B. [Texas A & M Univ., College Station, TX (United States)
2015-09-01
The real-world effect of accumulated surface roughness on wind-turbine power production is not well understood. To isolate specific blade roughness features and test their effect, field measurements of turbine-blade roughness were made and simulated on a NACA 633-418 airfoil in a wind tunnel. Insect roughness, paint chips, and erosion were characterized then manufactured. In the tests, these roughness configurations were recreated as distributed roughness, a forward-facing step, and an eroded leading edge. Distributed roughness was tested in three heights and five densities. Chord Reynolds number was varied between 0:8 to 4:8 × 10^{6}. Measurements included lift, drag, pitching moment, and boundary-layer transition location. Results indicate minimal effect from paint-chip roughness. As distributed roughness height and density increase, the lift-curve slope, maximum lift, and lift-to-drag ratio decrease. As Reynolds number increases, natural transition is replaced by bypass transition. The critical roughness Reynolds number varies between 178 to 318, within the historical range. At a chord Reynolds number of 3:2 × 10^{6}, the maximum lift-to-drag ratio decreases 40% for 140 μm roughness, corresponding to a 2.3% loss in annual energy production. Simulated performance loss compares well to measured performance loss of an in-service wind turbine.
Barros, Julio; Schultz, Michael; Flack, Karen
2016-11-01
Engineering systems are affected by surface roughness which cause an increase in drag leading to significant performance penalties. One important question is how to predict frictional drag purely based upon surface topography. Although significant progress has been made in recent years, this has proven to be challenging. The present work takes a systematic approach by generating surface roughness in which surfaces parameters, such as rms , skewness, can be controlled. Surfaces were produced using the random Fourier modes method with enforced power-law spectral slopes. The surfaces were manufactured using high resolution 3D-printing. In this study three surfaces with constant amplitude and varying slope, P, were investigated (P = - 0 . 5 , - 1 . 0 , - 1 . 5). Skin-friction measurements were conducted in a high Reynolds number turbulent channel flow facility, covering a wide range of Reynolds numbers, from hydraulic-smooth to fully-rough regimes. Results show that some long wavelength roughness scales do not contribute significantly to the frictional drag, thus highlighting the need for filtering in the calculation of surface statistics. Upon high-pass filtering, it was found that krms is highly correlated with the measured ks.
Fast Heat Pulse Propagation by Turbulence Spreading
DEFF Research Database (Denmark)
Naulin, Volker; Juul Rasmussen, Jens; Mantica, Paola
2009-01-01
The propagation of a cold pulse initiated by edge cooling in JET is compared to propagation of the heat wave originating from a modulation of the heating source roughly at mid radius. It is found that the propagation of the cold pulse is by far faster than what could be predicted on the basis of ...
Sea ice roughness: the key for predicting Arctic summer ice albedo
Landy, J.; Ehn, J. K.; Tsamados, M.; Stroeve, J.; Barber, D. G.
2017-12-01
Although melt ponds on Arctic sea ice evolve in stages, ice with smoother surface topography typically allows the pond water to spread over a wider area, reducing the ice-albedo and accelerating further melt. Building on this theory, we simulated the distribution of meltwater on a range of statistically-derived topographies to develop a quantitative relationship between premelt sea ice surface roughness and summer ice albedo. Our method, previously applied to ICESat observations of the end-of-winter sea ice roughness, could account for 85% of the variance in AVHRR observations of the summer ice-albedo [Landy et al., 2015]. Consequently, an Arctic-wide reduction in sea ice roughness over the ICESat operational period (from 2003 to 2008) explained a drop in ice-albedo that resulted in a 16% increase in solar heat input to the sea ice cover. Here we will review this work and present new research linking pre-melt sea ice surface roughness observations from Cryosat-2 to summer sea ice albedo over the past six years, examining the potential of winter roughness as a significant new source of sea ice predictability. We will further evaluate the possibility for high-resolution (kilometre-scale) forecasts of summer sea ice albedo from waveform-level Cryosat-2 roughness data in the landfast sea ice zone of the Canadian Arctic. Landy, J. C., J. K. Ehn, and D. G. Barber (2015), Albedo feedback enhanced by smoother Arctic sea ice, Geophys. Res. Lett., 42, 10,714-10,720, doi:10.1002/2015GL066712.
Shi, J.; Menenti, M.; Lindenbergh, R.
2013-01-01
Glaciers in the Tibetan mountains are expected to be sensitive to turbulent sensible and latent heat fluxes. One of the most significant factors of the energy exchange between the atmospheric boundary layer and the glacier is the roughness of the glacier surface. However, methods to parameterize
Numerical simulations of rough contacts between viscoelastic materials
Spinu, S.; Cerlinca, D.
2017-08-01
The durability of the mechanical contact is often plagued by surface-related phenomena like rolling contact fatigue, wear or crack propagation, which are linked to the important gradients of stress arising in the contacting bodies due to interaction at the asperity level. The semi-analytical computational approach adopted in this paper is based on a previously reported algorithm capable of simulating the contact between bodies with arbitrary limiting surfaces and viscoelastic behaviour, which is enhanced and adapted for the contact of real surfaces with microtopography. As steep slopes at the asperity level inevitably lead to localized plastic deformation at the tip of the asperities that are first brought into contact, the viscoelastic behaviour is amended by limiting the maximum value of the pressure on the contact area to that of the material hardness, according to the Tabor equation. In this manner, plasticity is considered in a simplified manner that assures the knowledge of the contact area and of the pressure distribution without estimation of the residual state. The main advantage of this approach is the preservation of the algorithmic complexity, allowing the simulation of very fine meshes capable of capturing particular features of the investigated contacting surface. The newly advanced model is expected to predict the contact specifics of rough surfaces as resulting from various manufacturing processes, thus assisting the design of durable machine elements using elastomers or rubbers.
Design, construction and characterization of pneumatic system for measurement of roughness
Directory of Open Access Journals (Sweden)
Germán A. Bacca-Bastidas
2015-07-01
Full Text Available This article aims to present the results obtained from the design, construction and characterization of a pneumatic flapper-nozzle amplifier, employed in the measurement of average surface roughness. In the construction of the sensor, low cost materials were used and most pieces were obtained by machining. The data acquisition was performed through PC, using an Arduino interface board. The nonlinear mathematical model of the sensor is based on equations of perfect gas flow through an orifice and the continuity law for a control volume. The characterization of physical parameters obtained through laboratory techniques based on the transient response of the gas pressure in the pressurization and depressurization processes of constant volume chambers, using computational tools for adjusting experimental curves. The validation of the model was based on the specifications of transient response that presents a dynamic system for a step input. For the measurement of the roughness, the mathematical model of average roughness, Ra, was used, and the measured data by the sensor were obtained in sandpapers from P1000 to P2000 size, with reference for validation values of average roughness indicated by the FEPA standard.
Slope-velocity equilibrium and evolution of surface roughness on a stony hillslope
Nearing, Mark A.; Polyakov, Viktor O.; Nichols, Mary H.; Hernandez, Mariano; Li, Li; Zhao, Ying; Armendariz, Gerardo
2017-06-01
Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and surface morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow rate independent of slope gradient. This study tests this hypothesis under controlled conditions. Artificial rainfall was applied to 2 m by 6 m plots at 5, 12, and 20 % slope gradients. A series of simulations were made with two replications for each treatment with measurements of runoff rate, velocity, rock cover, and surface roughness. Velocities measured at the end of each experiment were a unique function of discharge rates, independent of slope gradient or rainfall intensity. Physical surface roughness was greater at steeper slopes. The data clearly showed that there was no unique hydraulic coefficient for a given slope, surface condition, or rainfall rate, with hydraulic roughness greater at steeper slopes and lower intensities. This study supports the hypothesis of slope-velocity equilibrium, implying that use of hydraulic equations, such as Chezy and Manning, in hillslope-scale runoff models is problematic because the coefficients vary with both slope and rainfall intensity.
Influence of surface roughness of a desert
Sud, Y. C.; Smith, W. E.
1984-01-01
A numerical simulation study, using the current GLAS climate GCM, was carried out to examine the influence of low bulk aerodynamic drag parameter in the deserts. The results illustrate the importance of yet another feedback effect of a desert on itself, that is produced by the reduction in surface roughness height of land once the vegetation dies and desert forms. Apart from affecting the moisture convergence, low bulk transport coefficients of a desert lead to enhanced longwave cooling and sinking which together reduce precipitation by Charney's (1975) mechanism. Thus, this effect, together with albedo and soil moisture influence, perpetuate a desert condition through its geophysical feedback effect. The study further suggests that man made deserts is a viable hypothesis.
Aghaei Jouybari, Mostafa; Yuan, Junlin
2017-11-01
Direct numerical simulations of turbulent channel flows are carried out over two surfaces: a synthesized sand-grain surface and a realistic turbine roughness that is characterized by more prominent large-scale surface features. To separate the effects of wall-normal variation of the roughness area fraction from the (true) variation of flow statistics, the governing equations are area-averaged using intrinsic averaging, contrary to the usually practice based on the total area (i.e., superficial averaging). Additional terms appear in the mean-momentum equation resulted from the wall-normal variation of the solid fraction and play a role in the near-wall balance. Results from surfaces with a step solidity function (e.g., cubes) will also be discussed. Compared to the sand grains, the turbine surface generates stronger form-induced fluctuations, despite weaker dispersive shear stress. This is associated with more significant form-induced productions (comparable to shear production) in Reynolds stress budgets, weaker pressure work, and, consequently, more anisotropic redistribution of turbulent kinetic energy in the roughness sublayer, which potentially leads to different turbulent responses between the two surfaces in non-equilibrium flows.
International Nuclear Information System (INIS)
Chandran, Benjamin D. G.; Hollweg, Joseph V.
2009-01-01
We study the propagation, reflection, and turbulent dissipation of Alfven waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al., we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy and assume that there is much more energy in waves propagating away from the Sun than waves propagating toward the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al. by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfven critical point-that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfven-wave reflection and turbulent heating into fluid models of the solar wind.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces
International Nuclear Information System (INIS)
Jun, Ma; Li-Xin, Guo; An-Qi, Wang
2009-01-01
This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed. (classical areas of phenomenology)
Energy Technology Data Exchange (ETDEWEB)
Pielke, R
1976-01-01
The author firstly explains in a general manner the functioning of the heat pump. Following a brief look at the future heat demand and the possibilities of covering it, the various methods of obtaining energy (making use of solar energy, ground heat, and others) and the practical applications (office heating, swimming pool heating etc.) are explained. The author still sees considerable difficulties in using the heat pump at present on a large scale. Firstly there is not enough maintenance personnel available, secondly the electricity supply undertakings cannot provide the necessary electricity on a wide basis without considerable investments. Other possibilities to save energy or to use waste energy are at present easier and more economical to realize. Recuperative and regenerative systems are described.
Transport equation and shock waves
International Nuclear Information System (INIS)
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
A continuum-atomistic simulation of heat transfer in micro- and nano-flows
International Nuclear Information System (INIS)
Liu Jin; Chen Shiyi; Nie Xiaobo; Robbins, Mark O.
2007-01-01
We develop a hybrid atomistic-continuum scheme for simulating micro- and nano-flows with heat transfer. The approach is based on spatial 'domain decomposition' in which molecular dynamics (MD) is used in regions where atomistic details are important, while classical continuum fluid dynamics is used in the remaining regions. The two descriptions are matched in a coupling region where we ensure continuity of mass, momentum, energy and their fluxes. The scheme for including the energy equation is implemented in 1-D and 2-D, and used to study steady and unsteady heat transfer in channel flows with and without nano roughness. Good agreement between hybrid results and analytical or pure MD results is found, demonstrating the accuracy of this multiscale method and its potential applications in thermal engineering
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Hall, Eric Joseph; Hoel, Hå kon; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul
2016-01-01
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
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Urban Aerodynamic Roughness Length Mapping Using Multitemporal SAR Data
Directory of Open Access Journals (Sweden)
Fengli Zhang
2017-01-01
Full Text Available Aerodynamic roughness is very important to urban meteorological and climate studies. Radar remote sensing is considered to be an effective means for aerodynamic roughness retrieval because radar backscattering is sensitive to the surface roughness and geometric structure of a given target. In this paper, a methodology for aerodynamic roughness length estimation using SAR data in urban areas is introduced. The scale and orientation characteristics of backscattering of various targets in urban areas were firstly extracted and analyzed, which showed great potential of SAR data for urban roughness elements characterization. Then the ground truth aerodynamic roughness was calculated from wind gradient data acquired by the meteorological tower using fitting and iterative method. And then the optimal dimension of the upwind sector for the aerodynamic roughness calculation was determined through a correlation analysis between backscattering extracted from SAR data at various upwind sector areas and the aerodynamic roughness calculated from the meteorological tower data. Finally a quantitative relationship was set up to retrieve the aerodynamic roughness length from SAR data. Experiments based on ALOS PALSAR and COSMO-SkyMed data from 2006 to 2011 prove that the proposed methodology can provide accurate roughness length estimations for the spatial and temporal analysis of urban surface.
Roughness coefficient and its uncertainty in gravel-bed river
Directory of Open Access Journals (Sweden)
Ji-Sung Kim
2010-06-01
Full Text Available Manning's roughness coefficient was estimated for a gravel-bed river reach using field measurements of water level and discharge, and the applicability of various methods used for estimation of the roughness coefficient was evaluated. Results show that the roughness coefficient tends to decrease with increasing discharge and water depth, and over a certain range it appears to remain constant. Comparison of roughness coefficients calculated by field measurement data with those estimated by other methods shows that, although the field-measured values provide approximate roughness coefficients for relatively large discharge, there seems to be rather high uncertainty due to the difference in resultant values. For this reason, uncertainty related to the roughness coefficient was analyzed in terms of change in computed variables. On average, a 20% increase of the roughness coefficient causes a 7% increase in the water depth and an 8% decrease in velocity, but there may be about a 15% increase in the water depth and an equivalent decrease in velocity for certain cross-sections in the study reach. Finally, the validity of estimated roughness coefficient based on field measurements was examined. A 10% error in discharge measurement may lead to more than 10% uncertainty in roughness coefficient estimation, but corresponding uncertainty in computed water depth and velocity is reduced to approximately 5%. Conversely, the necessity for roughness coefficient estimation by field measurement is confirmed.
Roughness modification of surfaces treated by a pulsed dielectric barrier discharge
Dumitrascu, N; Apetroaei, N; Popa, G
2002-01-01
Local modifications of surface roughness are very important in many applications, as this surface property is able to generate new mechano-physical characteristics of a large category of materials. Roughness is one of the most important parameters used to characterize and control the surface morphology, and techniques that allow modifying and controlling the surface roughness present increasing interest. In this respect we propose the dielectric barrier discharge (DBD) as a simple and low cost method that can be used to induce controlled roughness on various surfaces in the nanoscale range. DBD is produced in helium, at atmospheric pressure, by a pulsed high voltage, 28 kV peak to peak, 13.5 kHz frequency and 40 W power. This type of discharge is a source of energy capable of modifying the physico-chemical properties of the surfaces without affecting their bulk properties. The discharge is characterized by means of electrical probes and, in order to analyse the heat transfer rate from the discharge to the tre...
Effects of Roof-Edge Roughness on Air Temperature and Pollutant Concentration in Urban Canyons
Aliabadi, Amir A.; Krayenhoff, E. Scott; Nazarian, Negin; Chew, Lup Wai; Armstrong, Peter R.; Afshari, Afshin; Norford, Leslie K.
2017-08-01
The influence of roof-edge roughness elements on airflow, heat transfer, and street-level pollutant transport inside and above a two-dimensional urban canyon is analyzed using an urban energy balance model coupled to a large-eddy simulation model. Simulations are performed for cold (early morning) and hot (mid afternoon) periods during the hottest month of the year (August) for the climate of Abu Dhabi, United Arab Emirates. The analysis suggests that early in the morning, and when the tallest roughness elements are implemented, the temperature above the street level increases on average by 0.5 K, while the pollutant concentration decreases by 2% of the street-level concentration. For the same conditions in mid afternoon, the temperature decreases conservatively by 1 K, while the pollutant concentration increases by 7% of the street-level concentration. As a passive or active architectural solution, the roof roughness element shows promise for improving thermal comfort and air quality in the canyon for specific times, but this should be further verified experimentally. The results also warrant a closer look at the effects of mid-range roughness elements in the urban morphology on atmospheric dynamics so as to improve parametrizations in mesoscale modelling.
Intuitive Understanding of Solutions of Partially Differential Equations
Kobayashi, Y.
2008-01-01
This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…
Convective heat transfer of supercritical CO_2 in a rock fracture for enhanced geothermal systems
International Nuclear Information System (INIS)
Zhang, Le; Jiang, Peixue; Wang, Zhenchuan; Xu, Ruina
2017-01-01
Highlights: • Contrasting experiments between a rough and a smooth fracture were performed. • A numerical model of rough fracture was reconstructed based on CT scanning data. • Heat transfer in rough fracture was affected by channeling and disturbance effects. - Abstract: Convective heat transfer characteristics of supercritical pressure fluid in a rock fracture are important for building an accurate heat transfer model of enhanced geothermal systems. This paper presents experimental investigations of laminar convection heat transfer of supercritical pressure CO_2 in an artificial smooth parallel-plate fracture and a rough and tortuous fracture that was created using the Brazilian technique. Hot rock with a relatively high initial temperature reserves more heat, which can ensure a larger heat extraction rate for a longer time when cold fluid flows through the fracture. Compared with the smooth parallel-plate fracture, CO_2 flowing through the rough and tortuous fracture with an equivalent hydraulic aperture extracted less heat from the hot rock due to the less efficient heat exchange in a rough fracture caused by channeling effect. This was illustrated by numerical simulation results of the reconstructed fracture based on micro-computed tomography scan data. The overall Nusselt number obtained from the numerical results was larger in a rough fracture with a larger Reynolds number due to disturbance effect on the boundary layer development. The heat transfer performance in a rough fracture is therefore influenced by interactions of the channeling and disturbance effects caused by the tortuous flow path.
On Shear Stress Distributions for Flow in Smooth or Partially Rough Annuli
Energy Technology Data Exchange (ETDEWEB)
Kjellstroem, B; Hedberg, S
1966-08-15
It is commonly assumed that for turbulent flow in annuli the radii of zero shear and maximum velocity are coincident. By inspection of the differential equations for such flow and by an integral analysis it is shown that this is not necessarily true. To check whether important differences could occur, experiments were made in which velocity and shear stress distributions were measured in one smooth and two partially rough annuli. The results show no difference in the radii for the smooth annulus, but for the partially rough annuli there was a small but significant difference. This difference explains the breakdown of Hall's transformation theory reported by other investigators. The error introduced by use of Hall's theory is however small, of the order of 10 % or less.
On Shear Stress Distributions for Flow in Smooth or Partially Rough Annuli
International Nuclear Information System (INIS)
Kjellstroem, B.; Hedberg, S.
1966-08-01
It is commonly assumed that for turbulent flow in annuli the radii of zero shear and maximum velocity are coincident. By inspection of the differential equations for such flow and by an integral analysis it is shown that this is not necessarily true. To check whether important differences could occur, experiments were made in which velocity and shear stress distributions were measured in one smooth and two partially rough annuli. The results show no difference in the radii for the smooth annulus, but for the partially rough annuli there was a small but significant difference. This difference explains the breakdown of Hall's transformation theory reported by other investigators. The error introduced by use of Hall's theory is however small, of the order of 10 % or less
The log mean heat transfer rate method of heat exchanger considering the influence of heat radiation
International Nuclear Information System (INIS)
Wong, K.-L.; Ke, M.-T.; Ku, S.-S.
2009-01-01
The log mean temperature difference (LMTD) method is conventionally used to calculate the total heat transfer rate of heat exchangers. Because the heat radiation equation contains the 4th order exponential of temperature which is very complicate in calculations, thus LMTD method neglects the influence of heat radiation. From the recent investigation of a circular duct in some practical situations, it is found that even in the situation of the temperature difference between outer duct surface and surrounding is low to 1 deg. C, the heat radiation effect can not be ignored in the situations of lower ambient convective heat coefficient and greater surface emissivities. In this investigation, the log mean heat transfer rate (LMHTR) method which considering the influence of heat radiation, is developed to calculate the total heat transfer rate of heat exchangers.
Transient turbulent heat transfer for heating of water in a short vertical tube
International Nuclear Information System (INIS)
Hata, Koichi; Kai, Naoto; Shirai, Yasuyuki; Masuzaki, Suguru
2011-01-01
The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (T in =296.93 to 304.81 K), the inlet pressures (P in =794.39 to 858.27 kPa) and the increasing heat inputs (Q 0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (L eff =56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (L eff /d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 μm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors' correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (L eff /d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors' studies for the
Transient turbulent heat transfer for heating of water in a short vertical tube
International Nuclear Information System (INIS)
Hata, Koichi; Kai, Naoto; Shirai, Yasuyuki; Masuzaki, Suguru
2011-01-01
The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (T in =296.93 to 304.81 K), the inlet pressures (P in =794.39 to 858.27 kPa) and the increasing heat inputs (Q 0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (L eff =56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (L eff /d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 μm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors' correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (L eff /d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors' studies for the
International Nuclear Information System (INIS)
Halfa, I.K.I
2008-01-01
.6 we have used the VPRS method to make a comparison between the estimated and the observed data. In chapter 4, we used topological space to generalize the approximation of variable precision rough set model, and solved the advection diffusion equation numerically and analytically to estimate the concentration of pollution and compared the estimated concentrations with the observed.In section 4.1 we have showed a general introduction about topology and solution of advection-diffusion equation to conclude the concentration of air pollutants. In section 4.2 we have introduced generalization of approximation of variable precision rough sets model (GVPRS-model). The GVPRS-model properties are proposed and many examples are discussed. Estimation of the concentration of atmospheric pollution is calculated numerically and analytically in section 4.3. Both analytical and numerical solutions are compared with observed data using GVPRS in section 4.4
Multi-scale analysis of the roughness effect on lubricated rough contact
DEMIRCI, Ibrahim
2014-01-01
Determining friction is as equally essential as determining the film thickness in the lubricated contact, and is an important research subject. Indeed, reduction of friction in the automotive industry is important for both the minimization of fuel consumption as well as the decrease in the emissions of greenhouse gases. However, the progress in friction reduction has been limited by the difficulty in understanding the mechanism of roughness effects on friction. It was observed that micro-surf...
Rough surface mitigates electron and gas emission
International Nuclear Information System (INIS)
Molvik, A.
2004-01-01
Heavy-ion beams impinging on surfaces near grazing incidence (to simulate the loss of halo ions) generate copious amounts of electrons and gas that can degrade the beam. We measured emission coefficients of η e (le) 130 and η 0 ∼ 10 4 respectively, with 1 MeV K + incident on stainless steel. Electron emission scales as η e ∝ 1/cos(θ), where θ is the ion angle of incidence relative to normal. If we were to roughen a surface by blasting it with glass beads, then ions that were near grazing incidence (90 o ) on smooth surface would strike the rims of the micro-craters at angles closer to normal incidence. This should reduce the electron emission: the factor of 10 reduction, Fig. 1(a), implies an average angle of incidence of 62 o . Gas desorption varies more slowly with θ (Fig. 1(b)) decreasing a factor of ∼2, and along with the electron emission is independent of the angle of incidence on a rough surface. In a quadrupole magnet, electrons emitted by lost primary ions are trapped near the wall by the magnetic field, but grazing incidence ions can backscatter and strike the wall a second time at an azimuth where magnetic field lines intercept the beam. Then, electrons can exist throughout the beam (see the simulations of Cohen, HIF News 1-2/04). The SRIM (TRIM) Monte Carlo code predicts that 60-70% of 1 MeV K + ions backscatter when incident at 88-89 o from normal on a smooth surface. The scattered ions are mostly within ∼10 o of the initial direction but a few scatter by up to 90 o . Ion scattering decreases rapidly away from grazing incidence, Fig. 1(c ). At 62 deg. the predicted ion backscattering (from a rough surface) is 3%, down a factor of 20 from the peak, which should significantly reduce electrons in the beam from lost halo ions. These results are published in Phys. Rev. ST - Accelerators and Beams
Diffusion phenomenon for linear dissipative wave equations
Said-Houari, Belkacem
2012-01-01
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.
Influence of edge roughness on graphene nanoribbon resonant tunnelling diodes
International Nuclear Information System (INIS)
Liang Gengchiau; Khalid, Sharjeel Bin; Lam, Kai-Tak
2010-01-01
The edge roughness effects of graphene nanoribbons on their application in resonant tunnelling diodes with different geometrical shapes (S, H and W) were investigated. Sixty samples for each 5%, 10% and 15% edge roughness conditions of these differently shaped graphene nanoribbon resonant tunnelling diodes were randomly generated and studied. Firstly, it was observed that edge roughness in the barrier regions decreases the effective barrier height and thickness, which increases the broadening of the quantized states in the quantum well due to the enhanced penetration of the wave-function tail from the electrodes. Secondly, edge roughness increases the effective width of the quantum well and causes the lowering of the quantized states. Furthermore, the shape effects on carrier transport are modified by edge roughness due to different interfacial scattering. Finally, with the effects mentioned above, edge roughness has a considerable impact on the device performance in terms of varying the peak-current positions and degrading the peak-to-valley current ratio.
A new fiber optic sensor for inner surface roughness measurement
Xu, Xiaomei; Liu, Shoubin; Hu, Hong
2009-11-01
In order to measure inner surface roughness of small holes nondestructively, a new fiber optic sensor is researched and developed. Firstly, a new model for surface roughness measurement is proposed, which is based on intensity-modulated fiber optic sensors and scattering modeling of rough surfaces. Secondly, a fiber optical measurement system is designed and set up. Under the help of new techniques, the fiber optic sensor can be miniaturized. Furthermore, the use of micro prism makes the light turn 90 degree, so the inner side surface roughness of small holes can be measured. Thirdly, the fiber optic sensor is gauged by standard surface roughness specimens, and a series of measurement experiments have been done. The measurement results are compared with those obtained by TR220 Surface Roughness Instrument and Form Talysurf Laser 635, and validity of the developed fiber optic sensor is verified. Finally, precision and influence factors of the fiber optic sensor are analyzed.
Numerical simulations of seepage flow in rough single rock fractures
Directory of Open Access Journals (Sweden)
Qingang Zhang
2015-09-01
Full Text Available To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures, a set of single fracture physical models were produced using the Weierstrass–Mandelbrot functions to test the seepage flow performance. Six single fractures, with various surface roughnesses characterized by fractal dimensions, were built using COMSOL multiphysics software. The fluid flow behavior through the rough fractures and the influences of the rough surfaces on the fluid flow behavior was then monitored. The numerical simulation indicates that there is a linear relationship between the average flow velocity over the entire flow path and the fractal dimension of the rough surface. It is shown that there is good a agreement between the numerical results and the experimental data in terms of the properties of the fluid flowing through the rough single rock fractures.
Effect of truncated cone roughness element density on hydrodynamic drag
Womack, Kristofer; Schultz, Michael; Meneveau, Charles
2017-11-01
An experimental study was conducted on rough-wall, turbulent boundary layer flow with roughness elements whose idealized shape model barnacles that cause hydrodynamic drag in many applications. Varying planform densities of truncated cone roughness elements were investigated. Element densities studied ranged from 10% to 79%. Detailed turbulent boundary layer velocity statistics were recorded with a two-component LDV system on a three-axis traverse. Hydrodynamic roughness length (z0) and skin-friction coefficient (Cf) were determined and compared with the estimates from existing roughness element drag prediction models including Macdonald et al. (1998) and other recent models. The roughness elements used in this work model idealized barnacles, so implications of this data set for ship powering are considered. This research was supported by the Office of Naval Research and by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Irregular wall roughness in turbulent Taylor-Couette flow
Berghout, Pieter; Zhu, Xiaojue; Verzicco, Roberto; Lohse, Detlef; Stevens, Richard
2017-11-01
Many wall bounded flows in nature, engineering and transport are affected by surface roughness. Often, this has adverse effects, e.g. drag increase leading to higher energy costs. A major difficulty is the infinite number of roughness geometries, which makes it impossible to systematically investigate all possibilities. Here we present Direct Numerical Simulations (DNS) of turbulent Taylor-Couette flow. We focus on the transitionally rough regime, in which both viscous and pressure forces contribute to the total wall stress. We investigate the effect of the mean roughness height and the effective slope on the roughness function, ΔU+ . Also, we present simulations of varying Ta (Re) numbers for a constant mean roughness height (kmean+). Alongside, we show the behavior of the large scale structures (e.g. plume ejection, Taylor rolls) and flow structures in the vicinity of the wall.
Bai, H. L.; Kevin, Hutchins, N.; Monty, J. P.
2018-05-01
Turbulence modifications over a rough wall with spanwise-varying roughness are investigated at a moderate Reynolds number Reτ ≈ 2000 (or Reθ ≈ 6400), using particle image velocimetry (PIV) and hotwire anemometry. The rough wall is comprised of spanwise-alternating longitudinal sandpaper strips of two different roughness heights. The ratio of high- and low-roughness heights is 8, and the ratio of high- and low-roughness strip width is 0.5. PIV measurements are conducted in a wall-parallel plane located in the logarithmic region, while hotwire measurements are made throughout the entire boundary layer in a cross-stream plane. In a time-average sense, large-scale counter-rotating roll-modes are observed in the cross-stream plane over the rough wall, with downwash and upwash common-flows displayed over the high- and low-roughness strips, respectively. Meanwhile, elevated and reduced streamwise velocities occur over the high- and low-roughness strips, respectively. Significant modifications in the distributions of mean vorticities and Reynolds stresses are observed, exhibiting features of spatial preference. Furthermore, spatial correlations and conditional average analyses are performed to examine the alterations of turbulence structures over the rough wall, revealing that the time-invariant structures observed are resultant from the time-average process of instantaneous turbulent events that occur mostly and preferentially in space.
Heat pipe heat storage performance
Energy Technology Data Exchange (ETDEWEB)
Caruso, A; Pasquetti, R [Univ. de Provence, Marseille (FR). Inst. Universitaire des Systemes; Grakovich, L P; Vasiliev, L L [A.V. Luikov Heat and Mass Transfer Inst. of the BSSR, Academy of Sciences, Minsk (BY)
1989-01-01
Heat storage offers essential thermal energy saving for heating. A ground heat store equipped with heat pipes connecting it with a heat source and to the user is considered in this paper. It has been shown that such a heat exchanging system along with a batch energy source meets, to a considerable extent, house heating requirements. (author).
Heat Flux Inhibition by Whistlers: Experimental Confirmation
International Nuclear Information System (INIS)
Eichler, D.
2002-01-01
Heat flux in weakly magnetized collisionless plasma is, according to theoretical predictions, limited by whistler turbulence that is generated by heat flux instabilities near threshold. Observations of solar wind electrons by Gary and coworkers appear to confirm the limit on heat flux as being roughly the product of the magnetic energy density and the electron thermal velocity, in agreement with prediction (Pistinner and Eichler 1998)
Incorporating Skew into RMS Surface Roughness Probability Distribution
Stahl, Mark T.; Stahl, H. Philip.
2013-01-01
The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.
Investigation of surface roughness influence on hyperbolic metamaterial performance
Directory of Open Access Journals (Sweden)
S. Kozik
2014-12-01
Full Text Available The main goal of this work was to introduce simple model of surface roughness which does not involve objects with complicated shapes and could help to reduce computational costs. We described and proved numerically that the influence of surface roughness at the interfaces in metal-dielectric composite materials could be described by proper selection of refractive index of dielectric layers. Our calculations show that this model works for roughness with RMS value about 1 nm and below.
Directory of Open Access Journals (Sweden)
Anil Singh Yadav
2013-01-01
Full Text Available Solar air heater is a type of heat exchanger which transforms solar radiation into heat energy. The thermal performance of conventional solar air heater has been found to be poor because of the low convective heat transfer coefficient from the absorber plate to the air. Use of artificial roughness on a surface is an effective technique to enhance the rate of heat transfer. A CFD-based investigation of turbulent flow through a solar air heater roughened with square-sectioned transverse rib roughness has been performed. Three different values of rib-pitch (P and rib-height (e have been taken such that the relative roughness pitch (P/e=14.29 remains constant. The relative roughness height, e/D, varies from 0.021 to 0.06, and the Reynolds number, Re, varies from 3800 to 18,000. The results predicted by CFD show that the average heat transfer, average flow friction, and thermohydraulic performance parameter are strongly dependent on the relative roughness height. A maximum value of thermohydraulic performance parameter has been found to be 1.8 for the range of parameters investigated. Comparisons with previously published work have been performed and found to be in excellent agreement.
Yadav, Anil Singh; Bhagoria, J L
2013-01-01
Solar air heater is a type of heat exchanger which transforms solar radiation into heat energy. The thermal performance of conventional solar air heater has been found to be poor because of the low convective heat transfer coefficient from the absorber plate to the air. Use of artificial roughness on a surface is an effective technique to enhance the rate of heat transfer. A CFD-based investigation of turbulent flow through a solar air heater roughened with square-sectioned transverse rib roughness has been performed. Three different values of rib-pitch (P) and rib-height (e) have been taken such that the relative roughness pitch (P/e = 14.29) remains constant. The relative roughness height, e/D, varies from 0.021 to 0.06, and the Reynolds number, Re, varies from 3800 to 18,000. The results predicted by CFD show that the average heat transfer, average flow friction, and thermohydraulic performance parameter are strongly dependent on the relative roughness height. A maximum value of thermohydraulic performance parameter has been found to be 1.8 for the range of parameters investigated. Comparisons with previously published work have been performed and found to be in excellent agreement.
Constraining the roughness degree of slip heterogeneity
Causse, Mathieu
2010-05-07
This article investigates different approaches for assessing the degree of roughness of the slip distribution of future earthquakes. First, we analyze a database of slip images extracted from a suite of 152 finite-source rupture models from 80 events (Mw = 4.1–8.9). This results in an empirical model defining the distribution of the slip spectrum corner wave numbers (kc) as a function of moment magnitude. To reduce the “epistemic” uncertainty, we select a single slip model per event and screen out poorly resolved models. The number of remaining models (30) is thus rather small. In addition, the robustness of the empirical model rests on a reliable estimation of kc by kinematic inversion methods. We address this issue by performing tests on synthetic data with a frequency domain inversion method. These tests reveal that due to smoothing constraints used to stabilize the inversion process, kc tends to be underestimated. We then develop an alternative approach: (1) we establish a proportionality relationship between kc and the peak ground acceleration (PGA), using a k−2 kinematic source model, and (2) we analyze the PGA distribution, which is believed to be better constrained than slip images. These two methods reveal that kc follows a lognormal distribution, with similar standard deviations for both methods.
Spectrophotometric Examination of Rough Print Surfaces
Directory of Open Access Journals (Sweden)
Erzsébet Novotny
2011-05-01
Full Text Available The objective was to assess the impact of the surface texture of individual creative paper types (coated or patternedon the quality of printing and to identify to what extent the various creative paper types require specific types ofspectrophotometers. We used stereomicroscopic images to illustrate unprinted and printed surfaces of creative papertypes. Surface roughness was measured to obtain data on the unevenness of surfaces. Spectrophotometric tests wereused to select the most suitable spectrophotometer from meters with different illumination setup for testing anygiven print. For the purpose of testing, we used spectrophotometers which are commonly available generally used totest print products for colour accuracy. With the improvement of measuring geometries, illumination setup, colourmeasurement becomes more and more capable of producing reliable results unaffected by surface textures. Our testshave proved this fact by showing that the GretagMacbeth Spectrolino with annular illumination is less sensitive tosurface texture than the X-Rite Spetrodensitometer and the Techkon SpetroDens with directional illumination. Furthertests have brought us to the conclusion that there is a difference even between the two devices with directionalillumination. While the X-Rite 530 Spectrodensitometer is more suitable for testing coated surfaces, the TechkonSpectroDens can come close to ΔE*ab values produced by the annular illuminated device for textured surfaces.
Radiosensitivity of the rough-skinned newt
International Nuclear Information System (INIS)
Willis, D.L.; Lappenbusch, W.L.
1974-01-01
Newts were collected locally and maintained unfed at 10 0 C both before and after irradiation. Whole-body exposures ranging up to 80 kR were given with 250 kVp x rays, 300 kVp x rays, and 60 Co gamma rays. The mean survival time-exposure curve was sigmoid, following the typical appearance of such curves for mammalian species. A dose-independent region extending from roughly 700 to 5,000 R was evident. A variety of skin lesions and depigmentation effects were noted at exposures above 250 R, whose time of appearance decreased with increasing dose. A total of 832 newts were used in this phase of the study. Assuming that hematopoietic damage was primarily responsible for deaths below 700-800 R, additional studies of hematopoiesis were initiated. The effect of a 650 R-exposure on liver weight, spleen weight and concentration of circulating red blood cells for 1 1 / 2 months post-irradiation was assessed. The results indicate a progressive state of anemia. This was further substantiated by a study of 59 Fe incorporation by red blood cells at intervals up to one month for five exposures ranging up to 1000 R. (U.S.)