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Variational Approach to 2D and 3D Heat Conduction Modeling
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作者 Slavko Đurić Ivan Aranđelović Milan Milotić 《Journal of Applied Mathematics and Physics》 2024年第4期1383-1400,共18页
The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximat... The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube. 展开更多
关键词 Classical Equation of heat conduction Generalized Equation of heat conduction Calculus of Variations Approximate Solution
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The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas
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作者 TIANChu-Shun LUQuan-Kang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第5期605-608,共4页
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrod... Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections. 展开更多
关键词 relativistic Landau collision integral relativistic correction of heat conductivity Coulomb electronic plasmas
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Preliminary Study to Show the Effect of Building Envelope Materials on Thermal Comfort of Buildings Located in Hot Humid Climate
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作者 Roa’a Mohammed Omar Shifana Fatima Kaafil Rehumaan 《World Journal of Engineering and Technology》 2022年第2期264-271,共8页
The main aim of this paper is to study the effect of building envelope constructed with different materials on thermal comfort of buildings located in Jeddah, Saudi Arabia. Four different buildings constructed with br... The main aim of this paper is to study the effect of building envelope constructed with different materials on thermal comfort of buildings located in Jeddah, Saudi Arabia. Four different buildings constructed with brick, glass, stone, and gypsum are taken into account to study the difference in temperature of the indoor and outdoor environments. Also, this paper explores the heat conducted by walls of different materials with different thicknesses. In addition, survey is conducted among the residents of Jeddah to know their perspective about thermal comfort of buildings. From the study, it is found that building envelope constructed with glass is more effective compared to envelope constructed with other materials of with least thickness of wall. Also, it is found that the envelope constructed with brick is more effective in absorbing the heat provided the thickness of the walls remains the same. 展开更多
关键词 Thermal Comfort Building Envelope conduction of heat BRICK GLASS
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NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS 被引量:5
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作者 袁益让 杨青 +1 位作者 李长峰 孙同军 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期259-279,共21页
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi... Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device. 展开更多
关键词 three dimensional transient behavior of heat conduction problem mixed finitevolume element modified upwind fractional step difference second-order error
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A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH
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作者 Yirang YUAN Changfeng LI Huailing SONG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1405-1428,共24页
The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differenti... The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application. 展开更多
关键词 three-dimensional semiconductor device of heat conduction block-centered upwind difference on a changing mesh local conservation of mass convergence analysis numerical computation
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Simulations of lunar equatorial regolith temperature profile based on measurements of Diviner on Lunar Reconnaissance Orbiter 被引量:1
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作者 RAN Zhen WANG ZhenZhan 《Science China Earth Sciences》 SCIE EI CAS 2014年第9期2232-2241,共10页
Lunar equatorial regolith temperature profiles were simulated using the half-limited solid heat conduction model. Based on the infrared data measured using the Diviner radiometer on the Lunar Reconnaissance Orbiter la... Lunar equatorial regolith temperature profiles were simulated using the half-limited solid heat conduction model. Based on the infrared data measured using the Diviner radiometer on the Lunar Reconnaissance Orbiter launched by the United Sates in June 2009, three factors influencing temperature profiles were analyzed. The infrared brightness temperature data from Diviner channel 7 were used to retrieve surface temperature. In simulating regolith temperature profiles, the retrieved temperature, rather than temperatures calculated from solar radiance at the lunar surface, were used as the input for surface temperature in solving the heat-conductive equation. The results showed that the bottom-layer temperature at depths of 6 m approached almost 246 K after 10000 iterations. The temperature was different to the temperature of 250 K at the same depth encountered in simulations using solar radiance. Simulations from both methods of surface temperatures over a lunar day gave similar variations. At lunar night, the temperature difference between the two was about 2 K; the main differences occurred when the solar elevation angle was very low when surface temperatures are largely affected by terrain topography. With no certainty in lunar temperature profiles at present, the advantage of the retrieval method using infrared sensor data as input to the boundary conditions in solving the lunar heat conduction equation is that simulations of surface temperature variations are more accurate. This is especially true in areas with large variations in terrain topography, where surface temperatures vary greatly because of shading from the sunlight. 展开更多
关键词 Diviner radiometer equation of heat conduction lunar temperature profile infrared brightness temperature
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