FINITE DIFFERENCE METHOD FOR SIMULATING PHONON HEAT TRANSPORT PROCESS
Chen Jianling1,2, Feng Yangde1
1 Computer Network Information Center, Department of High Performance Computing Technology and Application Development, CAS, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract：
The Equation of Phonon Radiative Transfer is a differential-integral equation. The finite difference method is used to numerically solve the Equation of Phonon Radiative Transfer with boundary conditions. The Gauss-Seidel method and the finite difference discretization can be used to ensure stable numerical solutions. Through one-dimensional numerical simulation of the phonon heat transport process of Ge/Si/Ge film at room temperature and by using the diffuse mismatch interface model at the interface,it can evaluate the influence of the temperature along the normal direction of the film and the thickness ratio of the Ge/Si film and the temperature jump at the interface on the thermal conductivity of the overall structure of the material, and the change of the thermal conductivity of the film as the thickness of the film increases. The two-dimensional numerical simulation of the phonon heat transport process of the silicon film can obtain the temperature along the the normal and orientation-oriented distribution of the film, and the change in temperature and the thermal conductivity when the film width and thickness ratio are different.
. FINITE DIFFERENCE METHOD FOR SIMULATING PHONON HEAT TRANSPORT PROCESS[J]. Journal on Numerical Methods and Computer Applicat, 2019, 40(3): 215-229.
[1]
Majumdar A. Microscale Heat Conduction in Dielectric Thin Films[J]. Journal of Heat Transfer, 1993, 115(1):7-16.
[2]
韩亚芬. 纳米复合隔热材料导热机理与特性研究[D]. 哈尔滨工业大学, 2013:13-37.
[3]
Venkatasubramanian R. Chapter 4——Phonon Blocking Electron Transmitting Superlattice Structures as Advanced Thin Film Thermoelectric Materials[J]. Semiconductors & Semimetals, 2001, 71:175-201.
[4]
Chen G. Nanoscale energy transport and conversion[M]. Oxford University Press, 2005:348-366.
[5]
Miyazaki K, Arashi T, Makino D, et al. Heat conduction in micro-structured materials[J]. IEEE Transactions on Components & Packaging Technologies, 2006, 29(2):247-253.
[6]
Yilbas B S, Mansoor S B. Phonon Transport in Two-Dimensional Silicon-Diamond Film Pair[J]. Journal of Thermophysics & Heat Transfer, 2013, 27(3):465-473.
[7]
Haider Ali. Heat transport characteristics in thin films[D]. King Fand University of Petroleum & Minerals, 2014:74-199.
[8]
Chu A J H. Phonon transport in two-dimensional silicon thin film:influence of film width and boundary conditions on temperature distribution[J]. European Physical Journal B, 2012, 85(7):1-9.
[9]
R.Yang, et al. Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation[J]. Journal of Heat Transfer, 2005, 127(3):298-306.
M.Mohamadi, et al. Numerical Study of Thermal Conductivity Reduction in Nanolayered Si-Ge Structures by Solving the Equation of Phonon Radiative Transfer[J]. Journal of the Serbian Society for Computational Mechanics, 2017, 11(1):29-45.
