An unconditionally stable finite difference scheme for solving a 3D heat transport equation in a sub-microscale thin film

被引:28
|
作者
Dai, WZ [1 ]
Nassar, R [1 ]
机构
[1] Louisiana Tech Univ, Coll Engn & Sci, Ruston, LA 71272 USA
关键词
finite difference; stability; heat transport equation; thin film; microscale;
D O I
10.1016/S0377-0427(01)00579-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation since a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study, we develop a finite difference scheme with two levels in time for the 3D heat transport equation in a sub-microscale thin film. It is shown by the discrete energy method that the scheme is unconditionally stable. The 3D implicit scheme is then solved by using a preconditioned Richardson iteration, so that only a tridiagonal linear system is solved for each iteration. The numerical procedure is employed to obtain the temperature rise in a gold sub-microscale thin film. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
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页码:247 / 260
页数:14
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