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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:145

Article

Dai, WZ ; Nassar, R

关键词: finite difference;    stability;    heat transport equation;    thin film;    microscale;   

DOI  :  10.1016/S0377-0427(01)00579-9

来源: Elsevier

【 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.

【 授权许可】

Free