A finite difference scheme for solving a three‐dimensional heat transport equation in a thin film with microscale thickness

Abstract

AbstractHeat 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 three‐dimensional heat transport equation. It is shown by the discrete energy method that the scheme is unconditionally stable. The three‐dimensional implicit scheme is then solved by using a preconditioned Richardson iteration, so that only a tridiagonal linear system is solved each iteration. Numerical results show that the solution is accurate. Copyright © 2001 John Wiley & Sons, Ltd.