A FINITE DIFFERENCE METHOD FOR SOLVING 3-D HEAT TRANSPORT EQUATIONS IN A DOUBLE-LAYERED THIN FILM WITH MICROSCALE THICKNESS AND NONLINEAR INTERFACIAL CONDITIONS

Abstract

We develop a finite difference method for solving 3-D heat transport equations in a double-layered thin film with microscale thickness and nonlinear interfacial conditions. The scheme is solved by using a preconditioned Richardson iteration, so that only two tridiagonal linear systems with nonlinear interfacial conditions are solved at each iteration. Applying a parallel Gaussian elimination coupled with Newton's iteration to solve these two linear systems with nonlinear interfacial conditions, we develop a domain decomposition algorithm for thermal analysis of the double-layered thin film. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained.