A NUMERICAL SCHEME FOR NON-FOURIER HEAT CONDUCTION, PART II: TWO-DIMENSIONAL PROBLEM FORMULATION AND VERIFICATION

Abstract

A flux-splitting algorithm based on the Godunov numerical scheme developed for the solution of the one-dimensional non-Fourier heat conduction equation by Yeung and Lam [1] is extended for the investigation of thermal wave propagation in rectangular media. The derivation of the solution method and the stability criteria are presented in detail. Physical problems subjected to various boundary conditions (e.g., first, second, and third kinds) can be studied with the numerical scheme. A comparison of the exact solution with the one calculated by the proposed procedure is presented to confirm the validity of the numerical procedure. The numerical scheme is applicable for the study of short-pulse heating in advanced materials, microstructures, thin films, semiconductor devices, and superconductors.