Green’s Function Solution of Dual-Phase-Lag Model

Abstract

In this study, the micro-scale heat conduction solution in a finite rigid slab computed with and without heat source is investigated. The analytical solution is derived by Laplace transform (LT) technique and Green’s function solution (GFS) method. The effect of heat source on the micro-scale heat conduction solution is also included in this paper. It is found that the temperature solution obtained by GFS method is smaller than that obtained by LT technique, and the GFS is in very good agreement with the solution obtained by the conventional Fourier’s law when τq = τT. Moreover, the temperature distributions computed by the LT technique are always overestimated in this study owing to the absence of the G2 effect. Hence, it is believed that the temperature solutions predicted by the GFS-LT method are more accurate than those evaluated by the LT technique. When time is increasing, the discrepancies of temperature solutions among various methods for τT > τq is increasing.