A note on the two temperature theory with dual-phase-lag delay: Some exact solutions

Abstract

In this note we present exact solutions of two initial-boundary value problems (IBVP)s in the setting of a recently-introduced theory of heat conduction, wherein the two temperature theory of the late 1960s is merged with Tzou’s dual-phase-lag flux relation. First, we solve a one-dimensional problem on a finite interval for a simple, parabolic initial condition. We then describe how to extend the analysis to the general three-dimensional case. In particular, it is demonstrated that the instability which generally arises in connection with the dual-phase-lag model can be avoided under this hybrid formulation.