Relaxation heat conduction and generation: an analysis of the semi-infinite body case by method of Laplace transforms

Abstract

The relaxation equation of heat conduction and generation is solved by method of Laplace transforms for the case of a semi-infinite body and an arbitrary dependence of the surface temperature on time. For the case of equality of the relaxation time of the heat flux ( τ k ) and the relaxation time of the internal heat source capacity ( τ g ) the Laplace domain solution is inverted analytically, otherwise numerically. Exemplary calculations are carried out for the surface temperature function in the form of a rectangular pulse. The results show that significant differences can occur between the relaxation and parabolic models, in qualitative as well as quantitative terms, which do not disappear for large times. A long-time relaxation solution for τ g = 0 tends to overlap with the corresponding parabolic solution of a case with heat generation, whilst a long-time relaxation solution for τ g = ∞ tends to overlap with the corresponding parabolic solution of a case without heat generation.