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 and the relaxation time of the internal
heat source capacity (tau_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
solutions for tau_g=0 tends to overlap with the corresponding parabolic
solution of a case with heat generation, whilst a long-time relaxation
solution for tau_g=infinity tends to overlap with the corresponding
parabolic solution of a case without heat generation.