The relaxation equation of heat conduction and generation permits the
relaxation of heat flux (a finite speed of heat propagation) as well as
the relaxation of heat source capacity. The parabolic and hyperbolic
heat conduction equations can be treated as special cases of the relaxation
equation. A one-dimensional case of the relaxation equation, in which the
relaxation of heat flux is neglected, is solved analytically by the Laplace
transforms method to investigate the effect of the inertia of the heat source
on the temperature field. The results of sample calculations show that as
the relaxation time of heat source capacity increases from zero to infinity
the temperature profile for a given time moves from the parabolic solution
with heat generation towards the parabolic solution without heat generation.
It is also demonstrated that differences between relaxation solutions and the
related parabolic solutions do not vanish with time.