RELAXATION EQUATION OF HEAT-CONDUCTION AND GENERATION - AN ANALYTICALSOLUTION BY LAPLACE TRANSFORMS METHOD

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