A relaxation model for heat conduction and generation is formulated and analysed which takes into account the relaxation of heat flux (the finite speed of heat flux propagation) and the relaxation of internal heat source capacity. The classical parabolic heat conduction equation and the hyperbolic equation of heat conduction can be treated as special cases of the newly formulated relaxation equation of heat conduction. A physical sense of the relaxation model for heat conduction and generation is discussed and its consistency with the second law based on classical and extended irreversible thermodynamics is examined. A number of initial and boundary value problems are solved analytically and numerically to ilustrate features of the new model. The results of exemplary calculations enabled to draw a number of general conclusions. Among other things it was ascertained that contrary to the solution of numerous hyperbolic cases, as a rule the relaxation solutions for long times do not tend to overlap the corresponding parabolic solutions.
This work is a review of seven original papers previously published by the author.