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.