  Analytic solutions for cylindrical thermal waves in solid medium is given
based on the nonlinear hyperbolic system of heat flux relaxation and energy
conservation equations. The Fourier-Cattaneo phenomenological law is
generalized where the relaxation time and heat propagation coefficient have a
general power law temperature dependence. From such laws one cannot form a
second order parabolic or telegraph-type equation. We consider the original
non-linear hyperbolic system itself with the self-similar Ansatz for the
temperature distribution and for the heat flux. As results continuous and
shock-wave solutions are presented. For physical establishment numerous
materials with various temperature dependent heat conduction coefficients are
mentioned.
