Analytic
solutions for cylindrical thermal waves in solid medium are 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 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.
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