Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium

Abstract

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 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.