జర్నల్ ఆఫ్ జెనరలైజ్డ్ లై థియరీ అండ్ అప్లికేషన్స్

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

Abstract

Barna IF and Kersner R

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.