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

Barna, Imre Ferenc and Kersner, Róbert (2016) Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium. JOURNAL OF GENERALIZED LIE THEORY AND APPLICATIONS, 10 (S2). ISSN 1736-5279

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Abstract

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.

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