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arXiv · 1204.4386

Heat conduction: hyperbolic self-similar shock-waves in solids

Imre Ferenc Barna·Robert Kersner
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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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Imre Ferenc Barna, Robert Kersner. 2012-04-19. Heat conduction: hyperbolic self-similar shock-waves in solids. https://doi.org/10.4172/1736-4337.s2-010

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