Open Access
2016 Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium
IF Barna, R Kersner
J. Gen. Lie Theory Appl. 10(S2): 1-4 (2016). DOI: 10.4172/1736-4337.1000S2-010


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.


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IF Barna. R Kersner. "Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium." J. Gen. Lie Theory Appl. 10 (S2) 1 - 4, 2016.


Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1373.35309
MathSciNet: MR3663979
Digital Object Identifier: 10.4172/1736-4337.1000S2-010

Keywords: Cattaneo heat conduction law , Non-linear heat conduction , self-similar solution , shock wave

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. S2 • 2016
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