alexa Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
Open Access

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Research Article

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

Barna IF1* and Kersner R2

1Wigner Research Center of the Hungarian Academy of Sciences, Konkoly Thege Miklós út 29-33, Budapest 1121, Hungary

2Department of Mathematics and Informatics, University of Pécs, PMMK, Boszorkány u. 2, Pécs, Hungary

*Corresponding Author:
Barna IF
Wigner Research Center of the Hungarian Academy of Sciences
Konkoly Thege Miklós út 29-33, Budapest, Hungary
Tel:
+36-1-392-2222/3504
Fax:
+36-1-392-2598
E-mail:
[email protected]

Received Date: February 29, 2016; Accepted Date: April 14, 2016; Published Date: May 03, 2016

Citation: Barna IF, Kersner R (2016) Heat Conduction: Hyperbolic Selfsimilar Shock-waves in Solid Medium. J Generalized Lie Theory Appl S2:010. doi:10.4172/1736-4337.S2-010

Copyright: © 2016 Barna IF, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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.

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