Journal of Generalized Lie Theory and Applications

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

IF Barna and R Kersner

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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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 10, Number S2 (2016), 4 pages.

Dates
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1479265229

Digital Object Identifier
doi:10.4172/1736-4337.1000S2-010

Mathematical Reviews number (MathSciNet)
MR3663979

Zentralblatt MATH identifier
1373.35309

Keywords
Self-similar solution Non-linear heat conduction Shock wave Cattaneo heat conduction law

Citation

Barna, IF; Kersner, R. Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium. J. Gen. Lie Theory Appl. 10 (2016), no. S2, 4 pages. doi:10.4172/1736-4337.1000S2-010. https://projecteuclid.org/euclid.jglta/1479265229


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