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

First available in Project Euclid: 16 November 2016

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


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.

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