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

Authors :: Barna, Imre Ferenc
Kersner, Robert
Source :: Journal of Generalized Lie Theory and Applications (special issue, Recent Advances of Lie Theory in differential Geometry, in memory of John Nash) 10, S2-10," (2016)
Publication Year :: 2012
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.<br />Comment: 5 pages, 2 figures, the manuscript is submitted to Eur. Phys. Letters

Database :: arXiv
Journal :: Journal of Generalized Lie Theory and Applications (special issue, Recent Advances of Lie Theory in differential Geometry, in memory of John Nash) 10, S2-10," (2016)
Publication Type :: Report
Accession number :: edsarx.1204.4386
Document Type :: Working Paper
Full Text :: https://doi.org/10.4172/1736-4337.S2-010