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SECOND SOUND AND SHOCK WAVES IN RIGID CRYSTALS: AN EXTENDED THERMODYNAMIC ANALYSIS

DOI: 10.1615/ICHMT.2008.CHT.220
15 pages

Georgy Lebon
Department of Astrophysics, Geophysics and Oceanography, 17 allée du 6 Août, Liège University, 4000 Liège, Belgium

Pierre C. Dauby
University of Liege, Thermodynamics of Irreversible Phenomena, Allee du 6-Aout, 17, 4000 Liege, Belgium

Th. Desaive
Department of Astrophysics, Geophysics and Oceanography, 17 allée du 6 Août, Liège University, 4000 Liège, Belgium

A. Valenti
Department of Mathematics and Informatics, 6 viale Doria, Catania University, 95125 Catania, Italy

Abstract

Second sound and shock waves propagation in rigid heat conductors are analyzed in the framework of Extended Irreversible Thermodynamics whose main feature is to upgrade the thermodynamic fluxes, as the heat flux, to the status of state variable. In comparison with earlier developments of this theory, two improvements are brought. First, the extra basic variable is no longer the heat flux but rather a renormalized expression, depending on the material properties of the body like the heat conductivity and the relaxation time of the heat flux. Second, in previous formulations of Extended Thermodynamics, the time evolution equation of the heat flux was generally described by the linear Cattaneo's relation. Our objective in the present work is to go beyond the linear regime and to propose a nonlinear evolution equation for the renormalized heat flux. Identification of all the phenomenological coefficients, at the exception of a single one, is obtained by examining the constraints placed by the second law of thermodynamics. The remaining undetermined coefficient is determined from an analysis of propagation of waves and shocks. As illustration, heat transport in NaF dielectric crystals at low temperature (<20 K) is studied.

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