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IssuesArchive of Issues2020-4pp.584-588

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L.A. Komar and A.L. Svistkov, "Thermodynamics of Elastic Material with Relaxing Heat Flux," Mech. Solids. 55 (4), 584-588 (2020)
Year 2020 Volume 55 Number 4 Pages 584-588
DOI 10.3103/S0025654420040056
Title Thermodynamics of Elastic Material with Relaxing Heat Flux
Author(s) L.A. Komar (Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Science, Perm, 614013 Russia, komar@icmm.ru)
A.L. Svistkov (Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Science, Perm, 614013 Russia, svistkov@icmm.ru)
Abstract To obtain the heat equation, the first and second laws of thermodynamics and the consequences from them, which are obtained from the requirement that the laws are independent in the sense of choosing the inertial reference frame, are used. To write the second law of thermodynamics, the Clausius-Duhem inequality has been used. In this article, the derivation of the heat equation from the laws of thermodynamics for elastic materials with a relaxing heat flux is carried out. The constituting equations are formulated for a medium operating under conditions of finite deformations. It is shown that the Cauchy stress tensor in an elastic material depends on the heat flux gradient. An approximate version of using the nonlinear heat equation in materials with a very short relaxation time of the heat flux is considered. These are processes in which the relaxing heat flux quickly becomes close to the flux determined by Fourier’s law. We consider a state, in which the temperature gradient is of great importance and the square of the modulus of the heat flux vector cannot be neglected in the heat conduction equation. In this case, it is advisable to talk about using the concept of "nonequilibrium heat capacity" of the material, which depends on the temperature gradient.
Keywords laws of thermodynamics, heat equation, relaxing heat flux, finite deformations
Received 31 January 2020Revised 03 March 2020Accepted 04 April 2020
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