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.

中文翻译：

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具有松弛热通量的弹性材料的热力学

摘要-

为了获得热方程，使用了热力学的第一定律和第二定律以及它们的结果，这些定律是从在选择惯性参考系的意义上定律是独立的要求中获得的。为了编写热力学第二定律，使用了克劳修斯-杜海姆不等式。在本文中，从热力学定律推导了具有松弛热通量的弹性材料的热方程。对于在有限形变条件下工作的介质，制定了组成方程。结果表明，弹性材料中的柯西应力张量取决于热通量梯度。考虑了在热通量的弛豫时间非常短的材料中使用非线性热方程的近似形式。在这些过程中，松弛热通量迅速接近傅立叶定律确定的通量。我们考虑一种状态，其中温度梯度非常重要，并且在热传导方程中不能忽略热通量矢量的模平方。在这种情况下，建议使用取决于温度梯度的材料“非平衡热容”概念。