内部张量变量和带有惯性、热粘性和涡度项的热传输方程

Liliana Restuccia, David Jou, Michal Pavelka
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引用次数: 0

摘要

考虑到前一篇论文在非平衡热力学内部变量(NET-IV)框架内获得的一些结果(其中推导出了热刚性导体中热流量的广义 Guyer-Krumhansl 演化方程),我们在本文中获得了描述声子传导、粘性和涡旋运动的热传输方程。为此,我们将内能、热通量和对称内变量作为自变量,其中对称部分和非对称部分与最终方程中的旋转项有关。除了通常声子流体力学中产生的剪切声子粘度之外,我们还提出了一种旋转声子粘度,它描述了从声子旋涡的有序旋转运动到构成复杂极性晶体的二原子粒子的旋转微观运动的转移,类似于经典微极性流体的流体力学。这种可能性强调了探索平均热流与某些声子流体力学模型中发现的热涡旋之间相互作用的意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Internal tensorial variables and a heat transport equation with inertial, thermal viscosity and vorticity terms
Taking into account some results obtained within the framework of non-equilibrium thermodynamics with internal variables (NET-IV) in a previous paper, where generalized Guyer-Krumhansl evolution equations for the heat flux in heat rigid conductors were derived, in this paper we obtain a heat transport equation describing conductive, viscous and vortical motions of phonons. To do so, we take as independent variables the internal energy, the heat flux, and a tensorial internal variable, with a symmetric part and an antisymmetric part, which turns out to be related to the rotational terms in the final equation. Besides the shear phonon viscosity arising in usual phonon hydrodynamics, we propose a rotational phonon viscosity, which would describe a transfer from ordered rotational motion of phonon vortices to rotational microscopic motions of diatomic particles constituting complex polar crystals, in analogy to the hydrodynamics of classical micropolar fluids. This possibility emphasizes the interest of exploring the interactions between the average heat flow and the heat vortices found in some models of phonon hydrodynamics.
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