Abstract

We consider the coupled processes of thermohydrodynamics and heat conduction and construct a variational model of such coupled problems using four-dimensional space-time continuum where time is an equal coordinate along with spatial coordinates. In this consideration 3D subspace of generalized four-dimensional pseudo-continuum is associated with three-dimension deformed media. In the general case we consider irreversible processes and use the variational principle of possible displacements and the variational Sedov’s principle to construct variation model. It is assumed that the 4D pseudo-continuum considered below is transversely isotropic in the direction of the unit vector of time. Thus, an asymmetric 4D stress tensor preserves the symmetry properties with respect to spatial tangential stresses in 3D subspaces. It is shown that the proposed version of the model allows us to formulate the full range of consistent thermomechanical and thermodynamic physical relations, and the system of governing equations includes, as special cases, the equations of thermoelasticity, thermohydrodynamics, the linear Navier–Stokes equations for compressible and incompressible media, the equations of heat balance with the laws of thermal conductivity of Fourier, Maxwell–Cattaneo.

中文翻译：

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热流体动力学和热导率耦合的线性方程的变分表示

摘要

我们考虑了热流体动力学和热传导的耦合过程，并使用四维时空连续体构造了此类耦合问题的变体模型，其中时间是与空间坐标相等的坐标。考虑到这一点，广义四维伪连续谱的3D子空间与三维变形媒体相关联。在一般情况下，我们考虑不可逆过程，并使用可能的位移的变分原理和变分的Sedov原理构造变分模型。假设下面考虑的4D伪连续谱在时间单位矢量的方向上是横向各向同性的。因此，非对称4D应力张量相对于3D子空间中的空间切向应力保持对称性。