Abstract

The flow of a viscous conductive incompressible fluid in a time-varying region is investigated. Based on the model of a layered fluid flow, the class of exact solutions of the equations of magnetohydrodynamics in the region moving in time is considered. We study the change in the structure of the fluid flow as a result of the volume effect by the magnetic field and the movement of the boundary of the flow region. The heat dissipation effect due to internal friction and Joule heating is considered. The presented results are relevant to the research on optimizing problems of controlling the dynamics of an incompressible fluid and creating the “digital field” using the domestic technology.

中文翻译：

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随时间变化的区域中分层粘性导电流体流动的建模

摘要

研究了粘性导电不可压缩流体在随时间变化的区域中的流动。基于分层流体流动的模型，考虑了随时间变化的区域中的磁流体动力学方程的精确解的类别。我们研究由于磁场的体积效应和流动区域边界的运动而导致的流体流动结构的变化。考虑了由于内部摩擦和焦耳热引起的散热效果。所提出的结果与优化控制不可压缩流体动力学和利用国内技术创造“数字场”的问题有关。