Abstract

The motions of a viscous electrically conductive incompressible fluid, which initially rotates as a solid with a constant angular velocity together with the parallel walls bounding it, under the action of suddenly beginning longitudinal vibrations of one of the walls have been studied. The angle between the walls and the axis of rotation is arbitrary. An unsteady flow is induced by longitudinal vibrations of one of the walls, injection (suction) of the medium produced perpendicular to the surface of the porous plate, and a magnetic field suddenly switched on and directed normal to the wall. Analytical solutions of the equations of magnetohydrodynamics have been constructed. The velocity field and vectors of tangential stresses of a viscous conductive fluid that acts on the walls of the gap have been determined. The induced magnetic field in the flow of an electrically conductive fluid has been determined. Some particular cases of wall motion are considered. Based on the results, the individual structures of the boundary layers adjacent to the walls of the gap have been investigated.

中文翻译：

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介质（磁场）吹（吸）向旋转平行壁之间的粘性导电流体的非稳态流动

摘要

已经研究了粘性导电不可压缩流体的运动，该流体最初以恒定角速度作为固体旋转，并与限制它的平行壁一起在其中一个壁的突然开始的纵向振动的作用下旋转。壁和旋转轴之间的角度是任意的。由于其中一个壁的纵向振动，垂直于多孔板表面产生的介质的注入（抽吸）以及磁场突然打开并垂直于壁而产生不稳定的流动。构造了磁流体动力学方程的解析解。确定了作用在间隙壁上的粘性导电流体的速度场和切向应力矢量。已经确定了导电流体流动中的感应磁场。考虑墙壁运动的一些特殊情况。根据结果​​，研究了与间隙壁相邻的边界层的各个结构。