Unsteady Flow of a Viscous Electrically Conductive Fluid between Rotating Parallel Walls with Blowing (Suction) of the Medium and a Magnetic Field

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.