Unsteady Motion of a Viscous Conducting Fluid between Rotating Parallel Walls in a Transverse Magnetic Field

Abstract

We study the motion of an incompressible viscous conducting fluid, which initially rotates as a solid at a constant angular velocity together with parallel bounding walls under the action of longitudinal vibrations of one of the walls beginning suddenly and a magnetic field suddenly applied to one of them. The walls make an arbitrary angle with the axis of rotation. The magnetic field is applied along the wall normal. In the general case, the solution is presented in the form of a series. The vectors of tangential stresses that act on the gap walls from the fluid are presented. Some particular cases of the wall motion are discussed. The results are used to study individual structures of the boundary layers at the walls. This study generalizes studies [1-3].