Analysis of Confined Magnetohydrodynamic Vortex Flows

Abstract

The vortex flow of a viscous, incompressible, and electrically conducting fluid confined between two finite flat plates (with a net radial mass flow) in the presence of an applied axial magnetic field is considered. The details of the velocity field including boundary‐layer thickness and redistribution of radial mass flow are of primary concern. The analysis is limited to the case of the separation distance between the two end plates being small compared with the radius of the plates; this allows the momentum equations to be uncoupled from the electromagnetic equations. The momentum equations are linearized and solved for the velocities and the pressure as Fourier series. It is found that magnetic effects tend to decrease the boundary‐layer thickness by a small percentage and tend to decrease substantially the mass flow drawn into the boundary layers.