Symmetric and asymmetric solutions of oscillatory MHD flow due to eccentrically rotating disks

Abstract

Exact solutions are obtained for the unsteady MHD now of a viscous, electrically conducting, homogeneous, incompressible fluid between two intinite parallel, insulated, porous disks rotating with angular velocity n about two non-coincident axes, The disk are subjected to non-torsional oscillations of different frequencies and a uniform magnetic field is applied normal to the disks. The symmetric or symmetric solutions contaming arbitrary constants  reduce to a single unique solution when one prescribed the pressure gradient. Necessary and sufficient conditions for a solution to be symmetric and asymmetric are obtained. In some special cases both the symmetric and asymmetric solutions for eccentrically rotating disks are evaluated numerically and discussed in detail.