Magnetohydrodynamic flow due to non-coaxial rotations of a porous oscillating disk and a fluid at infinity

An exact solution of the Navier-Stokes equations is constructed for the case of flow due to non-coaxial rotations of a porous disk and a fluid at infinity. The disk executes oscillations in its own plane and is non-conducting. The viscous fluid is incompressible and electrically conducting. Analytical solution is established by the method of Laplace transform. The velocity fields are obtained for the cases when the angular velocity is greater than, smaller than or equal to the frequency of oscillations. The structure of the steady and the unsteady velocity fields are investigated. The difficulty of the hydrodynamic steady solution associated with the case of resonant frequency is resolved in the present analysis.