Exact solution for the magnetohydrodynamic flows of an oldroyd-B fluid through a porous medium

Exact analytical solutions are obtained for the problem of unsteady flows of a magnetohydrodynamic Oldroyd-B fluid through a porous medium between two infinite plates. A modified Darcy's law is used in the flow modeling. The bottom plate moves in the presence of a uniform magnetic field. Graphs have been plotted for the velocity by giving numerical values to the parameters of interest. It is found that the velocity profile increases with an increase of retardation time and permeability, while it decreases as both the relaxation time and the magnetic parameter increase.