Abstract
This work generates approximate analytic solutions of the unsteady state of rotating magnetohydrodynamic (MHD) flow of a third grade fluid past a rigid plate in a porous medium. By using the modified Darcy's law of a third grade fluid, the equations governing the flow are modeled. Employing the homotopy analysis method (HAM), the approximate analytic solutions of the modeled equations are developed for the following two problems: (i) constant accelerated flow and (ii) variable accelerated flow. The obtained solutions clearly satisfy the governing equations and all the imposed initial and boundary conditions. Finally, the influences of emerging parameters are studied through graphs which emphasize the effects of magnetic field, rotating frame, and porosity parameters.