the transient mhd flow generated by a periodicwall motion in a porous space

The problem of transient flow of incompressible third grade fluid on the two-dimensional magnetohydrodynamic (mhd) flow in a porous space is analyzed. the flow is generated due to the motion of the plate in its plane with a periodic velocity. under the flow assumptions, the governing nonlinear partial differential equation is transformed into steady-state and transient nonlinear equations. the reduced equation for the transient flow is solved analytically using symmetry approach while the nonlinear steady-state equation is solved using a modified version of he’s homotopy perturbation method. the effect of several operating parameters on the flow hydromagnetic is discussed. the results indicated that for the considered case, t = 1:5 is the moment after which the time-dependent transient motion of the fluid can be approximated with the steady-state motion, described by the steady-state solution. it is clear that, after this value of time t the time-dependent transient solution can be neglected.