Department of Mathematics, School of Science and Technology, The Federal Polytechnic Bauchi, P.M.B. 0231, Off Dass Road, Bauchi, Nigeria
School of Mathematical Sciences,Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
Centre for Research in Computational Mathematics, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor, Malaysia
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.