Mathematical Model and Solution for an Unsteady MHD Fourth Grade Fluid Flow over a Vertical Plate in a Porous Medium with Magnetic Field and Suction/Injection Effects

This work investigates the mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with the effects of the magnetic field and suction/injection parameters using Homotopy Perturbation Method. The flow is considered to satisfy the constitutive equations of fourth grade fluid flow model and because of the Homotopy Perturbation Method used, only the momentum equation with initial and boundary conditions are solved as governing equations. After initializing stability test, the convergence of the governing equations are observed graphically using the results of Homotopy Perturbation Method with the new analytical method used by Yurusoy in literature and there is a perfect agreement in results. The impact of dimensionless second, third and fourth grade parameters with the effects of magnetic field and suction/injection parameters on the velocity field are displayed graphically and discussed. Increase in suction parameter decreases the momentum boundary layer thickness while injection parameter enhances velocity distribution in the boundary layer. Magnetic field reduces velocity throughout the boundary layer because the Lorentz force which acts as retarding force reduces the boundary layer thickness.