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Numerical treatments for the MHD flow of a viscous Newtonian fluid due to a porous shrinking sheet

In this paper, an efficient numerical treatment for magnetohydrodynamic flow and heat transfer calculations is presented, based on the differential transformation method (DTM), and the finite element method (FEM). This numerical treatment is obtained for the ordinary differential equation (ODE) which describes physically the boundary layer flow due to a permeable shrinking sheet. The DTM and FEM are utilized in this study because of their capacity to solve linear and nonlinear systems of ODEs, as well as their accuracy and convenience of use. These methods are approximate analytical that can usually get the solution in a series form. These numerical procedures are effective for this type of physical problem of varying degrees of complexity. The numerical calculations yield that the dimensionless velocity enhances when the wall mass suction for the flow is increased after the magnetic field is imposed. Also, the dimensionless velocity was found to increase for the large value of the magnetic parameter.