Unsteady MHD combined convection over a moving vertical sheet in a fluid saturated porous medium with uniform surface heat flux

The group transformation method is applied for solving the combined convection problem in an unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically-conducting fluid along a vertical continuous moving plate saturated porous medium in the presence of a uniform transverse magnetic field. The uniform surface heat flux boundary condition is considered. The application of two-parameter groups reduces the number of independent variables by two and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. The ordinary differential equations are solved numerically using a shooting method. A discussion is provided for the effect of magnetic parameter M , permeability of the porous medium k and Prandtl number, Pr, on the velocity and temperature fields within the boundary layer and on shear stress and heat transfer.