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 MM, permeability of the porous medium kk and Prandtl number, Pr, on the velocity and temperature fields within the boundary layer and on shear stress and heat transfer.