Lie group symmetry method for MHD double-diffusive convection from a permeable vertical stretching/shrinking sheet

Abstract

In this paper, the problem of the steady magnetohydrodynamics (MHD) double-diffusive convection of a viscous and electrically conducting fluid from a permeable vertical stretching/shrinking sheet with the presence of buoyancy force is investigated numerically. The effect of the MHD on the flow, heat transfer and species concentration has been also discussed. The partial differential equations are reduced to ordinary (similarity) equations using the method of the Lie group symmetry. Numerical solutions of the resulting nonlinear boundary value problem are carried out using the function bvp4c from Matlab for different values of the governing parameters. It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the stretching/shrinking, buoyancy, suction and magnetic parameters. It is shown that the reported results are in excellent agreement with those from the open literature for a forced convection flow when the concentration gradient is absent and the stretching sheet is impermeable. In order to establish which of upper and lower solutions are stable and which are not, a stability analysis has been performed. Thus, it is found that the upper branch solution is stable and, therefore, physically realizable in practice, while the lower branch solution is not stable and, thus, physically not realizable. The effects of the governing parameters on the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number are shown in tables and figures. It results in that the governing parameters affect considerably the flow, heat transfer and concentration characteristics. In our opinion, the results are new and original.