Effects of chemical reaction, heat and mass transfer and viscous dissipation over a MHD flow in a vertical porous wall using perturbation method

Analytical solution of a magnetohydrodynamic steady mixed convective flow of an incompressible, viscous, Newtonian, electrically-conducting and chemically-reacting fluid over an infinite vertical porous plate with combined heat and mass transfer is presented in the presence of the homogeneous chemical reaction of first order. A uniform magnetic field is assumed to be applied transversely to the direction of the flow, taking into account the induced magnetic field with viscous and magnetic dissipations of energy. The porous plate is subjected to a constant suction velocity as well as uniform mixed stream velocity. The governing equations are solved by perturbations technique. The expressions for the velocity field, induced magnetic field, Current density and the rate of heat transfer at the plate are obtained and demonstrated graphically for the various values of the parameters involved in the problem. The effects of the Hartmann number, the chemical reaction parameter, the magnetic Prandtl number, and the other parameters involved on the velocity field, temperature field, induced magnetic field, current density and the rate of heat transfer from the plate to the fluid are discussed. Velocity (u) is reduced considerably with a rise in Hartmann (M) or magnetic Prandtl number (Pm) whereas the temperature (θ) is found to be markedly boosted with an increase in the Hartmann number (M) or chemical reaction parameter (K). An increase in heat source/sink (α) or chemical reaction (K) is found to escalate induced magnetic field (bx) whereas an increase in magnetic body parameter (M) or magnetic Prandtl number (Pm) is shown to exert the opposite effect. Progressively weaker destructive chemical reaction (K > 0) lowers current density (J) values, whereas generative chemical reaction (K < 0) escalate current density. Rate of heat transfer is decreased with Hartmann number.