Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium

A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.