Effect of Radiation and Magnetic Field on Mixed Convection at a Vertical Plate in a Porous Medium with Variable Fluid Properties and Varying Wall Temperature

In this paper the effects of radiation, magnetic field, variable viscosity and variable thermal conductivity on similarity solutions of mixed convection at a vertical flat plate embedded in a porous medium are studied numerically. Temperature of the plate as well as the free stream velocity are assumed to vary as power functions of x, where x is the distance measured vertically along the plate. The flow and heat transfer quantities are found to be functions of C, lambda, gamma(mu), gamma(k), RP and Rd where C is magnetic field parameter, lambda is power of index of the plate temperature, gamma(mu) is viscosity variation coefficient, gamma(k) is thermal conductivity variation coefficient. RP, mixed convection parameter is ratio of the Rayleigh number to the Pe'clet number and Rd is radiation parameter. The cases of assisting and opposing flow are considered and in the opposing flow case dual solutions are found for certain values of the parameters. Ranges of values of the parameters for which there exist no solution or dual solutions or a unique solution are also obtained. The influences of magnetic field, thermal radiation, variable viscosity, variable thermal conductivity and varying wall temperature on the velocity and temperature fields are studied and discussed with the help of graphs.