MHD Flow and Heat Transfer in a Power-Law Liquid Film at a Porous Surface in the Presence of Thermal Radiation

In this paper, the effects of variable thermal conductivity and thermal radiation on the MHD flow and heat transfer of a non-Newtonian power-law liquid film at a horizontal porous sheet in the presence of viscous dissipation is studied. The governing time dependent boundary layer equations are transformed to coupled, non-linear ordinary differential equations with power-law index, unsteady parameter, film thickness, magnetic parameter, injection parameter, variable thermal conductivity parameter, thermal radiation parameter, the Prandtl number and the Eckert number. These coupled non-linear equations are solved numerically by an implicit, finite difference scheme known as the Keller box method. The obtained numerical results for velocity and temperature profiles are presented graphically. Also, the obtained results of our study for some special cases are compared with the previously published results, and the results are found to be in very good agreement. The effects of unsteady parameter on the skin friction, wall- temperature gradient and the film thickness are explored for different values of the power-law index and the magnetic parameter. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.

Keywords:

MHD flow , Thin liquid film , Power , law fluid , Heat transfer , variable thermal conductivity , Viscous dissipation , Finite difference method