Couette-Poiseuille flow with partial slip and uniform cross flow for power-law fluids

Exact solutions are obtained for the steady flow of a power-law fluid between parallel plates with partial slip conditions and uniform cross flow. The problem is properly formulated and similarities are exploited. The exact solutions are obtained in terms of integrals which can be performed, in closed form, in special cases of the power-law index n. Solutions to cases of n=1/2, 1, and 2; representing a pseudo-plastic, a Newtonian, and a dilatant fluid, respectively, are presented. Tendencies to corresponding degenerate cases in the literature are demonstrated. Depending on the strength of the cross flow and the pressure gradient, the flow may be of Couette-type with convex, linear, or concave velocity profile; or of Poiseuille-type. Borderline cases are identified.Comment: 20 pages, 1 table, 9 figures, 12 references, 1 appendi

Heat Transfer in MHD Flow due to a Linearly Stretching Sheet with Induced Magnetic Field

The traditionally ignored physical processes of viscous dissipation, Joule heating, streamwise heat diffusion, and work shear are assessed and their importance is established. The study is performed for the MHD flow due to a linearly stretching sheet with induced magnetic field. Cases of prescribed surface temperature, heat flux, surface feed (injection or suction), velocity slip, and thermal slip are considered. Sample numerical solutions are obtained for the chosen combinations of the flow parameters

MHD Flow due to the Nonlinear Stretching of a Porous Sheet

The MHD flow due to the nonlinear stretching of a porous sheet is investigated. A closed form solution is obtained when the stretching rate is inversely proportional to the distance from the origin. Otherwise a uniformly valid asymptotic expansion, for large magnetic interaction number β~∞, is developed. It coincides with a homotopy perturbation expansion for the problem. The asymptotic/homotopy perturbation expansion gives results in excellent agreement with accurate numerical results, for large as well as small values of β. For large β, the expansion, being asymptotic, needs a small number of terms, regardless of the mass transfer rate or the degree of nonlinearity. For small β, the expansion is a homotopy perturbation one. It needs considerably increasing number of terms with higher injection rates and/or with stretching rates approaching the inverse proportionality. It may even fail