DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

doi:10.1007/s10483-012-1643-9

Abstract

Abstract: An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.

Key words: topological degree, multivalued mappings, existence results

2010 MSC Number:

O357
O175

Xiao-hong SU;Lian-cun ZHENG;Xin-xin ZHANG. DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1555-1568.

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