Numerical Analysis of Two Dimensional non-Newtonian Magnetohydrodynamics Boundary Layer Flow Over a Moving Wedge with Power Law Fluids

Abstract

In the present paper, we give numerical solution of the Falkner-Skan equation for the study of two-dimensional magnetohydrodynamics steady boundary-layer viscous flow over a wedge in the presence of non-Newtonian power law fluid which is represented by a power-law model. The outer free stream velocity is defined in the form of a power-law manner i.e., it varies as a power of a distance from the leading boundary-layer. The governing nonlinear boundary layer equations have been transformed into a third order nonlinear Falkner-Skan equation through similarity transformations. This equation contains four flow parameters that is the stream-wise pressure gradient (β), the magnetic parameter (M), and boundary stretch parameter (λ), and non-Newtonian power-law fluid (m). The governing equations (nonlinear partial differential equations) have been converted to an equivalent nonlinear ordinary differential equation along with boundary conditions by means of similarity transformations which is solved using the Keller-box method. A far-field asymptotic solution is also obtained which has revealed oscillatory shapes when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer reduce the boundary layer thickness. The results are obtained for velocity profiles and skin friction for various values of physical parameters and are discussed in detail. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids. The Physical significance of the flow parameters are also discussed in detail.