Numerical study on magnetohydrodynamic boundary layer flow of the Carreau fluid in a porous medium: the Chebyshev collocation method

We study the hydrodynamics of the boundary layer flow of Carreau fluid over a moving wedge embedded in a porous medium in the presence of the applied magnetic field. The velocity of the wedge and mainstream is approximated by the power of distance from the leading boundary layer edge. Governing equations that model a non-Newtonian fluid in the boundary layer are reduced to an ordinary differential equation using the appropriate similarity transformations. The Chebyshev collocation and shooting algorithms based results show that there are non-unique solutions in the boundary-layer for the same system parameters. When the velocity ratio parameter is reduced the wall shear stress on the surface starts to increase till a critical value beyond which no solution exists. Thus, linear stability based on eigenvalue analysis helps to determine which of these non-unique solutions is physically realizable. When the magnetic field and permeability effects on the boundary-layer flow are increased the system shows unique solutions which are always stable. A detailed mechanism behind these results is discussed.