Similarity solutions to the MHD boundary layer equations with a negative parameter for power-law fluids

Abstract

We investigate the similarity solutions of a magnetohydrodynamics (MHD) boundary layer problem arising in the two-dimensional steady boundary layer system for an incompressible electrically conducting power-law fluid in the presence of magnetic and electric fields. In the self-similar case, the boundary layer system is converted into a third-order nonlinear differential equation depending on two parameters. When one of the two parameters is negative, the existence and uniqueness of normal convex solutions and generalized convex solutions to the boundary layer problem are established by the aid of the Helly selection theorem. The asymptotic behavior of normal convex solutions at infinity is also obtained.