MHD Stagnation-Point Flow over a Nonlinearly Stretching/Shrinking Sheet

Abstract

The steady laminar two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid impinging normal to a nonlinearly stretching/shrinking flat sheet in the presence of a nonuniform magnetic field applied in the positive y-direction normal to the flat sheet is considered. The governing system of partial differential equations is first transformed into ordinary differential equations and solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the magnetic parameter M, the velocity exponent parameter m, and the stretching/shrinking parameter ε on the flow field are discussed. It is found that the magnitude of the skin friction coefficient |f″(0)| increases with both the magnetic parameter M and the velocity exponent parameter m, when the stretching velocity differs from the free-stream velocity (ε≠1), and is zero when ε=1. For a fixed value of the magnetic parameter M, a unique or dual solutions are found for the shrinking sheet, depending on the values of the parameters m and ε.