Dual Solution of MHD Stagnation-Point Flow towards a Stretching Surface

Abstract

The effect of a uniform transverse magnetic field on two-dimensional stagnation-point flow of an incompressible viscous electrically conducting fluid over a stretching surface is investigated when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. This magnetohydrodynamic (MHD) flow problem is governed by the parameter b representing the ratio of the strain rate of the stagnation-point flow to that of the stretching sheet and the magnetic field parameter M. It is known from a previous paper [9] that if b > 1, the steady solution to the problem is monotonic increasing and the solution is also unique. But when 0 < b < bc (where bc (< 1) depends on M), there exists a dual solution which is non-monotonic in addition to a monotonic decreasing solution. It is found in this paper that bc decreases as M increases. Numerically it is shown that if M > 0.23919, the non-monotonic solution cannot exist and so in this case, the only solution is monotonic decreasing. A stability analysis reveals that when 0 < b < bc, the solutions along the upper branch corresponding to the monotonic solution are linearly stable while those along the lower branch for the non-monotonic solution are linearly unstable. It is also shown that the decay rate of a disturbance increases with increasing M for the stable solution but the growth rate of instability for the non-monotonic solution decreases with increasing M.