Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

In this paper, we have considered the two-dimensional stagnation point flow and heat transfer of an electrically conducting viscous fluid over an exponentially stretching sheet. The Navier-Stokes equations are reduced into a system of highly non-linear ordinary differential equations by similarity transformations. The resulting systems are then solved numerically by shooting method. The effects of suction/injection parameters on the boundary layer are discussed in detail. Our numerical results reveal that for a particular range of the velocity ratio parameter, dual solutions exist. Interestingly these two solution branches show opposite characters in the velocity and temperature profiles. Thus, it is worthwhile to carry a stability analysis of these two solutions to determine the feasible solution. A linear temporal stability analysis has been carried out, and the stability is tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found by two different numerical schemes, which agree well up to the desired accuracy. The effects of the pertinent flow parameters in the velocity and temperature profiles are discussed in detail and are shown graphically.