Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet

The MHD stagnation point flow of a viscous, incompressible and electrically conducting fluid over a stretching/shrinking permeable semi-infinite flat plate is numerically studied. The governing partial differential equations are transformed into an ordinary differential equation using a similarity transformation, before being solved numerically. Numerical solutions of this equation is obtained using bvp4c package in Matlab software. Dual (first and second or upper and lower branch) solutions are observed in a certain range of the pressure gradient and the stretching/shrinking parameter. A stability analysis is performed to show that the first (upper branch) solution is always stable, while the other (lower branch) solution is always unstable. It is observed that the range of the stretching/shrinking parameter (for which the physically realizable solution exists) increases with an increase of suction, pressure gradient as well as the magnetic parameter. It is also observed that with an increase in the pressure gradient, the first (upper branch) solution becomes more stable while unstable solution becomes more unstable. The variations of velocity inside the boundary layer for some values of the governing parameters, namely, the pressure gradient and the magnetic parameters are presented graphically. Comparison with published results of smallest eigenvalues for several values of suction and stretching/shrinking parameters are presented and it is found to be in excellent agreement.