Non-uniqueness of solutions to a MHD stagnation-point flow over an exponentially permeable stretching/shrinking sheet with velocity slip

Abstract

In this study, a magnetohydrodynamic (MHD) stagnation-point boundary layer flow over an exponentially stretching/shrinking sheet with suction/injection and velocity slip effects is presented. The governing equations were first transformed into a non-linear ordinary differential equations with the help of similarity transformations. Following from there, the equations obtained were solved numerically utilizing the bvp4c programme in MATLAB. It was determined that the non-linear ordinary differential equations possessed non-uniqueness of solutions (dual solutions). Stability analysis was performed to verify the stability of the dual solutions obtained. The results revealed that the first solution was stable while the second solution was unstable. Apart from that, it was also found that as the magnetic, suction and velocity slip parameters increased, the range of the non-uniqueness of solutions increased correspondingly. Hence, it is proposed that the existence of magnetic, suction and velocity slip effects delayed the boundary layer separation.