Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

• The stagnation point flow and heat transfer past a moving flat plate are simulated.
• Movements into and out of the origin of the flat plate are considered.
• It is found that dual solutions exist for the case of opposing flows.
• Physically realizable solutions are determined by a linear stability.

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.