Mixed convection stagnation point flow past a vertical flat plate with a second order slip: Heat flux case

Steady mixed convection stagnation point flow past a vertical flat plate with a second order slip when the plate is maintained at a variable heat flux is investigated. By selecting appropriate similarity variables, the partial differential equations are transformed into ordinary (similarity) differential equations, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection and velocity slip parameters. In order to establish which of these solutions are stable and which are not, a stability analysis has been performed. The effects of the mixed convection and velocity slip parameters on the skin friction coefficient, dimensionless wall temperature, and dimensionless velocity and temperature profiles are presented graphically, and discussed in details. It results in that the second order slip affects considerably the flow and heat transfer characteristics.