Numerical simulation of the stagnation point flow past a permeable stretching/shrinking sheet with convective boundary condition and heat generation

Abstract

Purpose – The purpose of this paper is the stagnation-point flow driven by a permeable stretching/shrinking surface with convective boundary condition and heat generation. Design/methodology/approach – It is known that similarity solutions of the energy equation are possible for the boundary conditions of constant surface temperature and constant heat flux. However, for the present case it is demonstrated that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is constant. Findings – The governing boundary layer equations are transformed to self-similar nonlinear ordinary differential equations using similarity transformations. Numerical results of the resulting equations are obtained using the function bvp4c from Matlab for different values of the governing parameters. In addition an analytical solution has been obtained for the energy equation when heat generation is absent. The streamlines for the upper branch solution show that the pattern is almost similar to the normal stagnation-point flow, but because of the existence of suction and shrinking effect, the flow seems like suck to the permeable wall. Originality/value – Dual solutions are found for negative values of the moving parameter. A stability analysis has been also performed to show that the first upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible. The streamlines for the lower branch solution are also graphically shown.