Analysis of oblique stagnation point flow over a rough surface

Abstract

The present study explores the partial slip effects on the oblique stagnation point flow of viscous fluid. The governing equations are formulated as a similarity solution of the Navier-Stokes equations, and the no-slip boundary conditions are replaced by the Navier's partial slip boundary conditions. The resulting system of nonlinear equations are governed by the dimensionless shear parameter γ, slip parameter λ and a free parameter β. The oblique stagnation point flow consists of classical orthogonal stagnation point flow along with a shear flow on the surface. Previous works of the oblique stagnation point were studied numerically, and several speculations regarding the behaviour of the solutions are made. Current work is to confirm the speculations. We prove the existence and the uniqueness results for the classical boundary layer flow near an orthogonal stagnation point flow for a rough surface. Moreover, a general solution is also given for shear flow which confirms the existence of negative shear flow for a large value of free parameter β and describes the effects of partial slip on reverse flow. Further, the detailed effects of physical parameters on the flow domain are shown through tables and graphs. It is observed that the streamlines are skewed towards left of orthogonal stagnation point for positive values of shear parameter γ and towards right for negative values.