Stagnation-point flow of a viscoelastic fluid towards a stretching surface

Abstract

An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B′ model), a boundary layer is formed when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases with increase in the elasticity of the fluid. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the velocity of the free stream and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. It is found that temperature at a point decreases with increase in the elasticity of the fluid.