Stagnation-point Flow of a Viscoelastic Fluid over a Lubricated Surface

Abstract

A stagnation point flow of a viscoelastic Walters' B fluid over a surface lubricated with a power-law non-Newtonian fluid is considered in this paper. It is assumed that the lubricant is spread over the sheet making a thin layer of variable thickness. We are interested in a similarity solution of the problem which in the present case exists only for the power-law index n = 1/2. For the other values of the power-law index the non-similar solutions are also presented in the present paper. A slip flow boundary condition is deduced for a viscoelastic fluid at the fluid-fluid interface which is then imposed on the surface due to reason that the lubrication layer is thin. This new slip boundary condition is different from the conventional slip boundary condition for viscoelastic fluids considered in the literature. The numerical solution of the governing nonlinear ordinary differential equation subject to a nonlinear slip boundary condition is obtained by a hybrid method that combines the features of the finite difference and shooting methods. The profiles of velocity under the influence of slip and viscoelastic fluid parameters are illustrated. Moreover, the behavior of the missing condition f″(0) under the influence of these parameters is also presented. The results for the no-slip and full slip flows can be recovered as limiting cases when λ → ∞ and λ → 0 respectively.