Unsteady Stagnation Point Flow of a Non-newtonian Second-grade Fluid

The unsteady two-dimensional flow of a viscoelastic second-grade fluid impinging on an infinite plate is considered. The plate is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained. 1. Introduction. In the past two decades, the importance of non-Newtonian viscoelastic liquids have become evident due to their occurrence in industrial processes. Behaviour of viscoelastic fluids cannot be accurately described by the Newtonian fluid model. The equations of motion of viscoelastic fluids are highly nonlinear and one order higher than the Navier-Stokes equations. The two-dimensional stagnation point flow is an interesting problem in the history of fluid dynamics and has received considerable attention. Beard and Walters [2] used boundary-layer equations to study two-dimensional flow near a stagnation point of a viscoelastic fluid. Dorrepaal et al. [3] investigated the behavior of a viscoelastic fluid impinging on a flat rigid wall at an arbitrary angle of incidence. Labropulu et al. [5] studied the oblique flow of a viscoelastic fluid impinging on a porous wall with suction or blowing. Unsteady stagnation point flow of a Newtonian fluid has also been studied extensively. Rott [8] and Glauert [4] have studied the stagnation point flow of a Newtonian fluid when the plate performs harmonic oscillations in its own plane. Srivastava [9] has studied the same problem for a non-Newtonian second-grade fluid. He used the Karman-Pohlhausen method to solve the resulting equations. This paper considers the unsteady two-dimensional flow of an incompress-ible viscoelastic second-grade fluid impinging on an infinite flat plate. We assume that the plate is making harmonic oscillations in its own plane. Series method is employed to evaluate the solution for small and large frequencies of the oscillations. The resulting differential equations are solved numerically using a finite difference method developed by Ariel [1].