Stagnation-point flow of the Walters' B' fluid with slip

The steady two-dimensional stagnation point flow of a non-Newtonian Walters' B' fluid with slip is studied. The fluid impinges on the wall either orthogonally or obliquely. A finite difference technique is employed to obtain solutions. 1. Introduction. Some rheologically complex fluids such as polymer solutions, blood, paints, and certain oils cannot be adequately described by the Navier-Stokes theory. For this reason, several theories of non-Newtonian fluids were developed. One important and useful model which has been used to describe the non-Newtonian behavior exhibited by certain fluids is the Walters' B' fluid [16]. The equations of motion of non-Newtonian fluids are highly nonlinear and one order higher than the Navier-Stokes equations. Due to the complexity of these equations, finding accurate solutions is not easy. One class of flows which has received considerable attention is stagnation-point flow. In a stagnation-point flow of a Newtonian fluid, a rigid wall occupies the entire x-axis, the fluid domain is y > 0, and the flow impinges on the wall either orthogonally [6, 7] or obliquely [4, 14, 15]. In a study of Newtonian fluid impinging on a flat rigid wall obliquely, Dorrepaal [4] found that the slope of the dividing streamline at the wall divided by its slope at infinity is independent of the angle of incidence. Beard and Wal-ters [2] used boundary-layer equations to study two-dimensional flow near a stagnation point of a viscoelastic fluid. Rajagopal et al. [11] have studied the Falkner-Skan flows of an incompressible second grade fluid. Dorrepaal et al. [5] investigated the behavior of a viscoelastic fluid impinging on a flat rigid wall at an arbitrary angle of incidence. Labropulu et al. [9] studied the oblique flow of a second grade fluid impinging on a porous wall with suction or blowing. In a recent paper, Wang [17] studied stagnation-point flows with slip. This problem appears in some applications where a thin film of light oil is attached to the plate or when the plate is coated with special coatings such as a thick monolayer of hydropho-bic octadecyltrichlorosilane [3]. Also, wall slip can occur if the working fluid contains concentrated suspensions [13]. When the molecular mean free path length of the fluid is comparable to the system's characteristic length, then rarefaction effects must be considered. The Knudsen number K n , defined as the ratio of the molecular mean free path to the characteristic length