Layer Thickness Variation in Two-Phase Flow of a Third Grade Fluid

Abstract

In this paper we consider the two-layer flow of a third grade fluid between two horizontal infinite parallel plates. The fluid in both layers is pressure driven in a horizontal direction (Poiseuille flow). We relax the assumption of symmetry and consider layers of variable thickness. To solve the non-linear differential equations describing the motion of a third grade fluid we use the Homotopy Analysis Method and provide a solution which accurate up to the second order. We apply this solution to attain the velocity profile in different cases for different layer thickness, pressure gradient and material constants that describe the non-Newtonian behavior of the fluid.