Homotopy analysis of Couette and Poiseuille flows for fourth grade fluids

Abstract

The steady flow of a fluid, called a fourth grade fluid, between two parallel plates is considered. Depending upon the relative motion of the plates we analyze four types of flows: Couette flow, plug flow, Poiseuille flow and generalized Couette flow. In each case, the nonlinear differential equation describing the velocity field is solved using perturbation technique and homotopy analysis method. The pressure distribution is also found. It is observed that the homotopy analysis method is more efficient and flexible than the perturbation technique.