Effect of couple stresses on flow of third grade fluid between two parallel plates using homotopy perturbation method

In this paper, an analytical analysis of the steady flow of an incompressible, third grade fluid between two parallel plates is carried out where the effect of couple stresses is taken into account. Depending on the relative motion of the plates, four different problems are studied: Couette flow, Plug flow, plane Poiseuille flow and generalized plane Couette flow. The solutions are obtained for the developed non-linear equations using the traditional perturbation method as well as the recently introduced homotopy perturbation method. Analytical expressions are given for the velocity field. It is observed that the homotopy perturbation method is more well-organized and flexible than the traditional perturbation method.