Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter β=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter β and the thickness δ of the fluid film on the fluid velocities