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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

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