An Optimal Homotopy Perturbation Approach to Thin Film Flow of a Fourth Grade Fluid

In this work, we introduce a new optimal homotopy approach, namely the Optimal Homotopy Perturbation Method (OHPM), to thin film flow of a fourth grade fluid down a vertical cylinder. This approach does not depend upon any small or large parameters contradistinguishing from other perturbation methods. The main advantage of this procedure consists in providing a convenient way to control the convergence of approximation series in a very rigorous way and allows adjustment of convergence regions where necessary. A very good agreement was found between approximate and numerical solution, which proves that OHPM is very efficient and accurate.