On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder

In this Letter a totally analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder is obtained using homotopy analysis method (HAM). The series solution is developed and the recurrence relations are given explicitly. Convergence of the solution and effects of rheological parameters are discussed. The comparison of the HAM results with HPM results is made. It is found that HPM results are divergent for strong nonlinearity. The results reveal that HAM is very simple and effective and provides a simple way to control and adjust the convergence region.