Solution of steady thin film flow of Johnson–Segalman fluid on a vertical moving belt for lifting and drainage problems using Adomian Decomposition Method

The steady thin film flow on a vertical belt of a non-Newtonian Johnson–Segalman fluid for lifting and drainage problems are investigated in this paper. The analytical solutions of the non-linear problems are obtained by Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM). Expressions for the velocity profile, average velocity, volume flux, the belt speed of the lifting and the shear stress at the belt have been derived. For Weissenberg number We=0We=0, we retrieve Newtonian cases for both the problems. We also obtain the results for Maxwell fluid by taking slip parameter a = 1. The manner in which the Stokes number StSt, Weissenberg number WeWe, the ratio of viscosities ϕϕ and the slip parameter a affect the structure of the velocity profile for lifting and drainage problems are delineated. Comparison between the ADM solutions and Homotopy Perturbation Method (HPM) solutions are made.