Thin-film flow of magnetohydrodynamic (MHD) Johnson–Segalman fluid on vertical surfaces using the Adomian decomposition method

In this paper, the magnetohydrodynamic (MHD) thin-film flow of Johnson–Segalman fluid for lifting and drainage problems on a vertical surfaces are investigated. The nonlinear differential equations arising from the mathematical modeling of the Johnson–Segalman fluid, the laws of momentum, mass and suitable boundary conditions are solved analytically using the Adomian decomposition method (ADM). A constant magnetic field is applied transversely to the direction of flow and particular attention is given to the effects of magnetic parameters on the velocity. The influence on the velocity field of various non-Newtonian parameters such as the Weissenberg number, Stokes number and applied magnetic field are investigated. Several graphs illustrate the influence of various pertinent parameters on the velocity. It is observed that increasing the applied magnetic field will generally reduce the flow velocity in the lifting case, while, in the drainage case, the magnetic field and the velocity field are shown to have a direct relation.