Nonlinear hydromagnetic stability analysis of a pseudoplastic film flow

The long-wave perturbation method is employed to investigate the nonlinear hydromagnetic stability of a thin electrically-conductive pseudoplastic liquid film flowing down the surface of a vertical wall in a magnetic field. The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The solution procedure commences by employing the normal mode approach to analyze the linear stability of the film flow. The multiple-scales method is then applied to obtain the weak nonlinear dynamics of the thin-film system for stability analysis. The modeling results reveal that the pseudoplastic film flow system may exhibit both subcritical instability and supercritical stability states. The flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.