Finite-amplitude long-wave instability of a thin power-law liquid film flowing down a vertical column in a magnetic field

The long-wave perturbation method is employed to investigate the nonlinear hydromagnetic stability of a thin electrically conductive power-law liquid film flowing down a vertical cylinder. In contrast to most previous studies presented in literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index.