The influence of both the Rossby number and the Hartmann number on the hydromagnetic stability of a thin liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results indicate that the stability of the liquid film is enhanced by increasing the strength of the magnetic field or reducing the speed at which the cylinder rotates. By contrast, the flow becomes relatively more unstable as the cylinder radius is increased at larger values of the Rossby number. Notably, this finding is the opposite of that observed for film flows along a stationary vertical cylinder.

The paper investigates the hydromagnetic stability theory of a thin electrically conductive fluid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results display that the degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. It is also observed that by increasing the effect of the magnetic field and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.