Hydromagnetic Stability Analysis of a Film Coating Flow Down a Rotating Vertical Cylinder

Abstract

ABSTRACTThe 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.