Wave regimes on a ferromagnetic viscous-fluid film flowing down a vertical cylinder

Axially symmetrical waves on the surface of a ferromagnetic viscous-fluid film flowing down a cylindrical conductor with alternating current are considered. In this case, in addition to the gravitational force, the film is affected by a spatially nonuniform time-dependent magnetic field. The film thickness was assumed to be small compared to the radius of the conductor. In the long-wave approximation, a model equation for the deviation of the film thickness from its undisturbed value is obtained. Some numerical solutions of this equations are reported.