Modeling of wave modes on a vertical film of a viscous ferromagnetic fluid flowing down a cylindrical electric conductor

The present study considers axially symmetrical waves on the surface of a ferromagnetic viscous fluid film flowing down a cylindrical conductor with a non-constant current. In addition to the gravitational force, the film is affected by a uniform magnetic field. Using the long-wave approximation, a model equation is obtained for the evolution of the film thickness from its undisturbed value. By showing that solutions with and without a constant magnetic field are self-similar, scaling parameters are identified and presented. Numerical solutions of the time-dependent non-linear partial differential equation are presented when current in the conductor is described by a ramp function (i.e., magnetic field onset).