Nonlinear Surface Waves of the Thin Gravity-Driven Liquid Film Flows Under Magnetohydrodynamic Field And Rotating Centrifugal Force

Abstract

The effects of magnetohydrodynamic field and rotating centrifugal force on nonlinear hydrodynamic stability in a layer of viscous gravity-driven fluid flow are considered. The multiple-scales method is used to examine the nonlinear dynamics of the liquid film. When the fluid film flows down the outside surface of a stationary vertical cylinder, the stability of the flow field is dominated by the radius of the cylinder and the magnitude of the magnetic force. As the cylinder starts to rotate, however, a centrifugal force is produced and thus the stability of the thin-film system is governed by the interaction between the cylinder radius and the speed of rotation. The size of the explosive supercritical instability region increases significantly as the cylinder rotates. At higher values of the Reynolds number, the tendency of the rotation effect to prompt thin-film instability increases with an increasing cylinder radius. Moreover, it is observed that by increasing the intensity of the magnetic field tends to increase the stability as traveling down along the rotating vertical cylinder.