The Nonlinear Instability of a Cylindrical Interface Between Two Hydromagnetic Darcian Flows

Abstract

This paper investigates the nonlinear instability of an interface between two magnetic fluids separated by a cylindrical interface in porous media. The system is influenced by a uniform axial magnetic field. The magnetic field intensities allow a presence of surface currents at the interface. The transfer of mass and heat across the interface is considered. The solutions of linearized equations of motion, under the appropriate nonlinear boundary conditions, lead to a nonlinear characteristic equation that is governed the behavior of the interface deflection. Drawing on the linear stability theory, Routh–Hurwitz’s criteria are utilized to judge the stability criteria. The coupling of Laplace transforms and Homotopy perturbation techniques are adopted to obtain an approximate analytical solution of the interface profile. The nonlinear stability analysis resulted in two levels of solvability conditions. By means of these conditions, a Ginzburg–Landau equation is conducted. The latter equation represented the nonlinear stability configuration. The magnetic field intensity was plotted versus the wave number of the surface waves. Therefore, the stability picture was divided into stable and as well as unstable regions. Subsequently, the influence of the various physical parameters was addressed.