The nonlinear stability of mass and heat transfer in magnetic fluids

The nonlinear analysis of the Rayleigh-Taylor stability of two superposed magnetic fluids with interfacial transfer of mass and heat is presented for two layers of finite thickness. The system is subjected to a tangential magnetic field. The method of multiple scale expansion is employed for the analysis. It is shown that the evolution of the amplitude is governed by a nonlinear Ginzburg-Landau equation. There is also obtained a nonlinear diffusion equation describing the evolution of wave packets near the marginal state. Further, the nonlinear Schrodinger equation is obtained when the influence of mass and heat transfer is neglected. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained. It is found that, in the linear theory, the stability criterion is independent of mass and heat transfer coefficient. While in the nonlinear theory it is found that, when this coefficient is large enough, the system which would be unstable classically, can be stabilized for finite amplitude disturbances.