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Nonlinear stability problem of ferromagnetic fluids with mass and heat transfer effect

100%

Elhefnawy A. R. F.

tom Vol. 5, nr 2

253-267

The nonlinear theory of Kelvin-Helmholtz instability is employed to analyze the instability phenomena of ferromagnetic fluids. The effect of both the magnetic field and the mass and heat transfer at the interface on the instability is investigated. The method of multiple scale expansion is. employed for the investigation. It is shown that, for the Rayleigh-Taylor problem, the mass and heat transfer has no effect. In absence of the magnetic field, the system cannot be stabilized by the finite amplitude effects for two semi-infinite fluid layers up to the third-order.

Nonlinear Instability of Two Superposed Magnetic Fluids in Porous Media Under Vertical Magnetic Fields

51%

Elhefnawy A. R. F. , Mahmoud M. A. , Mahmoud M. A. A. , Khedr G. M.

tom Vol. 11, nr 1

65-85

The nonlinear analysis of the Rayleigh - Taylor instability of two immiscible, viscous magnetic fluids in porous media, is performed for two layers, each has a finite depth. The system is subjected to both vertical vibrations and normal magnetic fields. The influence of both surface tension and gravity force is taken into account. Although the motions are assumed to be irrotational in each fluid for small perturbations, weak viscous effects are included in the boundary condition of the normal stress balance. The method of multiple scale expansion is used for the investigation. The evolution of the amplitude is governed by a nonlinear Ginzburg - Landau equation which gives the criterion for modulational instability. When the viscosity and Darcy's coefficients are neglected, the cubic nonlinear Schrodinger equation is obtained. Further, it is shown that, near the marginal state, a nonlinear diffusion equation is obtained in the presence of both viscosity and Darcy's coefficients. Stability analysis and numerical simulations are used to describe linear and nonlinear stages of the interface evolution and then the stability diagrams are obtained. Regions of stability and instability are identified.