JAMP  Vol.3 No.3 , March 2015
Dynamical System of Three Magnetic Layers in the Presence of Porous Media
Author(s) Sameh A. Alkharashi1,2*
ABSTRACT
This paper concerns the linear stability of three viscous fluid layers in porous media. The system is composed of a middle fluid embedded between two semi-infinite fluids, in which the effect of the normal magnetic field is to introduce. The principle aim of this work is to investigate the influence of fluid viscosity and the porosity effect on the growth rate in the presence of normal magnetic field. The parameters governing the layers flow system, the magnetic properties and porosity effects strongly influence the wave forms and their amplitudes and hence the stability of the fluid. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained, where regions of stability and instability are identified. It is found that the stabilizing role for the magnetic field is retarded when the flow is in porous media. Moreover, the increase in the values of permeability parameters plays a dual role, in stability behavior. It has been found that the phenomenon of the dual (to be either stabilizing or destabilizing) role is found for increasing the permeability parameter. It is established that both the viscosity coefficient and the magnetic permeability damps the growth rate, introducing stabilizing influence. The role of the magnetic field and Reynolds number is to increase the amplitude of the disturbance leading to the destabilization state of the flow system, promote the oscillatory behavior. Influence of the various parameters of the problem on the interface stability is thoroughly discussed.

Cite this paper
Alkharashi, S. (2015) Dynamical System of Three Magnetic Layers in the Presence of Porous Media. Journal of Applied Mathematics and Physics, 3, 310-321. doi: 10.4236/jamp.2015.33044.
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