TITLE:
Dynamical System of Three Magnetic Layers in the Presence of Porous Media
AUTHORS:
Sameh A. Alkharashi
KEYWORDS:
Viscous Fluids, Magnetic Field, Three Layers Stability, Porous Media
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.3,
March
23,
2015
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.