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1 Mechanics and Mechanical Engineering

1 2004

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Instability of Darcian flow in an alternating magnetic field

El-Dib Y. O., Abd El-Latif O. E.

Mechanics and Mechanical Engineering

2004

Vol. 7, nr 2

23-60

This paper treats the stability of an interface between two different fluids moving through two different porous media. There is an alternating magnetic field parallel to the interface and to the flow direction, and there is a concentrated sheet of electric current at the interface which produces jump in the magnetic field strength. The evolution of the amplitude of propagation surface waves is governed by a complex Mathieu equation which have damping terms. In the limiting case of non-streaming fluids a simplified damped Mathieu equation has been imposed. At a critical value of the stratified magnetic field, the ordinary Mathieu equation without the damping terms is derived. The contribution of viscosity to the existence of free electric surface currents on the fluid interface is discussed. It is found that at the critical stratified magnetic field, the surface currents density has disappeared from the interface whence the stratified viscosity has a unite value. The stability criteria are discussed theoretically and numerically in which stability diagrams are obtained. Regions of stability and instability are identified for the wave number versus the coefficient of free surface currents. It is found that the increase of the fluid velocity plays a destabilizing influence in the stability criteria. Porous permeability and viscosity ratio play a stabilizing or a destabilizing role in certain cases. It is found that the viscosity ratio plays a dual role in the stability behaviour at the resonance case. The field frequency plays a stabilizing influence in the case of weak viscosity analysis and at a special value of the magnetic field ratio. The destabilizing influence for the field frequency is observed for the case of the Rayleigh- Taylor model and at the resonance case.