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Journal of Porous Media
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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v17.i10.30
pages 869-881

EFFECTS OF THE IRROTATIONAL VISCOUS PRESSURE ON MAGNETOHYDRODYNAMIC KELVIN−HELMHOLTZ INSTABILITY WITH MASS TRANSFER THROUGH POROUS MEDIA

Mukesh Awasthi
Babasaheb Bhimrao Ambedkar University, Lucknow

ABSTRAKT

In this paper, we investigate the effects of irrotational, viscous pressure on the Kelvin−Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium and, when there is heat and mass transfer across the interface. The analysis extends our earlier work in which the Kelvin−Helmholtz instability of two viscous and electrically conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. The whole system is acted by a horizontal magnetic field to the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by selecting viscous contributions to the irrotational pressure. We use the Darcy−Brinkman model and a dispersion relation has been derived. Stability criterion is given in terms of a critical value of relative velocity as well as critical value of applied magnetic field. It has been observed that heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.


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