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Magneto-thermal convection in a couple-stress fluid in a porous medium and its characterization

Ajaib S. Banyal

A layer of couple-stress fluid heated from below in a porous medium is considered in the presence of uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any combination of perfectly conducting, free and rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical magnetic field opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime ( ) 2 4 2 2 1 2 p F P R l e £ p + p + p , Where R is the thermal Rayleigh number, F is the couple-stress parameter of the fluid, l P is the medium permeability, e is the porosity of the porous medium and 2 p is the magnetic Prandtl number. The result is important since the exact solutions of the problem investigated, in closed form are not obtainable for any arbitrary combinations of perfectly conducting dynamically free and rigid boundaries.