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Characterization of Non-oscillatory Motions in Magneto-Rotatory Thermal Convection in Couple-Stress Fluid in a Porous Medium

Ajaib S. Banyal and Kamal Singh

The thermal instability of a couple-stress fluid heated from below in a porous medium acted upon by uniform vertical magnetic field and rotation is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically established the conditions for characterizing the oscillatory motions which may be neutral or unstable for 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 and rotation, and a constant vertical adverse temperature gradient, are necessarily non-oscillatory in the regime 1 (2 2 1) (2 2 ) 2 2 £ - + �?¯�?£�?· �?¯�?£�?· �?¯�?£�?¸ �?¯�?£�?¶ �?¯�?£�?¬ �?¯�?£�?¬ �?¯�?£�?­ �?¯�?£�?« - l l A F P Qp PT p p p e , where A T is the Taylor number, Q is the Chandrasekhar number,e is the porosity, l P is the dimensionless medium permeability of the porous medium and F is the couple-stress parameter. The result is important since it holds for all wave numbers and the exact solutions of the problem investigated are not obtainable in closed form, when both the boundaries are perfectly conducting and rigid