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A linear stability analysis is carried out to discuss the effects of horizontal magnetic field and horizontal rotation on thermal instability problem of a couple-stress fluid through a Brinkman porous medium. After employing normal mode method on the dimensionless linearized perturbation equations, it is noted that for the stationary state, Taylor number A T promotes stabilization, whereas medium porosity hastens the onset of convection. The medium permeability P , magnetic field Q , couple-stress  and Darcy-Brinkman parameter A D play dual role in determining the stability/instability of the system under certain restrictions. Also, the sufficient conditions responsible for the non-existence of overstability are gained and the principle of exchange of stabilities holds good for a magneto-rotary system.

Effects of Horizontal Magnetic Field and Rotation on Thermal Instability of a Couple-Stress Fluid through a Porous Medium: a Brinkman Model