The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter P-l the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality R <= 4 pi(2)/P-l (1 + 2 pi(2) F + P(l)Q/2 epsilon), the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.