A mathematical theorem on the onset of Couple-Stress fluid permeated with suspended dust particles saturating a porous medium

In this paper, the effect of suspended particles on thermal convection in Couple-Stress fluid saturating a porous medium is considered. By applying linear stability theory and 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 suspended particles parameter B, satisfy the inequality R <= 4 pi F-4/BPl.