Linear Stability of Thermosolutal Convection in a Micropolar Fluid Saturating a Porous Medium

In the present paper, the theoretical investigation of the double-diffusive convection in a micropolar fluid layer heated and soluted from below saturating a porous medium is considered. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been used. For the case of stationary convection, the effect of various parameters like medium permeability, solute gradient and micropolar parameters (i.e., coupling parameter, spin diffusion parameter, micropolar heat conduction parameter and micropolar solute parameter arises due to coupling between spin and solute fluxes) has been analyzed and found that medium permeability, spin diffusion and micropolar solute parameter has destabilizing effect under certain conditions, whereas stable solute gradient, micropolar coupling parameter and micropolar heat conduction parameter has stabilizing effect on the system under certain conditions. The critical thermal Rayleigh number and critical wave numbers for the onset of instability are also determined numerically and results are depicted graphically. It is found that the oscillatory modes are introduced due to the presence of the micropolar viscous effects, microinertia and stable solute gradient, which were non-existence in their absence. The principle of exchange of stabilities is found to hold true for the micropolar fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and stable solute gradient. An attempt is also made to obtain sufficient conditions for the non-existence of overstability.