Mathematics, D.A.V.P.G College,Dehradun
biomaths, k.k.jain colleg khatauli,muzaffarnagar
Double-diffusive convection in a micropolar fluid layer heated and soluted from below in the presence of uniform rotation saturating a porous medium is theoretically investigated. An exact solution is obtained for a flat fluid layer contained between two free boundaries. To study the onset of convection, 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, rotation and micropolar parameters (i.e. coupling, spin diffusion, micropolar heat conduction and micropolar solute parameters arising due to coupling between spin and solute fluxes) have been analyzed. The critical thermal Rayleigh numbers for various values of critical wave numbers (found by Newton Raphson method) for the onset of instability are determined numerically and depicted, graphically. The oscillatory modes were introduced due to the presence of the micropolar viscous effects, microinertia, rotation 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, rotation and stable solute gradient. An attempt was also made to obtain sufficient conditions for the nonexistence of overstability.