Transient buoyancy-opposed double diffusive convection of micropolar fluids in a square enclosure

The present study considers transient buoyancy-opposed double diffusive free convection of a micropolar fluid consisting of rigid and non-deformable particles suspension with its own rotation in a square enclosure. The governing equations are written in terms of the primitive variables and a numerical solution of the complete set of nonlinear equations has been done without any scaling to the flow terms. The modified Market and Cell (MAC) method is used for the solution of the variables in the primitive form with the help of the Alternating Direction Implicit (ADI) scheme. In order to handle effectively the advection terms, the gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) and the operator-splitting algorithm have been employed. A parametric study is conducted to illustrate the effects of the Rayleigh number, Prandtl number, buoyancy ratio and the vortex viscosity parameter. Interesting features of stability at critical buoyancy ratios with the inclusion of the vortex viscosity parameter is reported. Detailed distributions of isotherms, isoconcentrations, flow lines and microrotation lines are provided to reveal the concealed physics of the complex phenomenon. A power spectrum analysis and phase plane maps are provided to bring clarity about the instability involved in the phenomenon. Correlations have been developed for the average Nusselt and Sherwood numbers based on the computed results. (C) 2014 Elsevier Ltd. All rights reserved.