Double-diffusive natural convection in a vertical porous annulus

A numerical study is carried out on double-diffusive natural convection in a vertical annular porous layer whose vertical wads are at constant temperatures and concentrations. The investigation covers the range 10 less than or equal to R-T less than or equal to 500, 1 less than or equal to Le less than or equal to 10, -50 less than or equal to N less than or equal to 50, 1 less than or equal to A less than or equal to 5, 1 less than or equal to kappa less than or equal to 10, where R-T, Le, N, A, and kappa are the thermal Rayleigh number, Lewis number, buoyancy ratio, aspect ratio, and radius ratio of the enclosure, respectively. The two extreme cases of heat-driven and solute-driven natural convection correlations, valid in the boundary layer regime, are derived to calculate the average Nusselt and Sherwood numbers in terms of the governing parameters of the problem. In order to investigate the effects of the combined thermal and solutal buoyancy forces on the average heat and mass transfer, results have been obtained for a large range of buoyancy ratios N. Streamlines, isotherms, and isosolutes in the system are produced to illustrate the flow structure transition from mass species dominated opposing to thermal dominated and mass species dominated aiding flows, respectively. The thermal Rayleigh and Lewis numbers and the radius ratio are found to influence the buoyancy ratio at which flow transition and flow reversal occurs.