Natural convection in a vertical porous annulus

Numerical studies are reported for steady free convection in a vertical annulus filled with a saturated porous medium and whose vertical walls are at constant temperatures, the horizontal walls being insulated. Curvature effects on temperature and velocity fields are significant, and completely disturb the centro-symmetrical nature found in the vertical cavity case. Convective velocities are higher in the upper half than the lower half of the annulus, and the local rate of heat transfer is much higher near the top edge of the cold wall. The average Nusselt number always increases as the radius ratio, κ, increases, though the rate of increase diminishes with the increase in curvature effects particularly at high Rayleigh numbers, Ra^*. In the case of a tall annulus the heat transfer rate in the boundary layer flow regime approaches that for a cylinder embedded in a porous medium, as κ increases. The Rayleigh number criteria for various flow regimes are obtained, and the average Nusselt number is correlated by a relation of the form Nu = const. Ra^*m Aⁿκ^p, where A is the aspect (height-to-gap width) ratio. In the boundary layer regime, the heat transfer rate for a tall cavity or annulus of fixed height is a very weak function of the aspect ratio.