Natural convection in porous cylindrical annuli

Natural convection in a porous layer between two horizontal, concentric cylinders is investigated numerically by solving the 2‐D Darcy‐Boussinesq equations on a very fine grid. The parabolic‐elliptic system was solved by a second order finite difference scheme based on the implicit alternating direction method coupled with successive under relaxation. The calculations show that for radius ratios above 1.7, the functional relationship between the mean Nusselt number and the Rayleigh number exhibits a closed hysteresis loop associated with the transition from a two to a four cell flow pattern. For very small radius ratios, steady state regimes containing 2, 4, 6, and 8 cells are progressively obtained as the Rayleigh number is increased, but no hysteresis behaviour is observed. For a radius ratio of 2, the numerical results are in good agreement with the experimental data. Multi‐cellular regimes and hysteresis loops have also been reported in the literature for fluid annuli but some differences between the two cases exist and are fully explained below.