NATURAL-CONVECTION IN A POROUS, HORIZONTAL CYLINDRICAL ANNULUS

Natural convection in a porous medium bounded by two horizontal cylind ers is studied by solving the two-dimensional Boussinesq equations num erically. An accurate second-order finite difference scheme using an a lternating direction method and successive underrelaxation is applied to a very fine grid. For a radius ratio above 1.7 and for Rayleigh num bers abo ve a critical value, a closed hysteresis loop (indicating two possible solutions depending on initial conditions) is observed. For a radius ratio below 1.7 and as the Rayleigh number is increased, the number of cells in the annulus increases without bifurcation, and no h ysteresis behavior is observed. Multicellular regimes and hysteresis l oops have also been reported for fluid layers of same geometry but sev eral differences between these two cases exist.