Dispersion in cellular thermal convection in porous layers

A numerical and experimental study is reported for the case of two-dimensional buoyancydriven convection in saturated horizontal packed beds. The classical Darcy model is extended by the Forchheimer (inertial) term and the effective thermal conductivity of the medium is represented by the sum of a stagnant and a (hydrodynamic) dispersive component, the latter being proportional to the local filtration velocity amplitude. Bifurcation analysis of the porous Bénard problem with dispersive and inertial terms proves that the results of the classical Darcy model still hold at the onset of convection for weak dispersion. Both terms are important for steady convection in shallow packed beds. The effect of dispersion on Nusselt number is stronger than that of inertia unless the Prandtl number of the porous medium is of order 0.01 or less. The ratio of layer thickness to bead diameter is shown to be a significant parameter of the problem that can help explain some contradictory experimental results.