The effect of combined vertical and horizontal heterogeneity on the onset of convection in a bidisperse porous medium

The effects of both horizontal and vertical hydrodynamic and thermal heterogeneity, on the onset of convection in a horizontal layer of a saturated bidisperse porous medium uniformly heated from below, are studied analytically using linear stability theory for the case of weak heterogeneity. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account, and to a first approximation are independent. The thermal heterogeneity of the p-phase can be quite significant when the thermal diffusivity of that phase is large relative to that of the f-phase.