Article,
The effect of combined vertical and horizontal heterogeneity on the onset of convection in a bidisperse porous medium
International Journal of Heat and Mass Transfer, (2007)
Abstract
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.
