The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium with horizontal throughflow

The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions, on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, with horizontal throughflow, are studied analytically for the case of weak heterogeneity. It is found that the horizontal throughflow has no effect on the stability of the longitudinal modes but it does affect the stability of the transverse modes. When the permeability decreases in the direction of the throughflow the transverse modes are stabilized (and so the longitudinal ones are favored). When the permeability increases in the direction of the throughflow a small amount of throughflow may destabilize the transverse modes and so destabilize the layer as a whole.