The Onset of Convection in a Porous Medium Occupying an Enclosure of Variable Width or Height

An analytical study is made of the onset of convection in a saturated porous medium occupying a two-dimensional enclosure of uniform height, but whose width is slowly varying in an arbitrary manner, or one of uniform width, but whose height is slowly varying in an arbitrary manner. It is found that the variation of width generally has a stabilizing effect, whereas variation of height generally has a destabilizing effect.