A fluid layer sandwiched between two flat plates (Hele-Shaw cell) has been assumed to model a saturated porous medium with permeability, d2/12, dependent only on the gap width, d. For situations where the properties of the porous matrix are important, such as thermal convection, the total cross-section (y) of the sandwich should enter into the computation of permeability. The decide which of these approaches is valid, we observed the onset of convection in a Hele-Shaw cell with constant gap width but spatially varying wall thickness. Convection begins in the thin-walled section at a lower temperature difference than it does where the walls are thick. Our data confirm that d3/12y is the permeability of Hele-Shaw cells used to model thermal convection in porous layers.