The onset of natural convection has been examined for a fluid-saturated porous material contained within a thin box under the influence of lateral heat losses. Thermal boundary conditions consist of an isothermal upper surface and either prescribed temperature or prescribed heat flux at the lower boundary. Both permeable and impermeable upper boundaries are considered.
Critical Rayleigh numbers and the preferred convective cellular modes at the onset of convection have been determined analytically as functions of the box geometry, ambient temperature and heat transfer coefficient. The results show that the critical Rayleigh number for a box with lateral heat loss is higher than thet predicted in the limit of no heat loss except for extremely small aspect ratios. And the case with no Neumann boundary condition has been found the most stable.