  In a range of physical systems, the first instability in Rayleigh-Bernard
convection between nearly thermally insulating horizontal plates is large
scale. This holds for thermal convection of fluids saturating porous media.
Large-scale thermal convection in a horizontal layer is governed by remarkably
similar equations both in the presence of a porous matrix and without it, with
only one additional term for the latter case, which, however, vanishes under
certain conditions (e.g., two-dimensional flows or infinite Prandtl number). We
provide a rigorous derivation of long-wavelength equations for a porous layer
with inhomogeneous heating and possible pumping.
