This Brief describes six basic models of buoyancy-driven convection in a fluid layer: three
configurations of internally heated convection and three configurations of Rayleigh-Bénard
convection. The author discusses the main quantities that characterize heat transport in each
model along with the constraints on these quantities. This presentation is the first to place
the various models in a unified framework and similarities and differences between the cases
are highlighted. Necessary and sufficient conditions for convective motion are given. For the
internally heated cases only parameter-dependent lower bounds on the mean fluid temperature
are proven and results of past simulations and laboratory experiments are summarized and
reanalyzed. The author poses several open questions for future study.
