Thermal convection is perhaps most studied within the Rayleigh-Bénard system, where a question of great interest is how the heat transport asymptotically scales with the imposed temperature difference for strongly non-linear states. Even for a simple convection roll in the no-slip system, multiple asymptotic structures have been proposed. We use a matched asymptotic analysis to suggest that these rolls have their heat transport maximised when they have aspect ratio Γ = Ra(-1/5), where Ra is the non-dimensional imposed temperature difference, yielding a heat transport of Nu = Ra(1/3). We also briefly consider the heat transport of an internally heated system via numerics.
