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While the heat transfer and the flow dynamics in a cylindrical Rayleigh-B\'enard (RB) cell are rather independent of the aspect ratio (diameter/height) for large, a small- cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given follows Ra₂, Ra₂, (1+C^-2) ^2, with C1. 49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32) 32, the rescaling RaRa_^2/ (C+^2) ^3/2 collapses various OB numerical and almost-OB experimental heat transport data Nu (Ra, ). Our findings predict the dependence of the onset of the ultimate regime Raₔ, ^2/ (C+^2) ^-3/2 in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for =1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small- cells, much larger Ra (namely, by a factor ^-3) must be achieved to observe the ultimate regime.
Ahlers et al. (Thu,) studied this question.