Aspect Ratio Dependence of Heat Transfer in a Cylindrical Rayleigh-Bénard Cell

Guenter Ahlers, Eberhard Bodenschatz, Robert Hartmann, Xiaozhou He, Detlef Lohse, Philipp Reiter, Richard J.A.M. Stevens, Roberto Verzicco, Marcel Wedi, Stephan Weiss, Xuan Zhang, Lukas Zwirner, Olga Shishkina*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)
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While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ 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 Γ follows Rac,Γ∼Rac,∞(1+CΓ-2)2, with C ≲ 1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling Ra→RaℓRa[Γ2/(C+Γ2)]3/2 collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Rau,Γ∼[Γ2/(C+Γ2)]-3/2 in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ-3) must be achieved to observe the ultimate regime.

Original languageEnglish
Article number084501
JournalPhysical review letters
Issue number8
Publication statusPublished - 24 Feb 2022


  • fluid mechanics
  • fluid dynamics
  • turbulence
  • heat transfer
  • theory
  • Rayleigh-Benard convection
  • convection


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