High-precision measurements of the Nusselt number Nu as a function of the Rayleigh number Ra have been made in water-filled 1m diameter cylindrical cells of aspect ratio Γ = 0.67, 1, 2, 5, 10 and 20. The measurements were conducted at the Prandtl number Pr ≈ 4 with Ra varying from 1× 10⁷ to 5× 10¹² . When corrections for the finite conductivity of the top and bottom plates are made, the estimates obtained of Nu∞ for perfectly conducting plates may be described by a combination of two power laws Nu∞ = C₁(Γ)Raβ₁+C₂(Γ)Raβ₂ for all the aspect ratios. The fitted exponents β₁ =0.211 and β₂ = 0.332 are very close to $1/5$ and $1/3$ respectively, which have been predicted by Grossmann & Lohse for the II ᵤ and IV ᵤ regimes in their model. It is also found that Nu∞ is generally smaller for larger Γ but the difference is only a few percent and for Γ 10 the asymptotic large- Γ behaviour may have been reached.
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Sun et al. (2005) studied this question.
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