2004/09/09 by Alexei Nikolaenko, Eric Brown, Denis Fünfschilling +2 · 2 citations
Engineering · Environmental Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Plant Water Relations and Carbon Dynamics #Wind and Air Flow Studies #physics.flu-dyn
paper · pdf · doi:10.1017/s0022112004002289
10 pages, 5 figures
arxiv created 2004/09/09 · openalex publication_date 2005/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present high-precision measurements of the Nusselt number \cal N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number σ = 4.4 ) with a diameter D of 49.7 cm and heights L = 116.3, 74.6 , and 50.6 cm, as well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Γ ≡ D/L = 0.28, 0.43, 0.67 , and 0.98 the data cover a range of a little over a decade of R . The maximum R ≃ 1012 and Nusselt number \cal N ≃ 600 were reached for Γ = 0.43 and D = 49.7 . The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of \cal N∞ for plates with infinite conductivity. The results for \cal N∞ and Γ ≥ 0.43 are nearly independent of Γ . For Γ = 0.275 \cal N∞ falls about 2.5% below the other data. For R \lesssim 1011 , the effective exponent γ_\hbox\scriptsize\it eff of \cal N∞ = N0 R^γ_\hbox\scriptsize\it eff is about 0.32, larger than those of the Grossmann–Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for Γ = 0.98, 0.67, and 0.43, γ_\hbox\scriptsize\it eff saturates at the asymptotic value γ = 1/3 of the Grossmann–Lohse model. The data do not reveal any crossover to a Kraichnan regime with γ_\hbox\scriptsize\it eff > 1/3 .