Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger

Abstract

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number σ = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Γ ≡ D/L ≃ 1 (L is the sample height). In addition, we present data for D = 49.7 and Γ = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For Γ ≃ 1 they jointly span the range 10Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the side walls on the heat transport in the fluid to obtain estimates of N ∞ for plates with infinite conductivity and sidewalls of zero conductivity. For Γ ≃ 1 the effective exponent γ ef f of N ∞ = N 0 R γ ef f ranges from 0.28 near R = 10 8 to 0.333 near R ≃ 7 × 10 10 . For R < ∼ 10 10 the results are consistent with the Grossmann-Lohse model. For larger R, where the data indicate that N ∞ (R) ∼ R 1/3 , the theory has a smaller γ ef f than 1/3 and falls below the data. The data for Γ > 1 are only a few percent smaller than the Γ = 1 results.

Laboratory-numerical models of rapidly rotating convection in planetary cores

“…Such scalings have been predicted theoretically and confirmed experimentally over wide ranges of parameter space (e.g. Rossby 1969;Castaing et al 1989;Glazier et al 1999;Funfschilling et al 2005). There are two well-known Nu ∼ Ra α scaling regimes of RBC heat transfer that are accessible with our experiments.…”

“…This scaling exponent of α = 0.284 is in good agreement with a 2/7 law. Beyond Ra = 10 10 , the data from the 80 and 160 cm tanks and Funfschilling et al (2005) rise more sharply than the α 2/7 green-dashed line. Instead, our 80 and 160 cm tank data then give a best-fitting scaling law of…”

“…The effective buoyancy force, Ra, is plotted on the x-axis; the resulting convective heat transfer, Nu, is plotted on the y-axis. Data from our 80 and 160 cm tall tank experiments are shown as purple-filled circles and diamonds, respectively, and are shown in comparison with data sets from previous RBC studies of Rossby (1969), Funfschilling et al (2005) and . The dashed green line N u = (0.162 ± 0.006)Ra 0.284±0.002 (14)…”

“…Laboratory Rayleigh-Bénard convection (RBC) heat transfer data alongside earlier data from Rossby (1969), Funfschilling et al (2005) and . The black-bordered yellow star denotes case V shown in Fig.…”

Prandtl-, Rayleigh-, and Rossby-Number Dependence of Heat Transport in Turbulent Rotating Rayleigh-Bénard Convection

“…[20]. Since the previous measurements [21] it had been completely dis-and reassembled. It had copper top and bottom plates, and a new plexiglas side wall of thickness 0.32 cm was installed for the current project.…”