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

By D. Funfschilling, Eric Brown, A. Nikolaenko, G. Ahlers. Journal of Fluid Mechanics, 2005

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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 $\sigma \,{=}\, 4.38$) with diameters $D \,{=}\, 49.7, 24.8,$ and 9.2cm, all with aspect ratio $\Gamma \,{\equiv}\, D/L \,{\simeq}\,1$ ($L$ is the sample height). In addition, we present data for $D \,{=}\, 49.7$ and $\Gamma \,{=}\, 1.5, 2, 3,$ and 6. For each sample the data cover a range of a little over a decade of $R$. For $\Gamma \,{\simeq}\,1$ they jointly span the range $10^7 \lesssim R \lesssim 10^{11}$. Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the sidewalls on the heat transport in the fluid to obtain estimates of $\cal{N}_{\infty}$ for plates with infinite conductivity and sidewalls of zero conductivity. For $\Gamma \,{\simeq}\,1$ the effective exponent $\gamma_{\hbox{\scriptsize\it eff}}$ of ${\cal N}_{\infty} \,{=}\, N_0 R^{\gamma_{\hbox{\scriptsize\it eff}}}$ ranges from 0.28 near $R \,{=}\, 10^8$ to 0.333 near $R \,{\simeq}\,7\,{\times}\,10^{10}$. For $R \lesssim 10^{10}$ the results are consistent with the Grossmann–Lohse model. For larger $R$, where the data indicate that ${\cal N}_\infty(R) \,{\sim}\, R^{1/3}$, the theory has a smaller $\gamma_{\hbox{\scriptsize\it eff}}$ than $1/3$ and falls below the data. The data for $\Gamma \,{>}\, 1$ are only a few percent smaller than the $\Gamma \,{=}\, 1$ results.

Subfields: Biomedical Engineering, Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/0787b57cbe630af45795a490be2e7d08232ee787

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Citations in the corpus

Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection (2009, background): “…are controversial (Heslot, Castaing & Libchaber 1987; Chavanne et al. 1997; Niemela et al. 2000, 2001; Roche et al. 2002; Niemela & Sreenivasan 2003; Funfschilling et al. 2005; Nikolaenko et al. 2005; Funfschilling, Bodenschatz & Ahlers 2009), so that the asymptotic behavior of Nu(Ra) is yet…”
The unifying theory of scaling in thermal convection: the updated prefactors (2013, methodology): “To provide information about the Ra-scaling we selected the measurements of Funfschilling et al. (2005) at Ra = 1.8× 107 and Ra = 2.25× 1010 with Pr = 4.38.”
Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection (2005, methodology): “However, we have corrected for tiny systematic errors in the data as discussed already by Funfschilling et al. (2005) (due primarily to errors in the geometry), which can be different for different cells, by a fraction of a percent by overlapping the Nusselt numbers (through tiny shifts) of the…”
Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection (2008, methodology): “The Nusselt number for Pr ≃ 4.38 obtained using water as the fluid For Pr ≃ 4.4 and Γ = 1.00 high-accuracy measurements of Nu (Funfschilling et al. (2005)) for 107 <∼ Ra <∼ 1011 using water and copper plates are shown in Fig.”
Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection (2010, background): “Third, Funfschilling et al. (2005) did not observe any sensitivity of the heat transfer on the aspect ratio.”
Scaling regimes in spherical shell rotating convection (2016, background): “The heat transport is not characterised by one single scaling exponent αeff but rather exhibits continuous changes, similarly to what is observed in classical RBC (e.g. Grossmann & Lohse 2000; Funfschilling et al. 2005).”