Heat Transport in Turbulent Rayleigh-Bénard Convection

Abstract

We present measurements of the Nusselt number $N$ as a function of the Rayleigh number $R$ in cylindrical cells with aspect ratios $0.5\le \Gamma \equiv D/d\le 12.8$ ( $D$ is the diameter and $d$ is the height). We used acetone with a Prandtl number $\sigma =4.0\mathrm{}$ for ${10}^5\lesssim R\lesssim 4\times {10}^{10}$. A fit of a power law $N=N_0{R}^{{\gamma }_{\mathrm{eff}}}$ over limited ranges of $R$ yielded values of ${\gamma }_{\mathrm{eff}}$ from 0.275 near ${R=10\mathrm{}}^7$ to 0.300 near ${R=10\mathrm{}}^{10}$. The data are inconsistent with a single power law for $N\left(R\right)$. For $R>\mathrm{}{10}^7$ they are consistent with $N=a{\sigma }^{-1\mathrm{}/12}{R}^{1/4}+b{\sigma }^{-1\mathrm{}/7}{R}^{3/7}$ as proposed by Grossmann and Lohse for $\sigma \gtrsim 2$.