Heat Transport in Turbulent Rayleigh-Benard Convection

We present measurements of the Nusselt number $\cal N$ as a function of the Rayleigh number $R$ in cylindrical cells with aspect ratios $0.5 \leq \Gamma \equiv D/d \leq 12.8$ ($D$ is the diameter and $d$ the height). We used acetone with a Prandtl number $\sigma = 4.0$ for $10^5 \alt R \alt 4\times10^{10}$. A fit of a powerlaw ${\cal N} = {\cal N}_0 R^{\gamma_{eff}}$ over limited ranges of $R$ yielded values of $\gamma_{eff}$ from 0.275 near $R = 10^7$ to 0.300 near $R = 10^{10}$. The data are inconsistent with a single powerlaw for ${\cal N}(R)$. For $R > 10^7$ they are consistent with ${\cal N} = a \sigma^{-1/12} R^{1/4} + b \sigma^{-1/7} R^{3/7}$ as proposed by Grossmann and Lohse for $\sigma \agt 2$.