Heat Transport in Turbulent Rayleigh-Benard Convection

We present measurements of the Nusselt number $\mathcal{N}$ as a function of the Rayleigh number $R$ in cylindrical cells with aspect ratios $0.5 \leq \Gamma \equiv D/d \leq 12.8$($D$isthediameterand$d$ the height). We used acetone with a Prandtl number $\sigma =4.0$ for ${10}^5\text{alt}R\text{alt}4\times {10}^{10}$. A fit of a powerlaw $\mathcal{N}={\mathcal{N}}_0{R}^{{\gamma }_{eff}}$ 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 ${\cal N}®$\mathrm{.}For$R > 10^7$theyareconsistentwith${\cal N} = a \sigma^{-1/12} R^{1/4} + b \sigma^{-1/7} R^{3/7}$asproposedbyGrossmannandLohsefor$\sigma \agt 2$.