Heat transport by turbulent Rayleigh-Benard Convection in cylindrical samples with aspect ratio one and larger

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 sigma = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Gamma = D/L = 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 = 1 they jointly span the range 10^7 < R < 10^11. Where 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_infinity for plates with infinite conductivity and sidewalls of zero conductivity. For Gamma = 1 the effective exponent gamma_eff of N_infinity = N_0 R^gamma_eff ranges from 0.28 near R = 10^8 to 0.333 near R = 7 times10^10. For R < 10^10 the results are consistent with the Grossmann-Lohse model. For larger R, where the data indicate that N_infinity(R) = R^1/3, the theory has a smaller gamma_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.