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We present high-precision measurements of the Nusselt number N as a functionof 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 = 49.7and Gamma = 1.5, 2, 3, and 6. For each sample the data cover a range of alittle 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 finiteconductivity of the top and bottom plates and of the side walls on the heattransport in the fluid to obtain estimates of N_infinity for plates withinfinite conductivity and sidewalls of zero conductivity. For Gamma = 1 theeffective exponent gamma_eff of N_infinity = N_0 R^gamma_eff ranges from 0.28near R = 10^8 to 0.333 near R = 7 times10^10. For R < 10^10 the results areconsistent with the Grossmann-Lohse model. For larger R, where the dataindicate that N_infinity(R) = R^1/3, the theory has a smaller gamma_eff than1/3 and falls below the data. The data for Gamma > 1 are only a few percentsmaller than the Gamma = 1 results.Comment: 10 pages, 5 figures. Under consideration for publication in J. Fluid  Mec

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