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 similar or equal to 1 (L is the sample height). In addition, we present data for D = 49.7 and F = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For F similar or equal to 1 they jointly span the range 10(7) less than or similar to R less than or similar to 10(11). Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the sidewalls 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 similar or equal to 1 the effective exponent gamma(eff) of N-infinity = N0R (gamma eff) ranges from 0.28 near R = 10(8) to 0.333 near R similar or equal to 7 x 10(10). For R less than or similar to 10(10) the results are consistent with the Grossmann-Lohsc model. For larger R, where the data indicate that N-infinity,(R) similar to R-1/3 the theory has a smaller gamma(eff) than 1/3 and falls below the data. The data for F > 1 are only a few percent smaller than the F = 1 results.