Efficiency of Heat Transfer in Turbulent Rayleigh-Benard Convection

We present an experimental study of turbulent Rayleigh-Benard convection (RBC) in a cylindrical cell of height 0.3 m, diameter 0.3 m. It is designed to minimize the influence of its structure on the convective flow of cryogenic He-4 gas of Prandtl number Pr approximate to 1, with the aim of resolving existing contradictions in Nusselt (Nu) versus Rayleigh number (Ra) scaling. For 7.2 X 10(6) <= Ra less than or similar to 10(11) our data agree with suitably corrected data from similar cryogenic experiments and are consistent with Nu proportional to Ra-2/7. On approaching Ra approximate to 10(11) our data display a crossover to Nu proportional to Ra-1/3 that approximately holds up to Ra congruent to 4.6 X 10(13); there is no sign of a transition to the ultimate Kraichnan regime. Differences in Nu(Ra) scaling observed in similar RBC experiments for Ra greater than or similar to 10(11) cannot be explained due to the difference in Pr, but seem to depend also on experimental details.