Heat transfer in turbulent Rayleigh-Bénard convection below the ultimate regime

A Rayleigh-Benard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range 0.7 < Pr < 21 and for the full range of soft and hard turbulences, up to Rayleigh number Ra ~- 10 11. The set-up benefits from the favourable characteristics of cryogenic helium-4 in fluid mechanics, in situ fluid property measurements, and special care on thermometry and calorimetric instrumentation. The cell is cylindrical with diameter/height = 0.5. The effective heat transfer Nu(Ra, Pr) has been measured with unprecedented accuracy for cryogenic turbulent convection experiments in this range of Rayleigh numbers. Spin-off of this study include improved fits of helium thermodynamics and viscosity properties. Three main results were found. First the Nu(Ra) dependence exhibits a bimodality of the flow with 4-7% difference in Nu for given Ra and Pr. Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the Nu(Pr) dependence is very small or null: the absolute value of the average logarithmic slope (d In Nul d In Pr)Ra is smaller than 0.03 in our range of Pr, which allows to discriminate between experiments with contradictory results.