Heat Transfer in Turbulent Rayleigh–Bénard Convection Below the Ultimate Regime

A Rayleigh–Bénard 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≃1011. 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 ln Nu/d ln Pr)Ra is smaller than 0.03 in our range of Pr, which allows to discriminate between experiments with contradictory results [Ashkenazi et al., Phys. Rev. Lett.83, 3641 (1999)] [Ahlers et al., Phys. Rev. Lett.86, 3320 (2001)].