We present an experimental study of turbulent Rayleigh-Bénard 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 (4)He gas of Prandtl number Pr≈1, with the aim of resolving existing contradictions in Nusselt (Nu) versus Rayleigh number (Ra) scaling. For 7.2×10(6)≤Ra≤10(11) our data agree with suitably corrected data from similar cryogenic experiments and are consistent with Nu∝Ra(2/7). On approaching Ra≈10(11) our data display a crossover to Nu∝Ra(1/3) that approximately holds up to Ra=4.6×10(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≥10(11) cannot be explained due to the difference in Pr, but seem to depend also on experimental details.

The heat transfer efficiency in turbulent Rayleigh-Bénard convection is investigated experimentally, in a cylindrical cell of height 0.3 m, diameter 0.3 m. We show that for Rayleigh numbers 10(12) < or approximately equal to Ra < or approximately equal to 10(15) the Nusselt number closely follows Nu is proportional to Ra(1/3 if the mean temperature of the working fluid-cryogenic helium gas-is measured by small sensors directly inside the cell at about half of its height. In contrast, if the mean temperature is determined in a conventional way, as an arithmetic mean of the bottom and top plate temperatures, the Nu(Ra) is proportional to Ra(γ) displays spurious crossover to higher γ that might be misinterpreted as a transition to the ultimate Kraichnan regime.

We present experimental results on the heat transfer efficiency of cryogenic turbulent Rayleigh-Bénard convection (RBC) in a cylindrical cell 0.3 m in both diameter and height which has improvements with respect to various corrections connected with finite thermal conductivity of sidewalls and plates. The heat transfer efficiency described by the Nusselt number Here H is the total convective heat flux density, g stands for the acceleration due to gravity, and ΔT is the temperature difference between the parallel top and the bottom plates separated by the vertical distance L. The properties of the working fluid are characterized by the thermal conductivity, λ, and by the combination α νκ ( ) , where α is the isobaric thermal expansion, ν is the kinematic viscosity, and κ denotes the thermal diffusivity. New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al 4 New J. Phys. 16 (2014) 053042 P Urban et al 5 3 Note that our Brno cryogenic data recently published in two Letters [43, 44] are erroneously treated by the authors as aspect ratio Γ = 1 2 data, while they have all been obtained for the Γ = 1 cell. New J. Phys. 16 (2014) 053042 P Urban et al 6 Figure 1. Schematic drawing of the helium cryostat [55] containing the cylindrical aspect ratio Γ = 1 RBC cell. New J. Phys. 16 (2014) 053042 P Urban et al 7 W K 1 25 38 50 New J. Phys. 16 (2014) 053042 P Urban et al 9 Pr Pr Ra c c c (white filled red circles). The black line illustrates the slope ∝ Pr Ra 0.5 . New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al 13 New J. Phys. 16 (2014) 053042 P Urban et alWe thank many colleagues for help and stimulating discussions, especially S Babuin, X He, M Jackson, R du Puits, P-E Roche, J Salort, and D Schmoranzer. This work was supported by the GAČR 203/12/P897, and the work of MLM and LS by GAČR P203/11/0442. Appendix. Tabulated experimental dataIn tables A1 and A2, values of Ra corr and Nu corr represent the corrected data, with corrections applied as discussed in the text. All remaining values of Rayleigh, Prandtl and Nusselt numbers are not corrected in any way.New J. Phys. 16 (2014) 053042 P Urban et al

An important question in turbulent Rayleigh-Bénard convection is the scaling of the Nusselt number with the Rayleigh number in the so-called ultimate state, corresponding to asymptotically high Rayleigh numbers. A related but separate question is whether the measurements support the so-called Kraichnan law, according to which the Nusselt number varies as the square root of the Rayleigh number (modulo a logarithmic factor). Although there have been claims that the Kraichnan regime has been observed in laboratory experiments with low aspect ratios, the totality of existing experimental results presents a conflicting picture in the highRayleigh-number regime. We analyse the experimental data to show that the claims on the ultimate state leave open an important consideration relating to non-Oberbeck-Boussinesq effects. Thus, the nature of scaling in the ultimate state of Rayleigh-Bénard convection remains open.

Published experiments on natural turbulent convection in cryogenic (4)He gas show contradictory results in the values of Rayleigh number (Ra) higher than 10(11). This paper describes a new helium cryostat with a cylindrical cell designed for the study of the dependence of the Nusselt number (Nu) on the Rayleigh number (up to Ra approximately 10(15)) in order to help resolve the existing controversy among published experimental results. The main part of the cryostat is a cylindrical convection cell of 300 mm in diameter and up to 300 mm in height. The cell is designed for measurement of heat transfer by natural convection at pressures ranging from 100 Pa to 250 kPa and at temperatures between 4.2 and 12 K. Parasitic heat fluxes into the convection medium are minimized by using thin sidewalls of the bottom and top parts of the cell. The exchangeable central part of the cell enables one to modify the cell geometry.