Heat Transfer in Turbulent Rayleigh-Benard Convection below the Ultimate Regime

P. -E. Roche; B. Castaing; B. Chabaud; B. Hebral

doi:10.1023/B:JOLT.0000016727.23228.78

paper

Heat Transfer in Turbulent Rayleigh-Benard Convection below the Ultimate Regime

arXiv:cond-mat/0307518 · doi:10.1023/B:JOLT.0000016727.23228.78

Abstract

A Rayleigh-BÃ©nard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range $0.7 < P r < 21$ and for the full range of soft and hard turbulences, up to Rayleigh number $R a ≃ 1 0^{11}$ . 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 $d iam e t er / h e i g h t = 0.5$ . The effective heat transfer $N u (R a, P r)$ 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 $N u (R a)$ dependence exhibits a bimodality of the flow with $4 - 7$ difference in $N u$ for given $R a$ and $P r$ . Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the $N u (P r)$ dependence is very small or null : the absolute value of the average logarithmic slope $(d l n N u / d l n P r)_{R a}$ is smaller than 0.03 in our range of $P r$ , which allows to disciminate between contradictory experiments [Ashkenazi \textit{et al.}, Phys. Rev.Lett. 83:3641 (1999)][Ahlers \textit{et al.}, Phys.Rev.Lett. 86:3320 (2001)].

submitted for publication to JLTP (august 2003)