Effect of Boundary Layers Asymmetry on Heat Transfer Efficiency in Turbulent Rayleigh-Bénard Convection at Very High Rayleigh Numbers

Abstract

The heat transfer efficiency in turbulent Rayleigh-B\'enard convection is investigated experimentally, in a cylindrical cell of height 0.3 m, diameter 0.3 m. We show that for Rayleigh numbers ${10}^{12}\ensuremath{\lesssim}\mathrm{Ra}\ensuremath{\lesssim}{10}^{15}$ the Nusselt number closely follows $\mathrm{Nu}\ensuremath{\propto}{\mathrm{Ra}}^{1/3}$ 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 $\mathrm{Nu}(\mathrm{Ra})\ensuremath{\propto}{\mathrm{Ra}}^{\ensuremath{\gamma}}$ displays spurious crossover to higher $\ensuremath{\gamma}$ that might be misinterpreted as a transition to the ultimate Kraichnan regime.