Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties. (20th July 2018)

• Record Type: Journal Article
• Authors: Weiss, Stephan; He, Xiaozhou; Ahlers, Guenter; Bodenschatz, Eberhard; Shishkina, Olga
• Is Part Of: Journal of fluid mechanics. Volume 851(2018)
• Page Start: 374
• Page End: 390
• Publication Date: 2018-07-20
• Subjects: Bénard convection, -- convection; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.507
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : We critically analyse the different ways to evaluate the dependence of the Nusselt number ( $\mathit{Nu}$ ) on the Rayleigh number ( $\mathit{Ra}$ ) in measurements of the heat transport in turbulent Rayleigh–Bénard convection under general non-Oberbeck–Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference temperature at which the fluid properties are evaluated. For the case when the fluid properties depend significantly on the temperature and any pressure dependence is insignificant we propose a method to estimate the centre temperature. The theoretical predictions show very good agreement with the Göttingen measurements by He et al. ( New J. Phys., vol. 14, 2012, 063030). We further show too the values of the normalized heat transport $\mathit{Nu}/\mathit{Ra}^{1/3}$ are independent of whether they are evaluated in the whole convection cell or in the lower or upper part of the cell if the correct reference temperatures are used.