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Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties

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Weiß,  Stefan
Research Group Clusterdynamik, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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He,  Xiaozhou
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Ahlers,  Guenter
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Bodenschatz,  Eberhard
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Shishkina,  Olga
Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Weiß, S., He, X., Ahlers, G., Bodenschatz, E., & Shishkina, O. (2018). Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties. Jouarnal of Fluid Mechanics, 851, 374-390. doi:10.1017/jfm.2018.507.


Cite as: http://hdl.handle.net/21.11116/0000-0002-710D-1
Abstract
We critically analyse the different ways to evaluate the dependence of the Nusselt number ( Nu) on the Rayleigh number ( 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 Nu/Ra1/3 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.