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

Published online by Cambridge University Press:  20 July 2018

Stephan Weiss Open the ORCID record for Stephan Weiss [Opens in a new window] ,
Xiaozhou He ,
Guenter Ahlers ,
Eberhard Bodenschatz  and
Olga Shishkina Open the ORCID record for Olga Shishkina [Opens in a new window]
Stephan Weiss
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
Xiaozhou He
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, China
Guenter Ahlers
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany Department of Physics, University of California, Santa Barbara, CA 93106, USA
Eberhard Bodenschatz
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany Institute for Nonlinear Dynamics, Georg-August-University Göttingen, 37073 Göttingen, Germany Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Olga Shishkina*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Convection: Convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , pp. 374 - 390
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Copyright
© 2018 Cambridge University Press 

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