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Conductive heat flux in measurements of the Nusselt number in turbulent Rayleigh-Bénard convection.

MPS-Authors
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Shiskina,  O.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Weiss,  S.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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

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Citation

Shiskina, O., Weiss, S., & Bodenschatz, E. (2016). Conductive heat flux in measurements of the Nusselt number in turbulent Rayleigh-Bénard convection. Physical Review Fluids, 1(6): 062301(R). doi:10.1103/PhysRevFluids.1.062301.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-B4CB-3
Abstract
We propose a recipe to calculate accurately the Nusselt number Nu in turbulent Rayleigh-Bénard convection, using the measured total heat flux q and known parameters of the fluid and convection cell. More precisely, we present a method to compute the conductive heat flux qˆ, which is a normalization of q in the definition of Nu, for conditions where the fluid parameters may vary strongly across the fluid layer. We show that in the Oberbeck-Boussinesq approximation and also when the thermal conductivity depends exclusively on the temperature, the value of qˆ is determined by simple explicit formulas. For a general non-Oberbeck-Boussinesq (NOB) case we propose an iterative procedure to compute qˆ. Using our procedure, we critically analyze some already conducted and some hypothetical experiments and show how qˆ is influenced by the NOB effects.