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  Mean temperature profiles in turbulent thermal convection

Shishkina, O., Horn, S., Emran, M. S., & Ching, E. S. C. (2017). Mean temperature profiles in turbulent thermal convection. Physical Review Fluids, 2(11): 113502. doi:10.1103/PhysRevFluids.2.113502.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002E-56E4-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-D97F-B
Genre: Journal Article

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 Creators:
Shishkina, Olga1, Author              
Horn, S., Author
Emran, Mohammad Shah1, Author              
Ching, E. S. C., Author
Affiliations:
1Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063287              

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Free keywords: Convection & buoyancy-driven flows; Turbulent convection
 Abstract: To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation including the effects of fluctuations has to be solved. In Shishkina et al. [Phys. Rev. Lett. 114, 114302 (2015)], the thermal BL equation with the fluctuations taken into account as an eddy thermal diffusivity has been solved for large Prandtl-number fluids for which the eddy thermal diffusivity and the velocity field can be approximated, respectively, as a cubic and a linear function of the distance from the plate. In the present work, we make use of the idea of Prandtl's mixing length model and relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal BL equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters for fluids with a general Prandtl number. With a proper choice of the parameters, our predictions of the temperature profiles are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10(7) to 10(9).

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Language(s): eng - English
 Dates: 2017-11-152017-11
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1103/PhysRevFluids.2.113502
 Degree: -

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Title: Physical Review Fluids
Source Genre: Journal
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Pages: 13 Volume / Issue: 2 (11) Sequence Number: 113502 Start / End Page: - Identifier: -