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Heat flux in turbulent Rayleigh-Bénard convection: Predictions derived from a boundary layer theory

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Zwirner,  Lukas
Laboratory for Fluid Physics, 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

Tai, N. C., Ching, E. S. C., Zwirner, L., & Shishkina, O. (2021). Heat flux in turbulent Rayleigh-Bénard convection: Predictions derived from a boundary layer theory. Physical Review Fluids, 6: 033501. doi:10.1103/PhysRevFluids.6.033501.


Cite as: https://hdl.handle.net/21.11116/0000-0009-1049-3
Abstract
Using a closed set of boundary layer equations [E. S. C. Ching et al., Phys. Rev. Research 1, 033037 (2019)] for turbulent Rayleigh-Bénard convection, we derive analytical results for the dependence of the heat flux, measured by the Nusselt number (Nu), on the Reynolds (Re) and Prandtl (Pr) numbers and two parameters that measure fluctuations in the regime where the horizontal pressure gradient is negligible. This regime is expected to be reached at sufficiently high Rayleigh numbers for a fluid of any given Prandtl number. In the high-Pr limit, Nu=F1(k1)Re1/2Pr1/3 and, in the low-Pr limit, Nu tends to π−1/2Re1/2Pr1/2, where F1(k1) has a weak dependence on the parameter k1 in the eddy viscosity that measures velocity fluctuations. These theoretical results further reveal a close resemblance of the scaling dependencies of heat flux in steady forced convection and turbulent Rayleigh-Bénard convection and this finding solves a puzzle in our present understanding of heat transfer in turbulent Rayleigh-Bénard convection.