• Letter

Heat flux and wall shear stress in large-aspect-ratio turbulent vertical convection

Emily S. C. Ching
Phys. Rev. Fluids 8, L022601 – Published 2 February 2023

Abstract

We present a theoretical analysis of large-aspect-ratio turbulent vertical convection that yields two relationships between heat flux and wall shear stress, measured respectively by the Nusselt number (Nu) and shear Reynolds number (Reτ), in terms of the Rayleigh (Ra) and Prandtl numbers (Pr): Reτ2Nu=f(Pr)Pr1Ra in the high-Ra limit and NuCPrɛReτ with ɛ=1/3 for Pr1 and ɛ=1 for Pr1, where f(Pr) is not a power law of Pr and C is a constant. These relationships imply Nu[C2f(Pr)]1/3Pr(12ɛ)/3Ra1/3 and Reτ[f(Pr)/C]1/3Pr(1+ɛ)/3Ra1/3 for high Ra.

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  • Received 8 September 2022
  • Accepted 20 January 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.L022601

©2023 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Emily S. C. Ching*

  • Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong

  • *ching@phy.cuhk.edu.hk

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Vol. 8, Iss. 2 — February 2023

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