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Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell

Published online by Cambridge University Press:  23 October 2023

Lu Zhang Open the ORCID record for Lu Zhang [Opens in a new window]  and
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]
Lu Zhang
Affiliation:
Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Ke-Qing Xia*
Affiliation:
Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: xiakq@sustech.edu.cn
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Abstract

We report an experimental and numerical study on Rayleigh–Bénard convection in a slender rectangular geometry with the aspect ratio $\varGamma$ varying from 0.05 to 0.3 and a Rayleigh number range of $10^5\leqslant Ra\leqslant 3\times 10^9$. The Prandtl number is fixed at $Pr=4.38$. It is found that the onset of convection is postponed when the convection domain approaches the quasi-one-dimensional limit. The onset Rayleigh number shows a $Ra_c=328\varGamma ^{-4.18}$ scaling for the experiment and a $Ra_c=810\varGamma ^{-3.95}$ scaling for the simulation, both consistent with a theoretical prediction of $Ra_c\sim \varGamma ^{-4}$. Moreover, the effective Nusselt–Rayleigh scaling exponent $\beta =\partial (\log Nu)/\partial (\log Ra)$ near the onset of convection also shows a rapid increase with decreasing $\varGamma$. Power-law fits to the experimental and numerical data yield $\beta =0.290\varGamma ^{-0.90}$ and $\beta =0.564\varGamma ^{-0.92}$, respectively. Near onset, the flow shows a stretched cell structure. In this regime, the velocity and temperature variations in a horizontal cross-section are found to be almost invariant with height in the core region of a slender domain. As the Rayleigh number increases, the system evolves from the viscous dominant regime to a plume-controlled one, a feature of which is enhancement in the heat transport efficiency. Upon further increase of $Ra$, the flow comes back to the classical boundary-layer-controlled regime, in which the quasi-one-dimensional geometry has no apparent effect on the global heat transfer.

JFM classification

Convection: Buoyancy-driven instability
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , R5
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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