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Effects of Prandtl number in quasi-two-dimensional Rayleigh–Bénard convection
Published online by Cambridge University Press: 16 March 2021
Abstract
We report an experimental study of the Prandtl-number effects in quasi-two-dimensional (quasi-2-D) Rayleigh–Bénard convection. The experiments were conducted in four rectangular convection cells over the Prandtl-number range of $11.7 \leqslant Pr \leqslant 650.7$ and over the Rayleigh-number range of
$6.0\times 10^8 \leqslant Ra \leqslant 3.0\times 10^{10}$. Flow visualization reveals that, as
$Pr$ increases from 11.7 to 145.7, thermal plumes pass through the central region much less frequently and their self-organized large-scale motion is more confined along the periphery of the convection cell. The large-scale flow is found to break down for higher
$Pr$, resulting in a regime transition in the Reynolds number
$Re$. For the
$Pr$ range with a large-scale flow of system size, the
$Re$ number, Nusselt number
$Nu$ and local temperature fluctuations were investigated systematically. It is found that
$Re$ scales as
$Re \sim Ra^{0.58}Pr^{-0.82}$ in the present geometry, which suggests that it is in line with the behaviour in the 2-D configuration. On the other hand, the measured
$Nu(Ra, Pr)$ relation
$Nu \sim Ra^{0.289}Pr^{-0.02}$ tends to be compatible with the finding in a three-dimensional (3-D) system. For the temperature fluctuations in the cell centre and near the sidewall, they exhibit distinct
$Ra$-dependent scalings that could not be accounted for with existing theories, but their
$Pr$ dependences for
$Pr \lesssim 50$ are in agreement with the predictions by Grossmann & Lohse (Phys. Fluids, vol. 16, 2004, pp. 4462–4472). These results enrich our understanding of quasi-2-D thermal convection, and its similarities and differences compared to 2-D and 3-D systems.
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- © The Author(s), 2021. Published by Cambridge University Press
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