https://doi.org/10.1140/epjp/s13360-023-04672-0
Regular Article
Effects of aspect ratio on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq effects in glycerol
1
Department of Mathematics, Shanghai University, 200444, Shanghai, China
2
School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, 03722, Seoul, Korea
3
Newtouch Center for Mathematics of Shanghai University, Shanghai University, 200444, Shanghai, China
Received:
28
June
2023
Accepted:
8
November
2023
Published online:
11
December
2023
This study investigates the non-Oberbeck–Boussinesq (NOB) Rayleigh–Bénard convection inside a two-dimensional rectangular cavity for a fluid with a high Prandtl number (
). The parametric study focuses on the aspect ratio (
, 
) dependence of heat transfer and fluid flows on the Rayleigh number (Ra) ranging from 
to 
and an NOB assumption with a temperature difference (
) of up to 50 K. We numerically find that the critical Ra (Ra
) for convection onset decreases as increases for small , while it increases as increases for large . Four flow regimes are classified based on kinetic and thermal energy dissipation rates in the –Ra plane. The aspect ratio dependency of the Nusselt number (Nu), Reynolds number (Re), and top and bottom thermal boundary layer (BL) thicknesses (
) is also investigated under both OB and NOB conditions. It is found that the effect on Re (up to 61%) is more serious than that on Nu (up to 4.5%), while does not obviously affect the generality of the classical NOB effects on scaling exponents of Nu, Re, and for fully chaotic regimes. Top–bottom asymmetry is confirmed, where the top BL is always thicker than the bottom one, and their ratio is up to 1.8 for 
K at 
. Although 
increases with an NOB effect enhancement for all aspect ratios, the compensation between 
and 
leads to small deviation (up to 7.0%) of from unity. This contributes to the robustness of Nu because it is confirmed that the NOB effects on Nu are dominated by the change in .
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
