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Effect of Prandtl number on heat transport enhancement in Rayleigh-Bénard convection under geometrical confinement

Kai Leong Chong1, Sebastian Wagner2, Matthias Kaczorowski1, Olga Shishkina2, and Ke-Qing Xia1,*

  • 1Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
  • 2Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany

  • *kxia@cuhk.edu.hk
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Phys. Rev. Fluids 3, 013501 – Published 9 January, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.013501

Abstract

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Bénard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number Pr, 0.1≤Pr≤40, with the Rayleigh number Ra fixed at 108. The width-to-height aspect ratio Γ spans between 0.025 and 0.25, while the length-to-height aspect ratio is fixed at one. We first find that for Pr≥0.5, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number Nu. For those cases, Nu is maximal at a certain Γ=Γopt and the maximal relative enhancement generally increases with Pr over the explored parameter range. As opposed to the situation of Pr≥0.5, confinement-induced enhancement in Nu is not realized for smaller values of Pr, such as 0.1 and 0.2. The Pr dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger Pr due to a smaller thermal diffusivity. We further show that Γopt is closely related to the crossing of thermal and momentum BLs and find that Nu declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and two-dimensional mode decomposition, it is found that for smaller Pr the large-scale circulation is robust against the geometrical confinement of the convection cell. We further found that Γopt exhibits a power-law relation with Pr as Γopt=0.11Pr−0.060±0.004. Together with the result Γopt=29.37Ra−0.31 found by Chong et al. [Phys. Rev. Lett. 115, 264503 (2015)], our findings provide a more complete picture of the geometrical confinement.

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Phys. Rev. Fluids 3, 013501– Published 9 January, 2018
  • Received 5 September 2017
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