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, , with the Rayleigh number Ra fixed at . The width-to-height aspect ratio spans between 0.025 and 0.25, while the length-to-height aspect ratio is fixed at one. We first find that for , 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 and the maximal relative enhancement generally increases with Pr over the explored parameter range. As opposed to the situation of , 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 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 exhibits a power-law relation with Pr as . Together with the result found by Chong et al. [Phys. Rev. Lett. 115, 264503 (2015)], our findings provide a more complete picture of the geometrical confinement.
5 More- Received 5 September 2017
DOI:https://doi.org/10.1103/PhysRevFluids.3.013501
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