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

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Benard 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 10(8). The width-to-height aspect ratio Gamma 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 Gamma = Gamma(opt) 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 Gamma(opt) is closely related to the crossing of thermal and momentum BLs and find thatNu 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 Gamma(opt) exhibits a power-law relation with Pr as Gamma(opt) = 0.11 Pr-0.060 +/- 0.004. Together with the result Gamma(opt) = 29.37 Ra-0.31 found by Chong et al. [Phys. Rev. Lett. 115, 264503 (2015)], our findings provide a more complete picture of the geometrical confinement.