Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container

Abstract

Moderate spatial confinement enhances the heat transfer in turbulent Rayleigh-Bénard (RB) convection (Chong K. L. et al., Phys. Rev. Lett., 115 (2015) 264503). Here, by performing direct numerical simulations, we answer the question how the shape of the RB cell affects this enhancement. We compare three different geometries: a box with rectangular base (i.e., stronger confined in one horizontal direction), a box with square base (i.e., equally confined in both horizontal directions), and a cylinder (i.e., symmetrically confined in the radial direction). In all cases the confinement can be described by the same confinement parameter Γ-1, given as height-over-width aspect ratio. The explored parameter range is 1 ≤ Γ-1 ≤ 64, 107 ≤ Ra ≤ 1010 for the Rayleigh number, and a Prandtl number of Pr = 4.38. We find that both the optimal confinement parameter Γ-1opt for maximal heat transfer and the actual heat transfer enhancement strongly depend on the cell geometry. The differences can be explained by the formation of different vertically coherent flow structures within the specific geometries. The enhancement is largest in the cylindrical cell, owing to the formation of a domain-spanning flow structure at the optimal confinement parameter Γ-1opt.