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Abstract

Moderate spatial confinement enhances the heat transfer in turbulent RayleighB´enard (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−1
opt 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−1
opt.