Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container^(a)

¹ Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, J. M. Burgers Center for Fluid Dynamics and MESA+ Research Institute, Department of Science and Technology, University of Twente - P.O. Box 217, 7500 AE Enschede, The Netherlands
² Dipartimento di Ingegneria Industriale, University of Rome “Tor Vergata” - Via del Politecnico 1, Roma 00133, Italy
³ Gran Sasso Science Institute - Viale F. Crispi, 7, 67100 L'Aquila, Italy
⁴ Max Planck Institute, for Dynamics and Self- Organization - Am Fassberg 17, 37077 Göttingen, Germany

^(b) r.hartmann@utwente.nl (corresponding author)
^(c) d.lohse@utwente.nl

Received: 14 April 2021
Accepted: 2 August 2021

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 , given as height-over-width aspect ratio. The explored parameter range is , for the Rayleigh number, and a Prandtl number of . We find that both the optimal confinement parameter 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 .