Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions

Chini, Gregory P.; Cox, Stephen M.

Abstract

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.

Citation

Chini, G. P., & Cox, S. M. (2009). Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions. Physics of Fluids, 21, https://doi.org/10.1063/1.3210777

• Journal Article Type: Article
• Publication Date: Jan 1, 2009
• Deposit Date: Mar 25, 2010
• Publicly Available Date: Mar 25, 2010
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 21
• DOI: https://doi.org/10.1063/1.3210777
• Public URL: https://nottingham-repository.worktribe.com/output/1014271
• Publisher URL: http://pof.aip.org/phfle6/v21/i8/p083603_s1