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

Chini, Gregory P.; Cox, Stephen M.

Authors

Gregory P. Chini

Stephen M. Cox stephen.cox@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Jan 1, 2009
Journal Physics of Fluids
Print ISSN 1070-6631
Electronic ISSN 1070-6631
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 21
APA6 Citation Chini, G. P., & Cox, S. M. (2009). Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions. Physics of Fluids, 21, doi:10.1063/1.3210777
DOI https://doi.org/10.1063/1.3210777
Publisher URL http://pof.aip.org/phfle6/v21/i8/p083603_s1
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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