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Rigid bounds on heat transport by a fluid between slippery boundaries

Published online by Cambridge University Press:  13 July 2012

Jared P. Whitehead  and
Charles R. Doering
Jared P. Whitehead*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Charles R. Doering
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109-1107, USA
*
†Email address for correspondence: [email protected]
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Abstract

Rigorous bounds on heat transport are derived for thermal convection between stress-free horizontal plates. For three-dimensional Rayleigh–Bénard convection at infinite Prandtl number (), the Nusselt number () is bounded according to where is the standard Rayleigh number. For convection driven by a uniform steady internal heat source between isothermal boundaries, the spatially and temporally averaged (non-dimensional) temperature is bounded from below by in three dimensions at infinite and by in two dimensions at arbitrary , where is the heat Rayleigh number proportional to the injected flux.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 241 - 259
Copyright
Copyright © Cambridge University Press 2012

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