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Relation between Nusselt number and Rayleigh number in turbulent thermal convection

Published online by Cambridge University Press:  29 March 2006

Robert R. Long
Robert R. Long
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
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Abstract

A theory is developed for the dependence of the Nusselt number on the Rayleigh number in turbulent thermal convection in horizontal fluid layers. The theory is based on a number of assumptions regarding the behaviour in the molecular boundary layers and on the assumption of a buoyancy-defect law in the interior analogous to the velocity-defect law in flow in pipes and channels. The theory involves an unknown constant exponent s and two unknown functions of the Prandtl number. For either s = ½ or s = 1/3, corresponding to two different theories of thermal convection, and for a given Prandtl number, constants can be chosen to give excellent agreement with existing data over nearly the whole explored range of Rayleigh numbers in the turbulent case. Unfortunately, comparisons with experiment do not permit a definite choice of s, but consistency with the chosen form of the buoyancy-defect law seems to suggest s = 1/3, corresponding to similarity theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 3 , 10 February 1976 , pp. 445 - 451
Copyright
© 1976 Cambridge University Press

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