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Prandtl number dependence of Nusselt number in direct numerical simulations

Published online by Cambridge University Press:  20 October 2000

ROBERT M. KERR  and
JACKSON R. HERRING
ROBERT M. KERR
Affiliation:
Geophysical Turbulence Program, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA
JACKSON R. HERRING
Affiliation:
Geophysical Turbulence Program, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA
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Abstract

The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 419 , 25 September 2000 , pp. 325 - 344
Copyright
© 2000 Cambridge University Press

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