Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-21T02:00:08.558Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)