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Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity

Published online by Cambridge University Press:  07 October 2009

FENG XU ,
JOHN C. PATTERSON  and
CHENGWANG LEI
FENG XU*
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
JOHN C. PATTERSON
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
CHENGWANG LEI
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity, which includes a lower intrusion under the fin, a starting plume bypassing the fin and a thermal flow entrained into the vertical thermal boundary layer downstream of the fin in a typical case, are investigated using a scaling analysis and direct numerical simulations. The obtained scaling relations show that the thickness and velocity of the transient natural convection flows around the fin are determined by different dynamic and energy balances, which can be either a buoyancy-viscous balance or a buoyancy-inertial balance, depending on the Rayleigh number, the Prandtl number and the fin length. A time scale of the transition from a buoyancy-viscous flow regime to a buoyancy-inertial flow regime is obtained. The major scaling relations quantifying the transient natural convection flows are also validated by direct numerical simulations. In general, there is a good agreement between the scaling predictions and the corresponding numerical results.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 639 , 25 November 2009 , pp. 261 - 290
Copyright
Copyright © Cambridge University Press 2009

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