Journal of Fluid Mechanics

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

FENG XUa1 p1 c1, JOHN C. PATTERSONa1 and CHENGWANG LEIa1

a1 School of Engineering, James Cook University, Townsville, QLD 4811, Australia

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.

(Received December 24 2008)

(Revised June 29 2009)

(Accepted July 01 2009)

(Online publication October 07 2009)

Correspondence:

c1 Email address for correspondence: f.xu@usyd.edu.au

p1 Present address: School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia.

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