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Convection in a long box driven by heating and cooling on the horizontal boundaries

Published online by Cambridge University Press:  26 April 2006

J. J. Sturman ,
G. N. Ivey  and
J. R. Taylor
J. J. Sturman
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia
G. N. Ivey
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia
J. R. Taylor
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia Present address: Australian Defense Force Academy, Northcott Drive, Campbell, ACT 2601, Australia.
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Abstract

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 310 , 10 March 1996 , pp. 61 - 87
Copyright
© 1996 Cambridge University Press

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