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Aspect ratio dependence of heat transport by turbulent Rayleigh–Bénard convection in rectangular cells

Published online by Cambridge University Press:  28 August 2012

Quan Zhou ,
Bo-Fang Liu ,
Chun-Mei Li  and
Bao-Chang Zhong
Quan Zhou*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Bo-Fang Liu
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Chun-Mei Li
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Bao-Chang Zhong
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
*
†Email address for correspondence: qzhou@shu.edu.cn
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Abstract

We report high-precision measurements of the Nusselt number as a function of the Rayleigh number in water-filled rectangular Rayleigh–Bénard convection cells. The horizontal length and width of the cells are 50.0 and 15.0 cm, respectively, and the heights , 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios , , , , , and . The measurements were carried out over the Rayleigh number range and the Prandtl number range . Our results show that for rectangular geometry turbulent heat transport is independent of the cells’ aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where is found to be in general a decreasing function of , at least for and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of for plates with perfect conductivity. The local scaling exponents of are calculated and found to increase from 0.243 at to 0.327 at .

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 260 - 276
Copyright
Copyright © Cambridge University Press 2012

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