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Measurements of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells of widely varying aspect ratios

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Abstract

High-precision measurements of the Nusselt number Nu for Rayleigh-Bénard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (Γ x ,Γ y ) varying between (1, 0.3) and (20.8, 6.3). For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6×105 < Ra<1011. The two implicit equations of the Grossmann-Lohse (GL) model together with the empirical finite conductivity correction factor f(X) were fitted to obtain estimates of Nu ∞ in the presence of perfectly conducting plates, and the obtained Nu ∞ is independent of the cells’ aspect ratios. A combination of two-power-law, Nu ∞ = 0.025Ra 0.357+0.525Ra 0.168, can be used to describe Nu ∞(Ra). The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the II u and IV u regimes of the GL model. Furthermore, a clear transition from the II u regime to the IV u regime with increasing Ra is revealed.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Quan Zhou, Hui Lu, BoFang Liu & BaoChang Zhong

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  1. Quan Zhou
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  2. Hui Lu
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  3. BoFang Liu
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  4. BaoChang Zhong
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Correspondence to Quan Zhou.

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Zhou, Q., Lu, H., Liu, B. et al. Measurements of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells of widely varying aspect ratios. Sci. China Phys. Mech. Astron. 56, 989–994 (2013). https://doi.org/10.1007/s11433-013-5063-z

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  • DOI: https://doi.org/10.1007/s11433-013-5063-z

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