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

Abstract

We report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh-Bénard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 cm and 15.0 cm, respectively, and the heights $H=49.9$, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios $({\Gamma }_x\equiv L/H,{\Gamma }_y\equiv W/H)=(1,0.3)$, $(2,0.6)$, $(4,1.2)$, $(7.3,2.2)$, $(14.3,4.3)$, and $(20.8,6.3)$. The measurements were carried out over the Rayleigh number range $6\times 10^5\lesssim Ra\lesssim 10^{11}$ and the Prandtl number range $5.2\lesssim Pr\lesssim 7$. 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 $Nu$ is found to be in general a decreasing function of $\Gamma$, at least for $\Gamma =1$ 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 $N{u}_{\infty }$ for plates with perfect conductivity. The local scaling exponents ${\beta }_l$ of $N{u}_{\infty }\sim R{a}^{{\beta }_l}$ are calculated and found to increase from 0.243 at $Ra\simeq 9\times 10^5$ to 0.327 at $Ra\simeq 4\times 10^{10}$.

15 pages, 7 figures, Accepted by Journal of Fluid Mechanics

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• Turbulent thermal superstructures in Rayleigh-Bénard convection
• Scaling of large-scale quantities in Rayleigh-Bénard convection
• Coherence of temperature and velocity superstructures in turbulent Rayleigh-Bénard flow
• Complexity of viscous dissipation in turbulent thermal convection
• Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection