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

摘要

We report high-precision measurements of the Nusselt number N 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 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 Γx}=L/ H, Γ y = W/ H)= (1, 0. 3) (2, 0. 6) (4, 1. 2) (7. 3, 2. 2) (14. 3, 4. 3) (20. 8, 6. 3)$. The measurements were carried out over the Rayleigh number range 6 ×10~5 Ra 10~ (11) and the Prandtl number range $5. 2 Pr 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 N is found to be in general a decreasing function of Γ $, at least for Γ = 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 Nu∞ for plates with perfect conductivity. The local scaling exponents β} _(-1) of ∞ ~ R~(β-1) are calculated and found to increase from 0.243 at Ra~ 9 × 1~5 to 0.327 at Ra~ 4× 1~(10).