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

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 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 (Γ ₓ ≡ L/ H, Γ y ≡ 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× 10⁵ Ra 10¹¹ 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 $Nu$ 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 ₗ of Nu∞ ~ Ra^β ₗ are calculated and found to increase from 0.243 at Ra 9× 10⁵ to 0.327 at Ra 4× 10¹⁰ .