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 (Γx ,Γy ) varying between (1...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 (Γx ,Γy ) 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 6x105<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∞=0.025Ra0.357+0.525Ra0.168 , 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 Ⅱu and Ⅳu regimes of the GL model. Furthermore, a clear transition from the Ⅱu regime to the Ⅳu regime with increasing Ra is revealed.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.11222222, 11161160554 and 11002085)Innovation Program of Shanghai Municipal Education Commission (Grant No.13YZ008)Shanghai Program for Innovative Research Team in Universities
文摘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 (Γx ,Γy ) 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 6x105<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∞=0.025Ra0.357+0.525Ra0.168 , 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 Ⅱu and Ⅳu regimes of the GL model. Furthermore, a clear transition from the Ⅱu regime to the Ⅳu regime with increasing Ra is revealed.
