High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） varying between （...High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） 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 cor- rection factorf（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∞= O.025Ra0.357＋O.525Ra0.168, can be used to de- scribe Nu∞（Ra）. The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.展开更多
We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial data.The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integr...We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial data.The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral operators is obtained.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-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） 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 cor- rection factorf（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∞= O.025Ra0.357＋O.525Ra0.168, can be used to de- scribe Nu∞（Ra）. The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.
基金supported by National Natural Science Foundation of China(Grant No.10325104)the Innovation Program at Chinese Academy of Sciences and National Basic Research Program of China under(Grant No.2011CB808002)
文摘We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial data.The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral operators is obtained.
