dorsal/arxiv
View SchemaHeat transport by turbulent Rayleigh-B'enard Convection in cylindrical cells with aspect ratio one and less
| Authors | Alexei Nikolaenko, Eric Brown, Denis Funfschilling, Guenter Ahlers |
|---|---|
| Categories | |
| ArXiv ID | physics/0409052 |
| URL | https://arxiv.org/abs/physics/0409052 |
| DOI | 10.1017/S0022112004002289 |
Abstract
We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number sigma = 4.4) with a diameter D of 49.7 cm and heights L = 116.3, 74.6, and 50.6 cm, as well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Gamma = D/L = 0.28, 0.43, 0.67, and 0.98 the data cover a range of a little over a decade of R. The maximum R ~= 10^12 and Nusselt number N ~= 600 were reached for Gamma = 0.43 and D = 49.7. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of N_infty for plates with infinite conductivity. The results for N_infty and Gamma >= 0.43 are nearly independent of Gamma. For Gamma = 0.275 N_infty falls about 2.5 % below the other data. For R ~<= 10^11, the effective exponent gamma_eff of N_infty = N_0 R^gamma_eff is about 0.321, larger than those of the Grossmann-Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for Gamma = 0.98, 0.67, and 0.43, gamma_eff saturates at the asymptotic value gamma = 1/3 of the Grossmann-Lohse model. The data do not reveal any crossover to a Kraichnan regime with gamma_eff > 1/3.
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"abstract": "We present high-precision measurements of the Nusselt number N as a function\nof the Rayleigh number R for cylindrical samples of water (Prandtl number sigma\n= 4.4) with a diameter D of 49.7 cm and heights L = 116.3, 74.6, and 50.6 cm,\nas well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Gamma = D/L =\n0.28, 0.43, 0.67, and 0.98 the data cover a range of a little over a decade of\nR. The maximum R ~= 10^12 and Nusselt number N ~= 600 were reached for Gamma =\n0.43 and D = 49.7. The data were corrected for the influence of the finite\nconductivity of the top and bottom plates on the heat transport in the fluid to\nobtain estimates of N_infty for plates with infinite conductivity. The results\nfor N_infty and Gamma \u003e= 0.43 are nearly independent of Gamma. For Gamma =\n0.275 N_infty falls about 2.5 % below the other data. For R ~\u003c= 10^11, the\neffective exponent gamma_eff of N_infty = N_0 R^gamma_eff is about 0.321,\nlarger than those of the Grossmann-Lohse model with its current parameters by\nabout 0.01. For the largest Rayleigh numbers covered for Gamma = 0.98, 0.67,\nand 0.43, gamma_eff saturates at the asymptotic value gamma = 1/3 of the\nGrossmann-Lohse model. The data do not reveal any crossover to a Kraichnan\nregime with gamma_eff \u003e 1/3.",
"arxiv_id": "physics/0409052",
"authors": [
"Alexei Nikolaenko",
"Eric Brown",
"Denis Funfschilling",
"Guenter Ahlers"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1017/S0022112004002289",
"title": "Heat transport by turbulent Rayleigh-B\u0027enard Convection in cylindrical cells with aspect ratio one and less",
"url": "https://arxiv.org/abs/physics/0409052"
},
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