Heat transport in turbulent Rayleigh-Bénard convection: Effect of finite top- and bottom-plate conductivities

Physics of Fluids

Volumn 17, Issue 7, 2005, Pages 1-10

  Brown, Eric ^a   Nikolaenko, Alexei ^a   Funfschilling, Denis ^a   Ahlers, Guenter ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALUMINUM; HEAT CONVECTION; HEAT RESISTANCE; HEAT TRANSFER; MEASUREMENT THEORY; NUSSELT NUMBER; THERMAL CONDUCTIVITY;

FINITE CONDUCTIVITY; HIGH-PRECISION MEASUREMENTS; RAYLEIGH NUMBERS; THERMAL SOURCES;

TURBULENT FLOW;

HEAT TRANSFER;

EID: 13844278651     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1964987     Document Type: Article

References (29)

1. See, for instance, E. D. Siggia, "High Rayleigh number convection," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/ annurev.fluid.26.1.137 26, 137 (1994) for early work.
2. L. Kadanoff, "Turbulent heat flow: Structures and scaling," Phys. TodayPHTOAD0031-9228 54(8), 34 (2001).
3. G. Ahlers, S. Grossmann, and D. Lohse, "Hochpräzision im Kochtopf," Physik Journal 1, 31 (2002).
4. S. Grossmann and D. Lohse, "Scaling in thermal convection: A unifying theory," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112099007545 407, 27 (2000).
5. S. Grossmann and D. Lohse, "Thermal convection for large Prandtl numbers," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.86.3316 86, 3316 (2001).
6. S. Grossmann and D. Lohse, "Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.66.016305 66, 016305 (2002).
7. G. Ahlers, "Effect of sidewall conductance on heat-transport measurements for turbulent Rayleigh-Bénard convection," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.63.015303 63, 015303(R) (2001).
8. P. Roche, B. Castaing, B. Chabaud, B. Hebral, and J. Sommeria, "Side wall effects in Rayleigh-Bénard experiments," Eur. Phys. J. BEPJBFY1434-602810.1007/s10051-001-8690-5 24, 405 (2001).
9. R. Verzicco, "Sidewall finite-conductivity effects in confined turbulent thermal convection," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112002002501 473, 201 (2002).
10. J. J. Niemela and K. R. Sreenivasan, "Confined turbulent convection," J. Fluid Mech.JFLSA70022-112010.1017/S0022112003004087 481, 355 (2003).
11. S. Chaumat, B. Castaing, and F. Chillá, in Advances in Turbulence IX, Proceedings of the Ninth European Turbulence Conference, edited by I. P. Castro and P. E. Hancock (CIMNE, Barcelona, 2002).
12. R. Verzicco, "Effects of nonperfect thermal sources in turbulent thermal convection," Phys. FluidsPHFLE61070-663110.1063/1.1723463 16, 1965 (2004).
13. G. Ahlers, D. S. Cannell, L. I. Berge, and S. Sakurai, "Thermal Conductivity of the Nematic Liquid Crystal 5CB," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.49.545 49, 545 (1994).
14. A. Nikolaenko and G. Ahlers, "Nusselt number measurements for turbulent Rayleigh-Bénard convection," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.91.084501 91, 084501 (2003).
15. A. Nikolaenko, E. Brown, D. Funfschilling, and G. Ahlers, "Heat transport by turbulent Rayleigh-Bénard Convection in cylindrical cells with aspect ratio one and less," J. Fluid Mech. JFLSA70022-1120 523, 251 (2005);
16. D. Funfschilling, E. Brown, A. N. Kolaenko, and G. Ahlers, "Heat transport by turbulent Rayleigh-Bénard Convection in cylindrical cells with aspect ratio one and larger," J. Fluid Mech.JFLSA70022-1120 (in press).
17. For the medium apparatus a circular area of a diameter of 24.8 cm was covered by parallel heater grooves of width of 0.30 cm and depth of 0.78 cm speed 0.51 cm apart. The heater wire was tetflon-covered AWG18 nichrome C and had a resistance of 12.8 Ω
18. General Magnaplate, 1331 Route 1, Linden, N.J. 07036.
19. P.-E. Roche, B. Castaing, B. Chabaud, and B. Hébral, "Heat transfer in turbulent Rayleigh-Bénard convection below the ultimate regime," J. Low Temp. Phys.JLTPAC0022-229110.1023/ B:JOLT.0000016727.23228.78 134, 1011 (2004).
20. R. Verzicco and R. Camussi, "Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell," J. Fluid Mech.JFLSA70022-112010.1017/S0022112002003063 477, 19 (2003).
21. We used Neslab RTE 740 temperature controlled circulations with a temperature stability of 0.01° C and a cooling capacity of 200 W. At the largest heat currents supplementary cooling of the circulating water was provided
22. For the medium apparatus the channel width and depth were 0.95 and 2.54 cm, respectively and the spacing between adjacent arms was 1.9 cm
23. We used Fenwall 120-503JAJ-Q01 thermistors with a nominal resistance of 50 kω at 25°C
24. X. Xu, K. M. S. Bajaj, and G. Ahlers, "Heat transport in turbulent Rayleigh-Bénard convection," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.84.4357 84, 4357 (2000).
25. G. Ahlers and X. Xu, "Prandtl-number Dependence of Heat Transport in Turbulent Rayleigh-Bénard Convection," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.86.3320 86, 3320 (2001).
26. 2 pressed against the sapphire window with a very thin layer of gylcerol in between, was measured to be 0.0286 K/W. The bottom-plate and sapphire contributions were estimated to have a thickness of 5μm and in that case would contribute about 0.003 K/W (if gylcerol had not been used and air had been between the plates, the air resistance would have dominated). This leaves about 0.009 K/W for the thermal resistance in the water bath between the top of the sapphire plate and the thermometer. The uncertainty of this result is quite large due mostly to the uncertainty of the thickness of the gylcerol layer. The original data of Ref. 7 were renanalyzed with this correction. The results differ slightly from those originally reported
27. X.-D. Shang, X.-L. Qiu, P. Tong, and K.-Q. Xia, "Measured local heat transport in turbulent Rayleigh-Bénard convection," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.074501 90, 074501 (2003).
28. S. Grossmann and D. Lohse, "Fluctuations in Rayleigh-Bénard convection: The role of plumes," Phys. FluidsPHFLE61070-663110.1063/ 1.1807751 16, 4462 (2004).
29. X.-Z. Wu and A. Libchaber, "Scaling relations in thermal turbulence: The aspect-ratio dependence," Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.45.842 45, 842 (1992).