Hostname: page-component-7dd5485656-glrdx Total loading time: 0 Render date: 2025-10-29T16:20:28.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent convection in a horizontal layer of water

Published online by Cambridge University Press:  29 March 2006

T. Y. Chu  and
R. J. Goldstein
T. Y. Chu
Affiliation:
Western Electric Co. Inc., Engineering Research Center, Princeton, New Jersey
R. J. Goldstein
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis
Get access Rights & Permissions [Opens in a new window]

Abstract

Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra0·278 in the range 2·76 × 105 < Ra < 1·05 × 108. Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107. Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 105) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z−2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z−1 power law is also found.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 141 - 159
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Busse, F. H. 1969 On Howard's upper bound for heat transport by turbulent convection J. Fluid Mech. 37, 457.Google Scholar
Catton, I. 1966 Natural convection in horizontal fluid layers Phys. Fluids, 9, 2521.Google Scholar
Catton, I. & Edwards, D. K. 1967 Effect of side walls on natural convection between horizontal plates heated from below J. Heat Transfer, 89, 295.Google Scholar
Chu, T. Y. 1971 Thermal convection in horizontal liquid layers. Ph.D. thesis, University of Minnesota.
Deardorff, J. W. 1965 A numerical study of pseudo three-dimensional parallel-plate convection J. Atmos. Sci. 22, 419.Google Scholar
Deardorff, J. W. & Willis, G. E. 1967a Investigation of turbulent convection between horizontal plates J. Fluid Mech. 28, 675.Google Scholar
Deardorff, J. W. & Willis, G. E. 1967b The free-convection temperature profile Quart. J. Roy. Met. Soc. 93, 166.Google Scholar
Garon, A. 1970 Velocity measurements in turbulent thermal convection using a laserdoppler technique. Ph.D. thesis, University of Minnesota.
Globe, S. & Dropkin, D. 1959 Natural convection heat transfer in liquids confined by two horizontal plates and heated from below J. Heat Transfer, 81, 24.Google Scholar
Goldstein, R. J. & Chu, T. Y. 1969 Thermal convection in a horizontal layer of air Prog. Heat & Mass Transfer, 2, 55.Google Scholar
Herring, J. R. 1963 Investigation of problems in thermal convection J. Atmos. Sci. 20, 325.Google Scholar
Herring, J. R. 1964 Investigation of problems in thermal convection: rigid boundaries. J. Atmos. Sci. 21, 227.Google Scholar
Howard, L. N. 1963 Heat transport by turbulent convection J. Fluid Mech. 17, 405.Google Scholar
Kraichnan, R. J. 1962 Mixing-length analysis of turbulent thermal convection at arbitrary Prandtl numbers Phys. Fluids, 5, 1374.Google Scholar
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. Roy. Soc. A 225, 185.Google Scholar
Malkus, W. V. R. 1954b The heat transfer and spectrum of thermal turbulence. Proc. Roy. Soc. A 225, 196.Google Scholar
O'Toole, J. L. & Silveston, P. L. 1961 Correlation of convective heat transfer in confined horizontal layers. Chem. Engng Progr. Symp. 32 (ser. 57), 81.Google Scholar
Rossby, H. T. 1966 An experimental study of Bénard convection with and without rotation. Dept. Geol. Geophys. M.I.T. Sci. Rep. HRF/SR27.Google Scholar
Silveston, P. L. 1958 Wärmedurchgang in Waagrechten Flüssigkeiksschichten Forsch. Ing, Wes. 24, 29.Google Scholar
Sommerscales, E. F. C. & Dropkin, D. 1966 Experimental investigation of the temperature distribution in a horizontal layer of fluid heated from below Int. J. Heat Mass Transfer, 9, 1189.Google Scholar
Sommerscales, E. F. C. & Gazda, I. W. 1969 Thermal convection in high Prandtl number liquids at high Rayleigh numbers Int. J. Heat Mass Transfer, 12, 1491.Google Scholar
Sparrow, E. M., Goldstein, R. J. & Jansson, V. 1964 Thermal instability in a horizontal fluid layer; effect of boundary conditions and non-linear temperature profile J. Fluid Mech. 18, 513.Google Scholar
Tilton, L. W. & Taylor, J. K. 1938 Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60°C Nat. Bur. Stand. J. Res. 20, 419.Google Scholar
Townsend, A. A. 1959 Temperature fluctuations over a heated surface J. Fluid Mech. 5, 209.Google Scholar
Veronis, G. 1966 Large-amplitude Bénard convection. J. Fluid Mech. 26, 49.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transitions or Malkus Phys. Fluids, 10, 1861.Google Scholar