Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T07:27:00.207Z Has data issue: false hasContentIssue false
  • English
  • Français

High-Rayleigh-number convection in a horizontal enclosure

Published online by Cambridge University Press:  26 April 2006

R. J. Goldstein ,
H. D. Chiang  and
D. L. See
R. J. Goldstein
Affiliation:
Department of Mechanical Engineering, University of Minnesota. Minneapolis, MN 55455, USA
H. D. Chiang
Affiliation:
Textron Lycoming, Stratford, CT 06497, USA
D. L. See
Affiliation:
Canterra Energy Ltd, Calgary, Alberta T2P 2K7, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

A review of the literature on natural convection in a horizontal layer heated from below shows the need for reliable data at high Rayleigh number (Ra) to determine the asymptotic Nusselt number (Nu) variation with Rayleigh number. The present study expands the data base by the use of an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc). The results of the present study give Sh = 0.0659 $Ra^{frac{1}{3}}$ for Sc ≈ 2750, 3 × 109 < Ra < 5 × 1012. Using the heat-mass transfer analogy, this indicates the high Prandtl number variation of Nu with Ra.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 111 - 126
Copyright
© 1990 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.)

References

Ahlers, G. 1974 Low-temperature studies of the Rayleigh—Bénard instability and turbulence. Phys. Rev. Lett. 33, 1185–1188.Google Scholar
Arpaci, V. S. 1986 Microscales of turbulence and heat transfer correlations. Intl J. Heat Mass Transfer 29, 1071–1078.Google Scholar
Busse, F. H. 1969 On Howard's upper bound for heat transport by turbulent convection. J. Fluid Mech. 33, 457–477.Google Scholar
Canuto, V. M. & Goldman, I. 1985 Analytical model for large-scale turbulence. Phys. Rev. Lett. 54, 430–433.Google Scholar
Chan, S.-K. 1971 Infinite Prandtl number turbulent convection. Stud. Appl. Maths 50, 13–49.Google Scholar
Chang, Y. P. 1957 A theoretical analysis of heat transfer in natural convection and in boiling. Trans. ASME 79, 1501–1513.Google Scholar
Chiang, H. D. & Goldstein, R. J. 1990 Application of the electrochemical mass transfer technique to the study of buoyancy-driven flows. (Submitted for publication.)
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent natural convection in a horizontal water layer heated from below. J. Fluid Mech. 60, 141–159.Google Scholar
Deardorff, J. W. 1965 A numerical study of pseudo three-dimensional parallel-plate convection. J. Atmos. Sci. 22, 419–435.Google Scholar
Deardorff, J. W. & Willis, G. E. 1965 The effect of two-dimensionality on the suppression of thermal turbulence. J. Fluid Mech. 23, 337–353.Google Scholar
Dropkin, D. & Somerscales, E. 1965 Heat transfer by natural convection in liquids confined by two parallel plates which are inclined at various angles with respect to the horizontal. Trans. ASME C: J. Heat Transfer 87, 77–84.Google Scholar
Fitzjarrald, D. E. 1976 An experimental study of turbulent convection in air. J. Fluid Mech. 73, 693–719.Google Scholar
Fromm, J. E. 1965 Numerical solutions of the non-linear equations for a heated fluid layer. Phys. Fluids 8, 1757–1769.Google Scholar
Garon, A. M. & Goldstein, R. J. 1973 Velocity and heat transfer measurements in thermal convection. Phys. Fluids 16, 1818–1825.Google Scholar
Globe, S. & Dropkin, D. 1959 Natural convection heat transfer in liquids confined by two horizontal plates and heated from below. Trans. ASME 81, 24–28.Google Scholar
Goldstein, R. J., Chiang, H. D. & Sayer, E. 1987 Natural convection mass transfer in an inclined enclosure at high Rayleigh number. 2nd Intl Symp. on Transport Phenomena in Turbulent Flows, Tokyo, October 25–29, 1987.
Goldstein, R. J. & Chu, T. Y. 1969 Thermal convection in a horizontal layer of air. Prog. Heat Mass Transfer 2, 55–75.Google Scholar
Goldstein, R. J. & Tokuda, S. 1980 Heat transfer by thermal convection at high Rayleigh numbers. Intl J. Heat Mass Transfer 23, 738–740.Google Scholar
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975 Modal equation for cellular convection. J. Fluid Mech. 68, 695–719.Google Scholar
Herring, J. R. 1964 Investigation of problems in thermal convection: rigid boundaries. J. Atmos. Sci. 21, 277–290.Google Scholar
Heslot, F., Castaing, B. & Libchaber, A. 1987 Transitions to turbulence in helium gas.. Phys. Rev. A 36, 5870–5873.Google Scholar
Hollands, K. G. T., Raithby, G. D. & Konicek, L. 1975 Correlation equations for free convection heat transfer in horizontal layer of air and water. Intl J. Heat Mass Transfer 18, 879–884.Google Scholar
Howard, L. N. 1963 Heat transport by turbulent convection. J. Fluid Mech. 17, 405–432.Google Scholar
Howard, L. N. 1966 Convection at high Rayleigh number. Proc. 11th Intl Congr. on Appl. Mech., pp. 1109–1115.Google Scholar
Howard, L. N. & Krishnamurti, R. 1986 Large-scale flow in turbulent convection: a mathematical model. J. Fluid Mech. 170, 385–410.Google Scholar
Jakob, M. 1946 Free heat convection through enclosed plane gas layers. Trans. ASME 68, 189–193.Google Scholar
Koschmieder, E. L. & Pallas, S. G. 1974 Heat transfer through a shallow, horizontal convecting fluid layer. Intl J. Heat Mass Transfer 17, 991–1002.Google Scholar
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 1374–1389.Google Scholar
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Lipps, F. B. 1976 Numerical simulation of three-dimensional Bénard convection in air. J. Fluid Mech. 75, 113–148.Google Scholar
Long, R. R. 1976 Relation between Nusselt number and Rayleigh number in turbulent thermal convection. J. Fluid Mech. 73, 445–451.Google Scholar
Malkus, W. V. R. 1954a Discrete transition in turbulent convection. Proc. R. Soc. Lond. A225, 185–195.Google Scholar
Malkus, W. V. R. 1954b The heat transport and spectrum of thermal turbulence.. Proc. R. Soc. Lond. A 225, 196–212.Google Scholar
Mizushina, T. 1971 The electrochemical method in transport phenomena. Adv. Heat Transfer 7, 87–161.Google Scholar
Mull, W. & Reiher, H. 1930 Der Warmeschutz van Luftschichten. Beihefte zum Gesundheits-Ingenieur 1, 28. Munich & Berlin.Google Scholar
Newman, J. S. 1973 Electrochemical Systems. Prentice-Hall.
Roberts, P. H. 1966 On non-linear Bénard convection. In Non-Equilibrium Thermodynamics, Variational Techniques, and Stability (ed. R. Donnelly, R. Hermann & I. Prigogine), pp. 125–162. University of Chicago Press.
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Schmidt, E. & Silveston, P. L. 1959 Natural convection in horizontal liquid layer. Chem. Engng Prog. Symp. Ser. 55, 163–169.Google Scholar
Selman, J. R. & Tobias, C. W. 1978 Mass transfer measurements by the limiting current technique. Adv. Chem. Engng 10, 211–318.Google Scholar
Somerscales, E. F. C. & Gazda, I. W. 1968 Thermal convection in high Prandtl number liquids at high Rayleigh numbers. Rensselaer Polytechnic Inst. ME Rep. HT-5.Google Scholar
Sparrow, E. M., Husar, R. B. & Goldstein, R. J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793–800.Google Scholar
Spiegel, E. A. 1962 On the Malkus theory of turbulence In Mécanique de la Turbulence, edition du CNRS Paris, pp. 181–201.
Spiegel, E. A. 1967 The theory of turbulent convection. 28th IAU Symp., pp. 348–366. Academic.
Strauss, J. M. 1976 On the upper bounding approach to thermal convection of moderate Rayleigh number, II. Rigid boundaries. Dyn. Atmos. Oceans 1, 77–90.Google Scholar
Tanaka, H. & Miyata, H. 1980 Turbulent natural convection in a horizontal water layer heated from below. Intl J. Heat Mass Transfer 23, 1273–1281.Google Scholar
Threlfall, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 17–28.Google Scholar
Townsend, A. A. 1959 Temperature fluctuations over a heated horizontal surface. J. Fluid Mech. 5, 209–241.Google Scholar
Townsend, A. A. 1962 Remarks on the Malkus theory of turbulent flow In Mécanique de la Turbulence, edition du CNRS Paris, pp. 167–180.
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transitions of Malkus. Phys. Fluids 10, 1861–1866.Google Scholar
Wragg, A. A. 1977 Application of the limiting diffusion current technique in chemical engineering. Chem. Engnr (Lond.) 316, 39–44. Review articles and papersGoogle Scholar
Adrian, R. J., Ferreira, R. T. D. S. & Boberg, T. 1986 Turbulent thermal convection in wide horizontal fluid layers. Expt Fluids 4, 121–141.Google Scholar
Busse, F. H. 1978a The optimum theory of turbulence. Adv. Appl. Mech. 18, 77–121.Google Scholar
Busse, F. H. 1978b Non-linear properties of thermal convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Busse, F. H. 1981 Transition to turbulence in Rayleigh — Bénard convection In Hydrodynamic Instabilities and Transition to Turbulence. Springer.
Catton, I. 1978 Natural convection in enclosures. Proc. 6th Intl Heat Transfer Conf. Toronto 6, 13–31.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Denton, R. A. & Wood, I. R. 1979 Turbulent convection between two horizontal plates. Intl J. Heat Mass Transfer 22, 1339–1346.Google Scholar
Gershuni, G. Z. & Zhukovitskii, E. M. 1976 Convective Stability of Incompressible Fluids (trans. from Russian by D. Louvish). Jerusalem: Keter.
Joseph, D. D. 1976 Stability of Fluid Motions, vols 1 and 2. Springer.
Koschmeider, E. L. 1974 Bénard convection. Adv. Chem. Phys. 26, 177–212.Google Scholar
Normand, C., Pomeau, Y. & Velarde, M. G. 1977 Convective instability: a physicist's approach. Rev. Mod. Phys. 49, 581–624.Google Scholar
Palm, E. 1975 Nonlinear thermal convection. Ann. Rev. Fluid Mech. 7, 39–61.Google Scholar
Priestley, C. H. B. 1959 Turbulent Transfer in the Lower Atmosphere. University of Chicago Press.
Raithby G. D. & Hollands, K. G. T. 1985 Natural convection In Handbook of Heat Transfer Fundamentals, 2nd edn. ch. 6.
Segel, L. A. 1966 Non-linear hydrodynamic stability theory and its applications to thermal convection and curved flows. In Non-Equilibrium Thermodynamics, Variational Techniques and Stability (ed. R. Donnelly, R. Herman & I. Prigogine), pp. 165–197. University of Chicago Press.
Spiegel, E. A. 1971 Convection in stars: I. Basic Boussinesq convection. Ann. Rev. Astro. Astrophys. 9, 323–352.Google Scholar
Spiegel, E. A. 1972 Convection in stars: II. Special effects. Ann. Rev. Astro. Astrophys. 10, 261–304.Google Scholar
Sutton, O. G. 1953 Micrometerology. McGraw-Hill.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.