F3 Wärmeübertragung bei freier Konvektion: Innenströmungen

  • André ThessEmail author
  • Robert Kaiser
Part of the Springer Reference Technik book series (SRT)


Dies ist ein Kapitel der 12. Auflage des VDI-Wärmeatlas.


  1. 1.
    Incropera, F.P., DeWitt, D.P.: Fundamentals of Heat and Mass Transfer. Wiley, New York (1996)Google Scholar
  2. 2.
    Siggia, E.: High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ahlers, G., Grossmann, S., Lohse, D.: Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81, 503–537 (2009)CrossRefGoogle Scholar
  4. 4.
    Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Dover, New York (1981)zbMATHGoogle Scholar
  5. 5.
    Busse, F.: Transition to turbulence in Rayleigh-Bénard convection. In: Swinney, H.L. (Hrsg.) Gollub JP: Hydrodynamic Instabilities and the Transition to Turbulence (Topics in Applied Physics 45), S. 97–133. Springer, Berlin (1985)Google Scholar
  6. 6.
    Cross, M.C., Hohenberg, P.C.: Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993)zbMATHCrossRefGoogle Scholar
  7. 7.
    Bodenschatz, E., Pesch, W., Ahlers, G.: Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32, 709–778 (2000)zbMATHCrossRefGoogle Scholar
  8. 8.
    Funfschilling, D., Brown, E., Nikolaenko, A., Ahlers, G.: Heat transport by turbulent Rayleigh-Bénard convection in cylindrical samples with aspect ratio one and larger. J. Fluid Mech. 536, 145–154 (2005)zbMATHCrossRefGoogle Scholar
  9. 9.
    Sun, C., Ren, L.Y., Song, H., Xia, K.Q.: Heat transport by turbulent Rayleigh-Bénard convection in 1m diameter cylindrical cells of widely varying aspect ratio. J. Fluid Mech. 542, 165–174 (2005)zbMATHCrossRefGoogle Scholar
  10. 10.
    Nikolaenko, A., Brown, E., Funfschilling, D., Ahlers, G.: Heat transport by turbulent Rayleigh-Bénard convection in cylindrical cells with aspect ratio one and less. J. Fluid Mech. 523, 251–260 (2005)zbMATHCrossRefGoogle Scholar
  11. 11.
    Niemela, J.J., Sreenivasan, K.R.: Confined turbulent convection. J. Fluid Mech. 481, 355–384 (2003)zbMATHCrossRefGoogle Scholar
  12. 12.
    Chavanne, X., Chilla, F., Chabaud, B., Castaing, B., Hebral, B.: Turbulent Rayleigh-Bénard convection in gaseous and liquid helium. Phys. Fluid. 13, 1300–1320 (2001)zbMATHCrossRefGoogle Scholar
  13. 13.
    Cioni, S., Ciliberto, S., Sommeria, J.: Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Glazier, J.A., Segawa, A., Sano, M.: Evidence against ‚ultrahard‘ thermal turbulence at very high Rayleigh numbers. Nature. 398, 307–310 (1999)CrossRefGoogle Scholar
  15. 15.
    Grossmann, S., Lohse, D.: Turbulent thermal convection: a unifying view. J. Fluid Mech. 407, 27–56 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Holling, M., Herwig, H.: Asymptotic analysis of heat transfer in turbulent Rayleigh-Bénard convection. Int. J. Heat Mass Transfer. 49, 1129–1136 (2006)zbMATHCrossRefGoogle Scholar
  17. 17.
    Probert, S.D., Brooks, R.G., Dixon, M.: Heat transfer across rectangular cavities. Chem. Process Eng. Heat Transf. Surv., 35–42 (1970)Google Scholar
  18. 18.
    Hollands, K.G.T., Raithby, G.D., Konicek, L.: Correlation equations for free convection heat transfer in horizontal layers of air and water. Int. J. Heat Mass Transf. 19, 879–884 (1975)CrossRefGoogle Scholar
  19. 19.
    Catton, I., Edwards, D.K.: Effect of side walls on natural convection between horizontal plates heated from below. J. Heat Transf. 89, 295–299 (1967)CrossRefGoogle Scholar
  20. 20.
    Churchill, S.W.: Free convection around immersed bodies. In: Schlünder, E.U. (Hrsg.) Heat Exchanger Design Handbook, Abschn. 2.5.7. Hemispheres Publishing, New York (1983)Google Scholar
  21. 21.
    Wagner, S., Shishkina, O.: Heat flux enhancement by regular surface roughness in turbulent thermal convection. J. Fluid Mech. 763, 109–135 (2015)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Liot, O., Salort, J., Kaiser, R., du Puits, R., Chilla, F.: Boundary layer structure in a rough Rayleigh–Bénard cell filled with air. J. Fluid Mech. 786, 275–293 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Landau, L., Lifshitz, E.: Fluid Mechanics, 2. Aufl. Course of Theoretical Physics. Butterworth-Heinemann, Oxford, Großbritannien (1987)Google Scholar
  24. 24.
    Du, Y.-B., Tong, P.: Turbulent thermal convection in a cell with ordered rough boundaries. J. Fluid Mech. 407, 57–84 (2000)zbMATHCrossRefGoogle Scholar
  25. 25.
    Tisserand, J.-C., Creyssels, M., Gasteuil, Y., Pabiou, H., Gibert, M., Castaing, B., Chilla, F.: Comparison between rough and smooth plates within the same Rayleigh–Bénard cell. Phys. Fluids. 23, 015105 (2011)CrossRefGoogle Scholar
  26. 26.
    Wei, P., Chan, T.-S., Ni, R., Zhao, X.-Z., Xia, K.-Q.: Heat transport properties of plates with smooth and rough surfaces in turbulent thermal convection. J. Fluid Mech. 740, 28–46 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Dropkin, D., Somerscales, E.: 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. 87, 77 (1965)CrossRefGoogle Scholar
  28. 28.
    Hollands, K.G.T., Unny, T.E., Raithby, G.D., Konicek, L.: Free convective heat transfer across inclined air layers. Trans. ASME J. Heat Transf. 98, 189–193 (1976)CrossRefGoogle Scholar
  29. 29.
    Randall, K.R., Mitchell, J.W., El-Wakil, M.M.: Natural convection heat transfer characteristics of flat plate enclosures. Trans. ASME J. Heat Transf. 101, 120–125 (1979)CrossRefGoogle Scholar
  30. 30.
    Hollands, K.G.T., Konicek, L.: Experimental study of the stability of differentially heated inclined air layers. Int. J. Heat Mass Transf. 16, 1467–1476 (1973)CrossRefGoogle Scholar
  31. 31.
    Inaba, H.: Experimental study of natural convection in an inclined air layer. Int. J. Heat Mass Transf. 27, 1127–1139 (1984)CrossRefGoogle Scholar
  32. 32.
    MacGregor, R.K., Emery, A.F.: Free convection through vertical plane layers – moderate and high Prandtl number fluids. Trans. ASME J. Heat Transf. Ser. C. 91, 391–403 (1969)CrossRefGoogle Scholar
  33. 33.
    Yin, S.H., Wung, T.Y., Chen, K.: Natural convection in an air layer enclosed within rectangular cavities. Int. J. Heat Mass Transf. 21, 307–315 (1978)CrossRefGoogle Scholar
  34. 34.
    Markatos, N.C., Pericleous, K.A.: Laminar and turbulent natural convection in an enclosed cavity. Int. J. Heat Mass Transf. 27, 755–772 (1984)zbMATHCrossRefGoogle Scholar
  35. 35.
    Merker, G.P., Mey, S.: Wärmeübergang bei freier Konvektion in seitlich beheizten Rechteckbehältern. Wärme- Stoffübertragung. 22, 291–301 (1988)CrossRefGoogle Scholar
  36. 36.
    Nishimura, T., Shiraishi, M., Nagasawa, F., Kawamura, Y.: Natural convection heat transfer in enclosures with multiple vertical partitions. Int. J. Heat Mass Transf. 31, 1679–1686 (1988)CrossRefGoogle Scholar
  37. 37.
    Bajorek, S.M., Lloyd, J.R.: Experimental investigation of natural convection in partitioned enclosures. J. Heat Transf. 104, 527–532 (1982)CrossRefGoogle Scholar
  38. 38.
    Nansteel, M.W., Greif, R.: Natural convection in undivided and partially divided rectangular enclosures. J. Heat Transf. 103, 623–629 (1981)CrossRefGoogle Scholar
  39. 39.
    Seki, N., Fukusako, S., Yamaguchi, A.: An experimental study of free corrective heat transfer in a parallelogrammic enclosure. J. Heat Transf. 105, 433–439 (1983)CrossRefGoogle Scholar
  40. 40.
    Smart, D.R., Hollands, K.G.T., Raithby, G.D.: Free convection heat transfer across rectangular-called diathermaneous honeycomb. J. Heat Transf. 102, 75–80 (1980)CrossRefGoogle Scholar
  41. 41.
    Itoh, M., Fujita, T., Nishiwaki, N., Hirata, M.: A new method of correlating heat-transfer coefficients for natural convection in horizontal cylindrical annuli. Int. J. Heat Mass Transf. 13, 1364–1368 (1970)CrossRefGoogle Scholar
  42. 42.
    Kühn, T.H., Goldstein, R.J.: Correlating equations for natural convection heat transfer between horizontal circular cylinders. Int. J. Heat Mass Transf. 19, 1126–1134 (1976)Google Scholar
  43. 43.
    Hessami, M.A., Pollard, A., Rowe, R.D., Ruth, D.W.: A study of free convective heat transfer in a horizontal annulus with a large radii ratio. J. Heat Transf. 107, 603–610 (1985)CrossRefGoogle Scholar
  44. 44.
    Projahn, U., Beer, H.: Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. Wärme- Stoffübertragung. 19, 248–254 (1985)CrossRefGoogle Scholar
  45. 45.
    Nagendra, H.R., Tirunarayanan, M.A., Ranachandran, A.: Free convection heat transfer in vertical annuli. Chem. Eng. Sci. 25, 605–610 (1970)CrossRefGoogle Scholar
  46. 46.
    Keyhani, M., Kulacki, F.A., Christensen, R.N.: Free convection in a vertical annulus with constant heat flux on the inner wall. J. Heat Transf. 105, 454–459 (1983)CrossRefGoogle Scholar
  47. 47.
    Prasad, V., Kulacki, F.A.: Free convective heat transfer in a liquid-filled vertical annulus. J. Heat Transf. 107, 596–602 (1985a)CrossRefGoogle Scholar
  48. 48.
    Wright, J.L., Douglas, R.W.: Natural convection in narrow-gap, spherical annuli. Int. J. Heat Mass Transf. 29, 725–739 (1986)zbMATHCrossRefGoogle Scholar
  49. 49.
    Himasekhar, K., Bau, H.H.: Large Rayleigh number convection in a horizontal, eccentric annulus containing saturated porous media. Int. J. Heat Mass Transf. 20, 702–712 (1986)zbMATHGoogle Scholar
  50. 50.
    Prasad, A., Kulacki, F.A.: Free convective heat transfer in a liquid-filled vertical annulus. J. Heat Transf. 107, 596–602 (1985b)CrossRefGoogle Scholar
  51. 51.
    Beckermann, C., Ramadhyami, S., Viskanta, R.J.: Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure. J. Heat Transf. 109, 363–370 (1987)CrossRefGoogle Scholar
  52. 52.
    Inaba, H., Sugawara, M., Blumenberg, J.: Natural convection heat transfer in an inclined porous layer. Int. J. Heat Mass Transf. 31, 1365–1374 (1988)CrossRefGoogle Scholar
  53. 53.
    Jonsson, T., Catton, I.: Prandtl number dependence of natural convection in porous media. J. Heat Transf. 109, 371–377 (1987)CrossRefGoogle Scholar
  54. 54.
    Rao, Y.F., Fukuda, K., Hasegawa, S.: Steady and transient analyses of natural convection in a horizontal porous annulus with the Galerkin method. J. Heat Transf. 109, 919–927 (1987)CrossRefGoogle Scholar
  55. 55.
    Prasad, V.: Numerical study of natural convection in a vertical, porous annulus with constant heat flux on the inner wall. Numer. Heat Transf. 29, 841–853 (1986)Google Scholar
  56. 56.
    Krischer, O., Kast, W.: Trocknungstechnik, Bd. 1. Springer, Berlin (1978)CrossRefGoogle Scholar
  57. 57.
    Acharya, S., Goldstein, R.J.: J. Heat Transf. 107, 855–866 (1985)CrossRefGoogle Scholar
  58. 58.
    Cheung, F.B.: Natural convection in a volumetrically heated fluid layer at high Rayleigh numbers. Int. J. Heat Mass Transf. 20, 499–506 (1977)CrossRefGoogle Scholar
  59. 59.
    Kikuchi, Y., Kawasaki, T., Shioyama, T.: Thermal convection in a horizontal fluid layer heated internally and from below. Int. J. Heat Mass Transf. 25, 363–370 (1982)CrossRefGoogle Scholar
  60. 60.
    Kulacki, F.A., Goldstein, R.J.: Thermal convection in a horizontal fluid layer with uniform volumetric energy sources. J. Fluid Mech. 55, 271–287 (1972)CrossRefGoogle Scholar
  61. 61.
    Lee, J.-H., Goldstein, R.J.: An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources. J. Heat Transf. 110, 345–349 (1988)CrossRefGoogle Scholar
  62. 62.
    Yücel, A., Acharya, S., Williams, M.L.: Natural convection and radiation in a square enclosure. Numer. Heat Transf. 15, 261–278 (1989)CrossRefGoogle Scholar
  63. 63.
    Kim, D.M., Viskanta, R.: Effect of wall conduction and radiation on natural convection in a rectangular cavity. Numer. Heat Transf. 7, 449–470 (1984)zbMATHCrossRefGoogle Scholar
  64. 64.
    Viskanta, R.: Radiative heat transfer. Fortschr. Verfahrenstechn. 22, 51 (1984)Google Scholar
  65. 65.
    Fusegi, T., Farouk, B.: Laminar and turbulent natural convection-radiation interactions in a square enclosure filled with a non-gray gas. Numer. Heat Transf. 15, 303–322 (1989)zbMATHCrossRefGoogle Scholar
  66. 66.
    Siegel, R., Howell, JR., Lohrengel, J.: Wärmeübertragung durch Strahlung, 1 bis 3. Springer, Berlin (1988/1993)Google Scholar
  67. 67.
    Ranganathan, P., Viskanta, R.: Natural convection in a square cavity due to combined driving forces. Numer. Heat Transf. 14, 35–59 (1988)CrossRefGoogle Scholar
  68. 68.
    Trevisan, O.V., Bejan, A.: Combined heat and mass transfer by natural convection in a vertical enclosure. Heat Transf. 109, 104–112 (1987)CrossRefGoogle Scholar
  69. 69.
    Jany, P., Bejan, A.: Scaling theory of melting with natural convection in an enclosure. Int. J. Heat Mass Transf. 31, 1221–1235 (1988)CrossRefGoogle Scholar
  70. 70.
    Lacroix, M.: Computation of heat transfer during melting of a pure substance from an isothermal wall. Numer. Heat Transf. 15B, 191–210 (1989)CrossRefGoogle Scholar
  71. 71.
    Betzel, T., Beer, H.: Solidification and melting heat transfer to an unifexed phase change material (PCM) encapsulated in a horizontal concentric annulus. Wärme- Stoffübertragung. 22, 335–344 (1988)CrossRefGoogle Scholar
  72. 72.
    Riviere, P., Beer, H.: Experimental investigation of melting of unfixed ice in an isothermal enclosure. Int. Commun. Heat Mass Transf. 14, 155–165 (1987)CrossRefGoogle Scholar
  73. 73.
    Patterson, J., Imberger, J.: Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–85 (1980)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für Technische ThermodynamikDeutsches Zentrum für Luft- und Raumfahrt (DLR)StuttgartDeutschland
  2. 2.LöwensteinDeutschland

Section editors and affiliations

  • Thomas Wetzel
    • 1
  1. 1.Institut für Thermische VerfahrenstechnikKarlsruher Institut für Technologie (KIT)KarlsruheDeutschland

Personalised recommendations