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Natural Convection at a Solid-Liquid Phase Change Interface

  • Dominique Gobin
Part of the International Centre for Mechanical Sciences book series (CISM, volume 449)

Abstract

In this course “Phase Change and Convection — Modelling and Validation”, the influence of convection on solid-liquid phase change processes is considered at different levels. The local effects of convection at the local scale on dendritic growth is addressed in the chapter by G. Amberg and the scaling-up from the local equations to the averaged macroscopic equations in a mushy zone is presented in the chapter by P. Furmanski. The present chapter deals with the interaction between a “smooth” phase change interface and laminar natural convection in the melt. It addresses the main features of solid-liquid phase change in situations where the interface between the solid and the liquid phase is clearly defined. The presentation is focused on the consequence of buoyancy forces in the liquid phase on heat and mass transfer at a solid-liquid interface through convective flows: thermal natural convection for pure substances, or thermosolutal convection in multi-component fluids.

Keywords

Heat Transfer Nusselt Number Natural Convection Prandtl Number Rayleigh Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. C. Beckermann and R. Viskanta. Double-diffusive convection due to melting. Int. J. Heat Mass Transfer, 31: 2077–2089, 1988.CrossRefGoogle Scholar
  2. A. Bejan. Mass and heat transfer by natural convection in a vertical cavity. Int. J. Heat Fluid Flow, 6 (3): 149–159, 1985.CrossRefGoogle Scholar
  3. A. Bejan. Convection heat transfer. (2nd Edition) Wiley, 1995.Google Scholar
  4. C. Bénard, R. Bénard, R. Bennacer, and D. Gobin. Melting driven thermosolutal convection. Physics of Fluids, 8 (1): 112–130, 1996.CrossRefGoogle Scholar
  5. C. Bénard, D. Gobin, and A. Zanoli. Moving boundary problem: heat conduction in the solid phase of a phase-change material during melting driven by natural convection in the liquid. Int. J. Heat Mass Transfer, 29: 1669–1681, 1986.CrossRefGoogle Scholar
  6. R. Bennacer and D. Gobin. Cooperating thermosolutal convection in enclosures: 1. Scale analysis and mass transfer. Int. J. Heat Mass Transfer, 39 (13): 2671–2681, 1996.CrossRefMATHGoogle Scholar
  7. R. F. Bergholz. Instability of steady natural convection in a vertical fluid layer. J. Fluid Mech., 84: 743–768, 1978.CrossRefGoogle Scholar
  8. O. Bertrand, B. Binet, H. Combeau, S. Couturier, Y. Delannoy, D. Gobin, M. Lacroix, P. LeQuéré, M. Medale, J. Mencinger, H. Sadat, and G. Vieira. Melting driven by natural convection–a comparison exercise: first results. Int. J. Thermal Sc., 38: 5–26, 1999.CrossRefGoogle Scholar
  9. B. Caroli, C. Caroli, and B. Roulet. Instabilities of Planar Solidification Fronts, chapter 2 of Solids far from Equilibrium, pages 155–296. Cambridge University Press, 1992.Google Scholar
  10. C. F. Chen, D. G. Briggs, and R. A. Wirtz. Stability of thermal convection in a salinity gradient due to lateral heating. Int. J. Heat Mass Transfer, 14: 57–65, 1971.CrossRefMATHGoogle Scholar
  11. J. Crank. Free and Moving Boundary Problems. Clarendon Press, 1984.Google Scholar
  12. J. A. Dantzig. Modelling liquid-solid phase-changes with melt convection. Int. J. Num. Methods Engin., 28: 1769–1785, 1989.MathSciNetCrossRefGoogle Scholar
  13. G. de Vahl Davis and G. D. Mallinson. A note on natural convection in a vertical slot. J. Fluid Mech., 72: 87–93, 1975.CrossRefMATHGoogle Scholar
  14. E.R.G. Eckert and W.O. Carlson. Natural convection in an air layer enclosed between two vertical plates with different temperatures. Int. J. Heat Mass Transfer, 2: 106–120, 1961.CrossRefGoogle Scholar
  15. J. W. Elder. Laminar free convection in a vertical slot. J. Fluid Mech., 23: 77–98, 1965.CrossRefGoogle Scholar
  16. M. C. Flemings. Solidification Processing. McGraw-Hill, New York, 1974.Google Scholar
  17. G. Z. Gershuni and E. M. Zhukhovvitskii. Convective stability of incompressible fluids. Israel Program for Scientific Translations, 1976.Google Scholar
  18. A. E. Gill. The boundary-layer regime for convection in a rectangular cavity. J. Fluid Mech., 26: 515–536, 1966.CrossRefGoogle Scholar
  19. A. E. Gill and A. Davey. Instabilities in a buoyancy system. J. Fluid Mech., 35: 775–798, 1969.CrossRefMATHGoogle Scholar
  20. D. Gobin and C. Bénard. Melting of metals driven by natural convection in the melt: influence of the prandtl and rayleigh numbers. J. Heat Transfer, 114: 521–524, 1992.CrossRefGoogle Scholar
  21. D. Gobin and P. LeQuéré. Melting from an isothermal vertical wall. synthesis of a numerical comparison exercise. Comp. Assist. Mech. Eng. Sc., 7–3: 289–306, 2000.Google Scholar
  22. T. R. Goodman. Applications of integral methods to transient non linear heat transfer. Adv. in Heat Transfer, pages 51–122, 1964.Google Scholar
  23. J.C. Grondin and B. Roux. Recherche de corrélations simples exprimant les pertes convectives dans une cavité bidimensionnelle, inclinée, chauffée différentiellement. Rev. Phys. Appl., 14: 49–56, 1979.CrossRefGoogle Scholar
  24. J. M. Hill. One-dimensional Stefan Problems: an Introduction. Longman Scientific and Technical, 1987.Google Scholar
  25. H. E. Huppert and J. S. Turner. Melting icebergs. Nature, 271: 46–48, 1978.CrossRefGoogle Scholar
  26. P. Jany and A. Bejan. Scaling theory of melting with natural convection in an enclosure. Int. J. Heat Mass Transfer, 31: 1221–1235, 1988.CrossRefGoogle Scholar
  27. C.G. Jeevaraj and J. Imberger. Experimental study of double-diffusive instability in sidewall heating. J. Fluid Mech., 222: 565–586, 1991.CrossRefGoogle Scholar
  28. S. A. Korpela, D. Gözüm, and C. B. Baxi. On the stability of the conduction regime of natural convection in a vertical slot. Int. J. Heat Mass Transfer, 16: 1683–1690, 1973.CrossRefGoogle Scholar
  29. W. Kurz and D. J. Fisher. Fundamentals of Solidification. Trans Tech. Publications, 4th edition, 1998.Google Scholar
  30. H. G. Landau. Heat conduction in a melting solid. Quart. Applied Math., 8: 81–94, 1950.MATHGoogle Scholar
  31. P. LeQuéré and D. Gobin. A note on possible flow instabilities in melting from the side. Int. J. Thermal Sc., 38: 595–600, 1999.CrossRefGoogle Scholar
  32. J. S. Lim and A. Bejan. The prandtl number effect on melting dominated by natural convection. J. Heat Transfer, 114: 784–787, 1992.CrossRefGoogle Scholar
  33. S. Ostrach. Natural convection in enclosures. Adv. in Heat Transfer, 8:161–227, 1972.Google Scholar
  34. S. V. Patankar. Numerical heat transfer and fluid flow. Hemisphere, 1980.Google Scholar
  35. J. Patterson and J. Imberger. Unsteady natural convection in a rectangular cavity. J. Fluid Mech., 100: 65–86, 1980.CrossRefMATHGoogle Scholar
  36. K. A. Rathjen and L. M. Jiji. Heat conduction with melting or freezing in a corner. J. Heat Transfer, 93: 101–109, 1971.CrossRefGoogle Scholar
  37. L. I. Rubinstein. The stefan problem. Transl. Math. Monographs, 27: 231–338, 1971.Google Scholar
  38. S. Thangam, A. Zebib, and C. F. Chen. Transition from shear to sideways diffusive instability in a vertical slot. J. Fluid Mech., 112: 151, 1981.CrossRefMATHGoogle Scholar
  39. A. W. Woods. Melting and dissolving. J. Fluid Mechanics, 239: 429–448, 1992.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Dominique Gobin
    • 1
  1. 1.FAST (UMR 7608)Campus UniversitaireOrsayFrance

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