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Phase Change with Convection: Modelling and Validation pp 127–170Cite as

Natural Convection at a Solid-Liquid Phase Change Interface

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Part of the book series: International Centre for Mechanical Sciences ((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.

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Bibliography

  • C. Beckermann and R. Viskanta. Double-diffusive convection due to melting. Int. J. Heat Mass Transfer, 31: 2077–2089, 1988.

    Article  Google Scholar 

  • A. Bejan. Mass and heat transfer by natural convection in a vertical cavity. Int. J. Heat Fluid Flow, 6 (3): 149–159, 1985.

    Article  Google Scholar 

  • A. Bejan. Convection heat transfer. (2nd Edition) Wiley, 1995.

    Google Scholar 

  • C. Bénard, R. Bénard, R. Bennacer, and D. Gobin. Melting driven thermosolutal convection. Physics of Fluids, 8 (1): 112–130, 1996.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • R. F. Bergholz. Instability of steady natural convection in a vertical fluid layer. J. Fluid Mech., 84: 743–768, 1978.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  MATH  Google Scholar 

  • J. Crank. Free and Moving Boundary Problems. Clarendon Press, 1984.

    Google Scholar 

  • J. A. Dantzig. Modelling liquid-solid phase-changes with melt convection. Int. J. Num. Methods Engin., 28: 1769–1785, 1989.

    Article  MathSciNet  Google Scholar 

  • G. de Vahl Davis and G. D. Mallinson. A note on natural convection in a vertical slot. J. Fluid Mech., 72: 87–93, 1975.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • J. W. Elder. Laminar free convection in a vertical slot. J. Fluid Mech., 23: 77–98, 1965.

    Article  Google Scholar 

  • M. C. Flemings. Solidification Processing. McGraw-Hill, New York, 1974.

    Google Scholar 

  • G. Z. Gershuni and E. M. Zhukhovvitskii. Convective stability of incompressible fluids. Israel Program for Scientific Translations, 1976.

    Google Scholar 

  • A. E. Gill. The boundary-layer regime for convection in a rectangular cavity. J. Fluid Mech., 26: 515–536, 1966.

    Article  Google Scholar 

  • A. E. Gill and A. Davey. Instabilities in a buoyancy system. J. Fluid Mech., 35: 775–798, 1969.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • T. R. Goodman. Applications of integral methods to transient non linear heat transfer. Adv. in Heat Transfer, pages 51–122, 1964.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • J. M. Hill. One-dimensional Stefan Problems: an Introduction. Longman Scientific and Technical, 1987.

    Google Scholar 

  • H. E. Huppert and J. S. Turner. Melting icebergs. Nature, 271: 46–48, 1978.

    Article  Google Scholar 

  • P. Jany and A. Bejan. Scaling theory of melting with natural convection in an enclosure. Int. J. Heat Mass Transfer, 31: 1221–1235, 1988.

    Article  Google Scholar 

  • C.G. Jeevaraj and J. Imberger. Experimental study of double-diffusive instability in sidewall heating. J. Fluid Mech., 222: 565–586, 1991.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • W. Kurz and D. J. Fisher. Fundamentals of Solidification. Trans Tech. Publications, 4th edition, 1998.

    Google Scholar 

  • H. G. Landau. Heat conduction in a melting solid. Quart. Applied Math., 8: 81–94, 1950.

    MATH  Google Scholar 

  • P. LeQuéré and D. Gobin. A note on possible flow instabilities in melting from the side. Int. J. Thermal Sc., 38: 595–600, 1999.

    Article  Google Scholar 

  • J. S. Lim and A. Bejan. The prandtl number effect on melting dominated by natural convection. J. Heat Transfer, 114: 784–787, 1992.

    Article  Google Scholar 

  • S. Ostrach. Natural convection in enclosures. Adv. in Heat Transfer, 8:161–227, 1972.

    Google Scholar 

  • S. V. Patankar. Numerical heat transfer and fluid flow. Hemisphere, 1980.

    Google Scholar 

  • J. Patterson and J. Imberger. Unsteady natural convection in a rectangular cavity. J. Fluid Mech., 100: 65–86, 1980.

    Article  MATH  Google Scholar 

  • K. A. Rathjen and L. M. Jiji. Heat conduction with melting or freezing in a corner. J. Heat Transfer, 93: 101–109, 1971.

    Article  Google Scholar 

  • L. I. Rubinstein. The stefan problem. Transl. Math. Monographs, 27: 231–338, 1971.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • A. W. Woods. Melting and dissolving. J. Fluid Mechanics, 239: 429–448, 1992.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. FAST (UMR 7608), Campus Universitaire, Bât. 502, 91405, Orsay, France

    Dominique Gobin

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  1. Dominique Gobin
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Editor information

Editors and Affiliations

  1. Academy of Sciences Warsaw, Poland

    Tomasz A. Kowalewski

  2. Campus Universitaire Orsay, France

    Dominique Gobin

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© 2004 Springer-Verlag Wien

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Gobin, D. (2004). Natural Convection at a Solid-Liquid Phase Change Interface. In: Kowalewski, T.A., Gobin, D. (eds) Phase Change with Convection: Modelling and Validation. International Centre for Mechanical Sciences, vol 449. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2764-3_3

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  • DOI: https://doi.org/10.1007/978-3-7091-2764-3_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-20891-5

  • Online ISBN: 978-3-7091-2764-3

  • eBook Packages: Springer Book Archive

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