Solidification in Convection-Diffusion

  • V. R. Voller
  • N. C. Markatos
  • M. Cross
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 18)


An energy equation, based on an enthalpy function, representing phase change under convection and diffusion is developed. This equation is easily formulated into the general transport-equation form and its application in the PHOENICS code in the modelling of phase change problems is readily achieved. Two examples of phase change problems are modelled by this approach:
  1. i

    solidification in a square cavity under heat conduction only,

  2. ii

    solidification in a square cavity under heat conduction and natural convection.


A comparison of the PHOENICS results with available analytical solutions and purpose written numerical codes is made.


Porosity Convection Enthalpy 


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  1. 1.
    J Crank ‘Free and Moving Boundary Problems’ Clarendon Press (1984).Google Scholar
  2. 2.
    S V Patankar ‘Numerical Heat Transfer and Fluid Flow’. Hemisphere (1980)Google Scholar
  3. 3.
    V R Voller ‘Interpretation of the enthalpy in a discretised multidimensional region undergoing a phase change’. Int.Comm.Heat Mass Transfer, 10, 323–328 (1983).CrossRefGoogle Scholar
  4. 4.
    V R Voller ‘Implicit finite-difference solutions of the enthalpy formulation of Stefan Problems’. IMA J.Num.Anal. 5, 201–214 (1984).CrossRefMathSciNetGoogle Scholar
  5. 5.
    V R Voller ‘Techniques for accounting for the moving interface in a N C Markatos convection/diffusion phase change and M Cross Numerical Methods in Thermal Problems (Vol.4), (eds.R W Lewis et al) 595–609, Pineridge (1985).Google Scholar
  6. 6.
    N C Markatos ‘Natural convection in an enclosed cavity’ and PDR/CHAM UK/16 (1982). Also in Int.J.Heat Mass Transfer, K A Pericleous Vol.27, No.5, pp.755–772, (1984).Google Scholar
  7. 7.
    K Morgan ‘A numerical analysis of freezing and melting with convection’.Comp.Meth.App.Mech.Eng. 28, 275–284, (1981).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1986

Authors and Affiliations

  • V. R. Voller
    • 1
  • N. C. Markatos
    • 1
  • M. Cross
    • 1
  1. 1.Centre for Numerical Modelling and Process AnalysisThames PolytechnicLondonUK

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