Mathematical Modelling of Phase Change with a Flowing Thin Film

  • Tim G. Myers
  • Sarah L. Mitchell
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


This paper concerns the practical applications and modelling of Stefan problems with a flowing thin liquid layer. The modelling will be discussed in the context of two practically important scenarios, Leidenfrost (when a liquid droplet floats above a hot surface) and contact melting. The governing equations will be derived and then reduced to a more tractable system. Along the way we will introduce an accurate variant of the Heat Balance Integral Method, which allows us to approximate the solution to the Stefan problem on a finite domain. In both cases excellent agreement between the model results and experimental data will be demonstrated.


Phase Change Material Stefan Problem Perturbation Solution Vapour Layer Contact Melting 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Centre de Recerca Matemàtica, Edifici CBellaterraBarcelona
  2. 2.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland

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