Generalization of the Stefan model to allow for both velocity and temperature jumps

E. Fried, Amy Q. Shen

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We obtain an expression for the energy dissipation due to an evolving nonmaterial interface across which the mass density, velocity, stress, energy density, heat flux, entropy density, and temperature may be discontinuous. This expression is a sum of three terms: the product of the interfacial mass flux with the interfacial energy release; the scalar product of the interfacial velocity slip with the interfacial friction; and, the product of the interfacial temperature jump, scaled by the interfacial temperature average, with the interfacial heating. When the surface in question is a phase interface, we propose, on the basis of the interfacial dissipation inequality, supplemental relations that determine the interfacial energy release, the interfacial friction, and the interfacial heating constitutively as functions of the interfacial mass flux, the interfacial velocity slip, and the scaled interfacial temperature jump. As a step toward an understanding of the role that such interfacial relations may serve in theories for phase transitions, we investigate a problem involving the solidification of a pure substance in the absence of flow.

Original languageEnglish (US)
Pages (from-to)277-296
Number of pages20
JournalContinuum Mechanics and Thermodynamics
Issue number5
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)


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