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Continuum Mechanics and Thermodynamics

, Volume 11, Issue 5, pp 277–296 | Cite as

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

  • E. Fried
  • A.Q. Shen
Original Articles

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.

Keywords

Entropy Phase Transition Heat Flux Energy Density Energy Dissipation 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • E. Fried
    • 1
  • A.Q. Shen
    • 1
  1. 1.Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2935, USA US

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