Generalization of the Stefan model to allow for both velocity and temperature jumps |
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Authors: | E Fried AQ Shen |
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Institution: | (1) Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2935, USA , US |
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Abstract: | 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.
Received February 17, 1999 |
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