On the Two-Phase Stefan Problem with Interfacial Energy and Entropy.

Abstract

The classical Stefan theory for the melting of a solid or the freezing of a liquid is too simplistic to describe phenomena such as supercooling, in which a liquid supports temperatures below its freezing point, or superheating, the analog for solids, or dendritic growth, in which simple shapes evolve to complicated tree-like structures. This paper develops a general theory for two-phase phenomena of this type. It develops partial differential equations satisfied in the phase regions and free-boundary conditions satisfied on the interface between phases, and gives arguments which indicate that the resulting boundary-value problems predict the formation of dendrites. Keywords: Equilibrium; Liapunoo functions; Mathematical physics.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1985
Accession Number
ADA163715

Entities

People

  • Morton E. Gurtin

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Constitutive Equations
  • Curvature
  • Differential Equations
  • Energy
  • Equations
  • Equations Of State
  • Formulas (Mathematics)
  • Free Energy
  • Freezing
  • Heat Energy
  • Latent Heat
  • Mathematics
  • Partial Differential Equations
  • Thermodynamics
  • Transition Temperature
  • United States

Readers

  • Fluid Dynamics.
  • Materials Science and Engineering.
  • Mathematical Modeling and Probability Theory.