The Bidimensional Stefan Problem with Convection: The Time-Dependent Case.

Abstract

This paper considers the time dependent Stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries. The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments. Consider a phenomenon (such as melting of ice) where there is a change of phase, say liquid-solid. In the liquid phase the thermal energy is transported both by diffusion and convection, and the effects of convection are reflected in the movement of the free-boundary separating the two phases. This paper shows that such a problem can be formulated mathematically and that it admits a solution in a week sense. Also investigated are some local regularity properties of the distribution of temperature and the field of velocities in the liquid phase.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1982
Accession Number
ADA124377

Entities

People

  • E. Dibenedetto
  • G. H. Knightly
  • J. R. Cannon

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Continuity
  • Convection
  • Differential Equations
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Flow
  • Fluids
  • Heat Capacity
  • Heat Energy
  • Heat Flux
  • Heat Of Fusion
  • Latent Heat
  • Liquid Phases
  • Mathematics
  • Navier Stokes Equations
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.