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A finite element free boundary formulation for the problem of multiphase heat conduction
Author(s) -
Wellford L. Carter,
Ayer Robert M.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110603
Subject(s) - finite element method , boundary knot method , free boundary problem , thermal conduction , boundary (topology) , mathematical analysis , boundary value problem , mathematics , mixed finite element method , stefan problem , heat flux , mechanics , heat transfer , boundary element method , physics , thermodynamics
The problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two‐dimensional, discontinuous, space–time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.