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Transient non‐linear heat conduction–radiation problems—a boundary element formulation
Author(s) -
Blobner Jutta,
Białecki Ryszard A.,
Kuhn Günther
Publication year - 1999
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/(sici)1097-0207(19991220)46:11<1865::aid-nme748>3.0.co;2-d
Subject(s) - boundary element method , mathematics , discretization , mathematical analysis , boundary value problem , thermal conduction , reciprocity (cultural anthropology) , boundary knot method , robin boundary condition , boundary (topology) , ordinary differential equation , singular boundary method , finite element method , mixed boundary condition , differential equation , physics , thermodynamics , psychology , social psychology
A novel boundary‐only formulation for transient temperature fields in bodies of non‐linear material properties and arbitrary non‐linear boundary conditions has been developed. The option for self‐irradiating boundaries has been included in the formulation. Heat conduction equation has been partially linearized by Kirchhoff's transformation. The result has been discretized by the dual reciprocity boundary element method. The integral equation of heat radiation has been discretized by the standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by static condensation of the radiative heat fluxes arising in both sets. The final set of ordinary differential equations has been solved using the Runge–Kutta solver with automatic time step adjustment. The algorithm proved to be robust and stable. Numerical examples are included. Copyright © 1999 John Wiley & Sons, Ltd.