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Non‐linear heat conduction in composite bodies: A boundary element formulation
Author(s) -
Azevedo J. P. S.,
Wrobel L. C.
Publication year - 1988
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.1620260103
Subject(s) - boundary value problem , thermal conduction , discretization , mathematical analysis , classification of discontinuities , mathematics , mixed boundary condition , neumann boundary condition , robin boundary condition , finite element method , boundary element method , boundary knot method , boundary (topology) , physics , thermodynamics
The present paper discusses the numerical solution of steady‐state non‐linear heat conduction problems in composite bodies by using the boundary element method. Two kinds of non‐linearities are considered: the temperature dependence of the thermal conductivity and boundary conditions of the radiative type. By introducing the integral of conductivity as a new variable the governing equation of the problem becomes linear in the transform space. Transformed boundary conditions of the Dirichlet and Neumann types are also linear but convective boundary conditions become non‐linear. Also, discontinuities arise in the value of the integral of conductivity across the interface between materials with different properties since continuity of temperature is imposed. The problem is numerically solved by discretizing the external and interface boundaries of the region under consideration with constant boundary elements and applying an iterative scheme of the Newton–Raphson type.