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A finite difference solution of non‐linear systems of radiative–conductive heat transfer equations
Author(s) -
Asllanaj F.,
Milandri A.,
Jeandel G.,
Roche J. R.
Publication year - 2002
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.490
Subject(s) - finite difference , heat transfer , thermal conduction , radiative transfer , finite difference method , thermal radiation , mathematics , mathematical analysis , differential equation , partial differential equation , mechanics , physics , thermodynamics , optics
A finite difference solution for a system of non‐linear integro–differential equations modelling the steady‐state combined radiative–conductive heat transfer is proposed. A new backward–forward finite difference scheme is formulated for the Radiative Transfer Equation. The non‐linear heat conduction equation is solved using the Kirchhoff transformation associated with a centred finite difference scheme. The coupled system of equations is solved using a fixed‐point method, which relates to the temperature field. An application on a real insulator composed of silica fibres is illustrated. The results show that the method is very efficient. Copyright © 2002 John Wiley & Sons, Ltd.