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Experiences in non‐linear analysis of temperature fields with finite elements
Author(s) -
Stelzer J. F.,
Welzel R.
Publication year - 1987
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.1620240105
Subject(s) - convergence (economics) , thermal conductivity , matrix (chemical analysis) , field (mathematics) , convection , conductance , thermal conduction , radiation , temperature gradient , thermal radiation , thermal , natural convection , mathematics , mathematical analysis , mechanics , physics , materials science , meteorology , thermodynamics , optics , pure mathematics , combinatorics , economics , composite material , economic growth
This paper describes practical experiences in dealing with non‐linearities in temperature field calculations. First the use of the load vector for representing the heat radiation on the outer surfaces is reported. However, if there are also additional non‐linearities in the conductance matrix, then it may happen that because of possible counteractions of the non‐linearities no convergence is achieved, at least with the direct iteration. Therefore it is more appropriate to put the radiation terms into the conductance matrix where the other non‐linearities, such as temperature dependent thermal conductivity and natural convection also appear. It is shown how the Newton–Raphson iteration can be applied in an easy way. In the case of temperature dependent heat sources the load vector also needs to be considered. The appropriate special measures are described.