Finite element analysis of linear and nonlinear heat transfer

• Published in: Nuclear engineering and design 1974-01, Vol.29 (1), p.110-124
• Main Authors: Wilson, E.L., Bathe, K.J., Peterson, F.E.
• Format: Article
• Language: English
• ISSN: 0029-5493; 1872-759X
• DOI: 10.1016/0029-5493(74)90101-0

The finite element method is rapidly becoming a popular procedure for the evaluation of thermal stresses in complex structures. In linear analysis the method has been used extensively and has been coupled with stress analysis computer programs in order to automate thermal stress analysis. However, for the method to be effective, efficient numerical techniques need to be used. The purpose of this paper is to survey the recent developments in linear heat transfer analysis and, specifically, to present the techniques that permit the practical analysis of large and complex three-dimensional heat conduction problems. Typical practical problems are described and solution times are presented. In the analysis of systems with nonlinear thermal properties the method has had limited application. In this paper the general formulation of the incremental equations used in nonlinear heat transfer analysis are presented. An efficient numerical solution of the equations is given. Several types of nonlinearities are discussed and the solutions of some typical problems are presented.