ANALYSIS OF HEAT TRANSFER PROBLEMS BY COUPLING OF FINITE AND INFINITE ELEMENT

摘要

The finite element method (FEM) is used as a strong formulation to solve partial differential equations of engineering problems. The solution found is only an approximate solution rather than the analytical one which could not be obtained only for certain simplified cases. In general, the finite element formulation deal with problems of structural systems. However, finite element analysis procedures have also gained increasing importance in solution of non structural problems (heat transfer and fluid flow etc.). However, in the application of the finite element method in the far field problems, some difficulties in the analysis arise due mostly to the necessity to use a great number of elements to accurately model the physical system. In order to overcome these difficulties, coupling between the finite element method and the method of infinite elements is proposed to analyse some heat conduction problems in an attractive manner, taking into account the advantages that both methods offer with respect to the near and the far field (excellent accuracy in the results and sensible reduction of number of elements used in the model). In this study, finite elements are used to model the near field either for finite rectangle plates or infinite thick fins, where as in the remainder part of the domain, we use infinite elements which have a specific decaying mapping function that, correspond to the heat conduction problems. The types of elements used are respectively the isoparametric four-node finite element (Q4) and the quadratic six-node infinite element (Q6). Finally, it is worth noting that in order to avoid numerical difficulties in the calculations, the transformation from the global to local mapping of the infinite element should not fail in the far region. This is may be achieved when some care is observed.