A DUAL RECIPROCITY BOUNDARY ELEMENT APPROACH TO THREE-DIMENSIONAL TRANSIENT HEAT CONDUCTION AS APPLIED TO MATERIALS PROCESSING

The dual reciprocity boundary element method (DRBEM) is implemented to solve three-dimensional transient heat conduction problems in the presence of arbitrary sources, typically as these problems arise in materials processing. The DRBEM has a major advantage over conventional BEM, since it avoids the computation of volume integrals. These integrals stem from transient, nonlinear, and/or source terms. Thus there is no need to discretize the inner domain, since only a number of internal points are needed for the computation. The validity of the method is assessed upon comparison with results from benchmark problems where analytical solutions exist. There is generally good agreement. Comparison against finite element results is also favorable. Calculations are carried out in order to assess the influence of the number and location of internal nodes. The influence of the ratio of the numbers of internal to boundary nodes is also examined.

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