Optimization method for steady conduction in special geometry using a boundary element method

In some steady heat conduction problems in special geometries which consist of a closely spaced surface and circular holes in an in nite domain, thermal system designers may want to optimize the con guration of circular holes in terms of their radii and locations to achieve the goal of uniform temperature distribution over a closely spaced surface. In this paper, an e cient optimization procedure for this kind of problem is proposed utilizing (i) the special boundary element analysis, (ii) the corresponding design sensitivity analysis and (iii) the CONMIN algorithm. Three sample problems were solved to demonstrate the e ciency and the usefulness of the proposed optimization procedure. Some industrial engineering examples of such problems can be found in the injection molding process, the compression molding process, and so on