Determination of optimal hole locations in a two-dimensional heat conductor using boundary integral method

Steady state, two-dimensional conduction heat transfer problems in regions containing interior circular holes are considered. Such problems arise in the thermal design and analysis of molds and dies, where one of the objectives is to maintain a uniform temperature on the cavity surface.

In this study a boundary integral equation method especially developed for circular internal holes is used to develop a computer code. This code is used to accomplish two tasks. First, it is used to obtain the unknown values of temperature and heat transfer on the boundaries of an arbitrary two-dimensional heat conductor representing a mold or a die. Next, this computer code is used in conjunction with the subroutine CONMIN to determine the optimal locations of heating or cooling lines in order to minimize the variation of temperature on the die cavity surface.