Analysis of conduction heat transfer problems in steady, 2D regions with circular holes using a special boundary integral method

A special boundary integral method developed for two-dimensional regions containing circular holes is used to calculate temperature and heat transfer on the boundaries of several selected regions. The geometrical configuration of the region is arbitrary and convective boundary conditions are assumed. An important feature of the method is analytic representation of temperature and its normal derivative on the interior circular holes in the form of a harmonic series. This makes the application of the boundary integral method convenient and free from conditioning problems associated with small interior boundaries. Heat transfer from circular isothermal interior holes are calculated for several illustrative examples using three terms of the harmonic series representation for heat transfer at each of the circular boundaries. The results are presented and discussed.