Interaction effects on heat conduction and thermal stress in an infinite elastic plane with two circular holes

Numerous researches have focused on the physical behavior of an elastic material in the vicinity of a single hole under the assumption that the interaction effects arising from the introduction of multiple holes remain negligible if the holes are placed sufficiently far from each other. In an effort to understand hole interaction effects on heat conduction and thermal stress, we consider the case when two circular holes are embedded in an infinite elastic material and use complex variable methods together with numerical analysis to obtain solutions describing temperature and elastic fields in the vicinity of the two circular holes. The results indicate that the interaction effects on temperature distribution and stress strongly depend on the relative size of the two holes and the distance placed between them but not on the actual size of the holes.