Conduction heat transfer in semi-infinite and infinite regions with discrete heat sources

The steady state temperature distribution in semi-infinite slabs and infinite quadrants due to two- and three-dimensional discrete heating sources shaped in the form of thin electric current carrying wires has been determined. The temperature field is obtained using Green's function integral techniques. The solutions obtained here are compared with numerical solutions obtained from a commercial software package. It is shown that for the cases considered here we get closed form solutions or solutions in the form of simple numerically calculable integrals which are far superior to numerical methods in terms of elegance and labor involved for parametric studies. The behavior of the non-dimensional temperature with the various relevant parameters is discussed.