Analysis of conduction heat transfer in semi-infinite slabs and infinite quadrants with discrete heat generation sources using Green's function integral methods

The problem of steady state heat conduction in semi-infinite plates and infinite quadrants of constant thermal conductivity, with discrete heat generating sources and with constant boundary temperature was solved using the method of Green's functions with integral techniques. The Green's functions for the geometries were found by the method of images. Five cases of semi-infinite slabs with heat generation sources of different geometry and one case of an infinite quadrant with a heat generation source in the form of a thin current carrying wire bent to form a square were considered. Solutions found with this method always yield closed form algebraic expressions or analytical solutions or "almost analytical" solutions (in the form of an integral). Results found in this work were validated and compared with the numerical method of finite elements (Ansys 6.0). It was concluded that the method used in the present work is elegant and superior in terms of computational requirements.