Mathematical Analysis of Heat Radiation Problems

- In this thesis we focus on the analytical aspects of the Fredholm integral equation a rising as a result of the heat energy exchange inside a convex and non-convex enclosure geometries. The phenomenon of heat radiation plays a very dominant role in a wide range of applications in science and technology. The general characteristicsof heat transfer modes ; namely: heat conduction, heat convection and heat radiation will be addressed. - A systematic derivation of the heat radiation equation using some physical properties of heat transfer modes will be presented. Some important properties of the integral operator for the Fredholm integral equation will be investigated. The Banach fixed-point theorem will be introduced and used to show the existence and the uniqueness of the solution of the integral equation. A problem of coupling radiation with conduction will be solved and analyzed.