Green’s Function Approach to Nonlinear Conduction and Surface Radiation Problems

Abstract

An exact approach for solving both transient and steady state conduction and surface radiation problems is presented. The method is based on the use of Green’s function, and the temperature field is obtained by solving an integral equation. This is in contrast to the approach presented in radiative heat transfer texts in which temperature profiles are obtained from the simultaneous solution of coupled integral and differential equations. The analysis presented in this paper provides insight into the solution of this important class of problems. The method is illustrated by solving two representative problems. The first problem considered is the steady state analysis of a radiating fin. The second problem considered is the transient analysis of a radiating target, which is used to determine the temporal response of radiation thermometers.