An integral equation approach to radiative heat transfer between heat conducting solids of arbitrary shape

The main purpose of this paper is to present a nonlinear integral equation formulation to numerically solve composite boundary value problems encountered in the physical problem of radiative heat transfer between solids of arbitrary shape. The main difficulty in solving these types of boundary value problems is due to the nonlinear boundary conditions, which impose additional difficulties on the use of other techniques like the finite difference, the finite element, and variational methods. The fundamental Green's function of the two dimensional Laplace's operator is used to obtain a nonlinear Green's boundary formula, which is used to solve the temperature distribution on the boundaries of the region. The method is then applied to the problem of radiative heat transfer between a thick-walled cylinder and a thick plate.