EXISTENCE UNIQUENESS AND CONSTRUCTION OF THE SOLUTION OF THE ENERGY-TRANSFER PROBLEM IN A RIGID AND NONCONVEX BLACK-BODY

This paper is concerned with an important class of heat transfer problems, which arises when the radiation heat transfer is the mechanism for energy transfer from/to a rigid and nonconvex black body. In such situations there will exist a direct energy interchange among points of the body boundary that do not belong to a given "small neighborhood". Such phenomena are mathematically described by a partial differential equation subjected to nonlinear boundary conditions. It is demonstrated that the problem always admits a solution, which is unique. In addition, an algorithm for solving such problems is presented.