Existence uniqueness and construction of the solution of the energy transfer problem in a rigid and nonconvex black body

Abstract

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.