The Heat Transfer Problem in a Non-Convex Body—A New Procedure for Constructing Solutions

Abstract

The subject of this work is the coupled steady-state conduction-radiation-convection heat transfer phenomenon in a non-convex blackbody, which is represented by a second-order partial differential equation (representing the heat conduction inside the body) subjected to nonlinear (and non-local) boundary conditions (due to the thermal radiation heat transfer). Moreover, anon-convex body emits thermal radiant energy to itself, which must be taken into account in the boundary conditions when high temperatures are involved. The unknown is the absolute temperature. A procedure is proposed for constructing the solution tothe problem by means of a sequence whose elements are obtained from linear problems, such asthe classical ones involving linear Robin boundary conditions.