An-Najah Staff

In this present paper we represent some important mathematical results on the physical model describing the heat transfer by conduction and radiation. The problem to be considered is the heat radiation exchange inside a non-convex body _ containing two conducting and opaque enclosures which are bounded by diffuse and grey surfaces and are surrounded by perfectly transparent and non-conductive medium. The combination of the radiation heat exchange with the normal heat conduction in yields a boundary value problem for the absolute temperature in stationary situation. Some properties of the heat radiative operator are represented and proved. The existence and the uniqueness of a weak solution of the non-local problem is also investigated

In this article we consider heat transfer in a non-convex system that consists of a union of finitely many opaque, conductive and bounded objects which have diffuse and grey surfaces and are surrounded by a perfectly transparent and non-conducting medium (such as vacuum). The resulting problem is non-linear and in general is non-coercive due to the non-locality of the boundary conditions. We discuss the solvability of the problem by proving the existence of a weak solution. We extend the analysis to address the parabolic case and to the case with non-linear material properties. Also we consider some cases when coercivity is obtained and state the corresponding stronger existence results.