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

This article gives very signi…cant and up–to–date analytical results on the conductive– radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by di/use–gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.

This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.