Existence and Uniqueness of The Solution of The Coupled Conduction Radiation Energy Transfer on Diffuse Gray Surfaces

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Journal Title, Volume, Page: 
Surveys in Mathematics and its Applications, Volume 2 (2007), 43- 58
Year of Publication: 
2007
Authors: 
Naji Qatanani
Department of Mathematics Al-Quds University, P.O. Box 20002 Abu-Dies, Jerusalem
Current Affiliation: 
Department of Mathematics, Faculty of Sciences, An-Najah N. University, PO Box 7, Nablus, Palestine
Amjad Barham
Palestine Polytechnic University, P.O. Box 20002 Abu-Dies, Jerusalem. Hebron, Palestine
Qasem Heeh
Department of Mathematics Al-Quds University, P.O. Box 20002 Abu-Dies, Jerusalem
Preferred Abstract (Original): 

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.

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