Mathematics

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Browsing Mathematics by Author "Imad Ali Hamdan Al Atrash"

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    Analysis of radiant heat exchange and interaction with conduction
    (Al-Quds University, 2009-04-09) Imad Ali Hamdan Al Atrash; عماد علي حمدان الأطرش
    This work deals with the three fundamental concepts of heat transfer modes (radiation, conduction and convection) with great emphasis on heat radiation and interaction with conduction. Determining radiation interchange between surface areas is needed in heat transfer, illumination engineering and applied optics. In fact, since 1960 the study of radiant interchange has been given impetus by technological advances that provides systems in which thermal radiation is very important. The geometric configuration factors derived here are an important component for analyzing radiation exchange. The computation of configuration factors involves integration, either analytically or numerically, over the solid angles by which surfaces can view each other. Some examples are given to demonstrate analytical integrations arise in radiant heat analysis. Moreover, the question of coupling heat radiation with conduction has been dealt with. To analyze this problem we consider a conductive - radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse - grey surfaces. Some properties of the radiative integral operator are presented. The question of existence and uniqueness of weak solutions for this problem is investigated. The existence of weak solution is proved by showing that our problem is pseudo-monotone and coercive. The uniqueness of solution is proved using some ideas from the analysis of nonlinear heat conduction.