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Etude et analyse numérique des transferts de chaleur couplés par rayonnement et conduction dans les milieux semi-transparents : application aux milieux fibreux

Abstract : The mm of this work ls the study and the numerical analysis of heat transfer coupled by radiation and conduction through semi-transparent media. The model used is a system of partial differential equations coupling the intFgro-differential equation of the radiative transfer (RTE), which has as unknown the radiation intensity, and a nonlinear heat equation governing the temperature in the medium. In the frrst chapter of the thesis, we detail the modelling and the simplifying assumptions. In the second chapter, we show the existence and unicity of the coupled system of equations in steady state. The third chapter is devoted to the numerical solution of the equations in steady state. In order to solve the RTE, the angular space is ruscretized according to several directions and a quadrature rule is used to approach the integral of the equation. Then, it results a frrst order linear differential equation system which was solved by three different methods. The second equation is solved using the Kirchhoff transformation associated with a centered finite difference scheme. The coupled system of equations is solved using a fIxed-point method. In the fourth chapter, we study the convergence of a numerical scheme in steady state. In the fifth chapter, we present a numerical method achieved to solve the coupled system in transient state, firstly when the temperatures are imposed at the boundaries and, secondly, when the medium is subjected to flux conditions. The heat equation is solved in space by the finite element method P[exponent 2]. The differential system in time is solved by a implicit Runge-Kutta method, adapted to stiff equations. The last chapter of this work analyses the numerical results obtained by the simulation applied on a insulator composed of silica fibers.
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https://hal.univ-lorraine.fr/tel-01748569
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Fatmir Asllanaj. Etude et analyse numérique des transferts de chaleur couplés par rayonnement et conduction dans les milieux semi-transparents : application aux milieux fibreux. Autre. Université Henri Poincaré - Nancy 1, 2001. Français. ⟨NNT : 2001NAN10208⟩. ⟨tel-01748569⟩

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