Heat transfer inside cathode ray tubes (CRT) is governed dominantly by radiation. Due to this radiation, the temperature of a particular object in the CRT is closely connected with the thermal behaviour of the complete CRT. Because radiation depends on how boundaries of objects see each other, it is necessary to incorporate their viewfactors. This can be modelled effectively by means of an integral operator. The heat transfer in the interior of the materials is described by the usual heat transfer equation. Hence, the complete problem is governed by a linear partial differential equation that uses a non-linear integral operator in the description of the net fluxes at boundaries. Finite-element modelling results in a non-linear system of equations that may be solved by some iterative non-linear solver like the Newton-Raphson method. Due to the viewfactors between parts of all components, intermediate linear systems that have to be solved for such a method have a fairly full coefficient matrix. A good initial solution will speed up the convergence of the non-linear solver. In this paper we describe a construction of such an initial solution for the non-linear solver. Our approach exploits some general geometrical properties, such as thinness, of the objects within the cavity. We also study efficient linear solvers that can deal with the intermediate large and full linear systems.
|Title of host publication||Numerical methods in thermal problems VIII (Proceedings Eighth Internatiobal Conference, Swansea, UK, July 12-16, 1993)|
|Place of Publication||Swansea|
|Publication status||Published - 1993|