Use of geometry in finite element thermal radiation combined with ray tracing

• Published in: Journal of computational and applied mathematics 2010-08, Vol.234 (7), p.2319-2326
• Main Authors: Vueghs, P., de Koning, H.P., Pin, O., Beckers, P.
• Format: Article
• Language: English
• Subjects: Conduction; Exact sciences and technology; Finite element method; Geometrical model; Geometry; Heat exchangers; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Radiation; Ray tracing; Reflectors; Representations; Satellites; Sciences and techniques of general use; Space applications
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2009.08.088

In heat transfer for space applications, the exchanges of energy by radiation play a significant role. In this paper, we present a method which combines the geometrical definition of the model with a finite element mesh. The geometrical representation is advantageous for the radiative component of the thermal problem while the finite element mesh is more adapted to the conductive part. Our method naturally combines these two representations of the model. The geometrical primitives are decomposed into cells. The finite element mesh is then projected onto these cells. This results in a ray tracing acceleration technique. Moreover, the ray tracing can be performed on the exact geometry, which is necessary if specular reflectors are present in the model. We explain how the geometrical method can be used with a finite element formulation in order to solve thermal situation including conduction and radiation. We illustrate the method with the model of a satellite.