cient numerical computation of direct exchange areas in thermal radiation analysis

The analysis of thermal radiation in multi-surface enclosures typically involves multiple integrals with four, five, or six variables. Major difficulties for the numerical evaluation of these integrals are non-convex geometries and singular integral kernels. This paper presents hierarchical visibility concepts and coordinate transformations which eliminate these difficulties. In the transformed form, standard quadrature techniques are applied and accurate results are achieved with moderate numerical effort. In benchmark example problems, the effectiveness and accuracy of the method are validated. A simulation model of an industrial furnace demonstrates the applicability of the method for large-scale problems. NOMENCLATURE α tuple Bα bounding box b radiosity, W/m2 C(α) function for computing the visibility D integration domain d side length, m2 ε emissivity f continuous function or part of the kernel k, m4 g part of the integral kernel k, 1/m2 H heat flux density absorbed by a volume zone, W/m2 θ incident or emergent angle, rad h irradiance, W/m2 I total intensity, W/(m2sr) Λ coordinate transformation K absorption coefficient, 1/m k integral kernel, 1/m4 M order of quadrature NS number of surface zones NV number of volume zones ∗Corresponding author. Email: [email protected] September 07, 2015