Orthogonal function extension to enclosure theory

Abstract Enclosure theory is widely used to solve radiative heat transfer problems. This paper proposes a mathematical model to handle radiative heat transfer between spatially inhomogeneous surfaces and volumes by using sets of orthogonal functions to represent the spatial variation of surface and volume radiative intensities and properties. This method facilitates development of finely tuned solvers to exploit the properties of the basis functions while providing an improved pedagogical framework behind Hottel’s zone method. Additionally, this interpretation provides insight into error analysis for these types of computations. A simple case study is performed on a two-dimensional empty box with homogeneous, diffuse-gray emissivity, utilizing indicator functions, Fourier series, and Legendre polynomials as sample function bases. An additional proof-of-concept study with participating media was performed with the orthogonal functions using a ray tracing solver in a Monte Carlo wrapper. The studies show that this orthogonal function method can be practically used to mitigate truncation error without any increase in the amount of run-time calculations compared to standard zonal methods.