Radiation transfer through specular passages - A simple approximation

A technique is developed for approximating exchange factors for specular radiation passages. It is shown that for a large class of configurations, even with curved reflector surfaces, the average number of reflections, avg n, can be calculated by a simple analytic formula and without any ray tracing. The fraction of radiation transmitted through the passage, tau (one of the exchange factors), can then be approximated by the formula tau is approximately equal to rho raised to the power avg n if the specular reflectivity (rho) of the passage wall is high. A rigorous lower bound is derived which agrees with the exact result within a few percent for any reflector emissivity, provided the product of reflector emissivity and avg n is not too large. Several examples are discussed, including cylindrical passages, V-troughs and compound parabolic concentrators. The method is particularly useful for calculating transmission and absorption of radiation in solar concentrators.