Predicting radiation emitted from planar and fractal surfaces

Analytical solutions for the radiation view factor between either a planar surface or a plane-based fractal surface and an arbitrarily-positioned and arbitrarily-oriented receptive element were obtained. Deterministic fractal surfaces, whose planar cross sections are the Koch curve or a Cantor set, were considered. For surfaces facing each other the view factor exhibits a monotonic behavior as a function of the distance separating them. Otherwise, a maximum appears. Experiments using planar emitting surfaces were conducted which confirm this trend. It was also found that the non-monotonic behavior is strengthened for Cantor and Koch fractal surfaces. Size effects were discussed.