Radiative Characteristic of Spherical Cavities With Specular Reflectivity Component

An exact analytical method is presented for determination of emissive as well as absorptive performance of spherical cavities having diffuse-specular reflective walls. The method presented utilizes a novel coordinate transformation technique, which provides convenient means for setting up the governing radiant exchange integral equations. These equations are then solved by the usual iterative method devized for the Fredholm integral equation of the second kind. The suggested coordinate transformation is also utilized for determination of directional absorptivity of a fully specular spherical cavity when collimated radiation enters through its mouth from a specified direction. Results show that for a spherical cavity the dependence of the apparent emissivity on the degree of specularity is high when the emissivity of the cavity wall is low, but this dependence decreases as the emissivity of the cavity wall increases. Also there are situations, unlike cases of cylindrical and conical cavities, for which the purely diffuse spherical cavity is a more efficient emitter than the purely specular cavity having an identical geometry and wall emissivity. Moreover, it is shown that the apparent directional absorptivity of specular spherical cavities having small openings becomes highly fluctuating as the direction of the incident radiation changes