Investigation of approximate methods for calculation of the diffuse radiation configuration view factor between two spheres

Abstract

The view factor calculated by a numerical integration procedure is used to evaluate the error involved by using the view factor obtained by various approximate methods, such as: a) the well known spherical point sources approximation, b) a spherical point source approximation utilizing the reciprocity relationship, and c) the closed form integration over the spherical surface, where the cones from any point subtend the other sphere. The approximation (c) is shown to be identical to (b) if the viewed sphere is replaced by an infinitesimal sphere. The regions where the approximate method is accurate to within 1% are determined. Detailed results obtained by numerical integration are presented for the region close to zero separation where all the approximate methods are inaccurate.