Analytical view factor solutions of a spherical cap from an infinitesimal surface

Abstract

Under the assumption of diffuse surfaces, the amount of radiative heat transfer between two surfaces can be evaluated by a view factor. In the past, analytical view factor solutions were derived for many types of geometries. However, view factor solutions of a spherical cap, which is a part of a sphere cut off by a plane, from an infinitesimal surface have not been thoroughly investigated. In this study, geometrical configurations of a spherical cap and an infinitesimal surface are classified into different cases, and an analytical solution is derived for each case. Actual view factor values are calculated for various configurations, and the results are verified by view factors acquired by the numerical methods.