The geometrical factor of spherical radiation sources

¹ Faculty of Mathematical Studies, University of Southampton Southampton SO17 1BJ, UK
² Candida Oancea Institute of Solar Energy, Faculty of Mechanical Engineering Polytechnic University of Bucharest - Spl Independentei 313, Bucharest 79590, Romania

Corresponding authors: ptl@maths.soton.ac.uk badescu@theta.termo.pub.ro

Received: 26 July 1999
Accepted: 13 April 2000

Abstract

The geometrical factor of a spherical isotropic source of radiation when viewed from a flat cosine (Lambertian) receiver is , where Ω is the solid angle subtended by the source, while is the source's zenith angle. Two different derivations of this result are given in this paper. It holds also for diffuse radiation received from a hemispherical dome. Geometrical factors can also be defined for non-isotropic sources of radiation. Taking into account the limb darkening effect leads to solar temperatures of about 6100 K or 6000 K in a better approximation. These are higher than the value derived assuming the Sun to emit radiation isotropically (5770 K).