The Exchange Factor Method: An Alternative Basis for Zonal Analysis of Radiating Enclosures

Abstract

In zonal analysis of an enclosure containing a radiatively participating medium, the volume and bounding surface are divided into volume and area elements which are assumed to be isothermal. For a system of M elements consisting of N surfaces and Γ volume elements (M = N + Γ), M2 relationships (direct- or total-exchange areas of conventional zonal analysis) define all possible radiant interchange between element pairs. Due to reciprocity there are at most M(M + 1)/2 unique direct-exchange areas. The use of symmetry may greatly reduce the number of unique exchange areas. In the alternative form presented, exchange factors are defined such that a gray medium’s gas-to-gas exchange factors describe only the redistribution of radiative source terms. Only surface-to-surface and surface-to-gas (gas-to-surface) relationships are required to wholly define the system in radiative equilibrium. That is, a system in radiative equilibrium may be characterized by as many as Γ(Γ + 1)/2 fewer factors. These same exchange factors may be augmented by gas-to-gas exchange factors to analyze media not in radiative equilibrium. In an isotropically scattering, gray medium, exchange factors are functions of system geometry and total extinction only. The degree of extinction due to scattering does not affect exchange factors. Transformations between direct-exchange areas and exchange factors are developed.