Development of a Network Analogy and Evaluation of Mean Beam Lengths for Multidimensional Absorbing/Isotropically Scattering Media

Based on Hottel’s zonal formulation, a network analogy is developed for the analysis of radiative transfer in general multidimensional absorbing/isotropically scattering media. Applying the analogy to the analysis of an isothermal medium and assuming that the incoming and outgoing flux density is homogeneous within the medium, the effect of scattering on the evaluation of mean beam lengths is illustrated. Two concepts of mean beam length, an absorption mean beam length (AMBL) and an extinction mean beam length (EMBL), are introduced and shown to be important for the analysis of radiative transfer in practical systems. Both mean beam lengths differ significantly from the conventional mean beam length in systems of moderate and large optical thickness. Relations between AMBL and EMBL and their limiting behavior are developed analytically. Numerical results for a sphere radiating to its surface and an infinite parallel slab radiating to one of its surfaces are presented to demonstrate quantitatively the mathematical behavior of the two mean beam lengths.