Radiative Transfer With Dependent Scattering by Particles: Part 1—Theoretical Investigation

Abstract

Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.