Modification of Planck Black Body Emissive Power and Intensity in Particulate Media Due to Multiple and Dependent Scattering

Abstract

Dispersion relation for electromagnetic wave is obtained in particulate media using effective field approximation (EFA) and quasi crystalline approximation (QCA). Due to multiple and dependent scattering the density of states, phase velocity and group velocity of photons are modified. Modification of these parameters modifies the Planck black body equilibrium radiation intensity. This modification affects the temperature and the heat flux predictions in multiple and dependent scattering particulate media. Results show that EFA can accurately capture the dependence of density of states, phase velocity and the group velocity on volume fraction of scatterers whereas QCA can capture the dependence of effective attenuation as well as density of states, phase velocity and the group velocity. Comparisons of the temperature, heat flux, and effective attenuation are made between EFA, QCA and work done by C.L Tien and coworkers. Results show that heat flux and temperature predictions made by models in the literature for multiple and dependent scattering are not correct as these models do not take the modification of the equilibrium intensity into account. Finally we introduce a new model called Dependent Effective Field Approximation (DEFA) which accurately captures the effect of volume fraction on the equilibrium intensity, and effective attenuation. All relations derived in the paper are for spherical particles.