Evaluation of Total Emittance of an Isothermal Nongray Absorbing, Scattering Gas-Particle Mixture Based on the Concept of Absorption Mean Beam Length

A general methodology to evaluate the total emittance of an isothermal, nongray, isotropically scattering particle-gas mixture is illustrated. Based on the concept of absorption mean beam length (AMBL), the methodology is demonstrated to be computationally efficient and accurate. As an illustration, the total emittance of a slab containing carbon particles and CO₂ is evaluated. The nongray extinction coefficient and scattering albedo of carbon particles are calculated based on Mie theory and the available index of refraction data. The narrow-band fixed-line-spacing model (Edwards et al., 1967) is used to characterize the nongray spectral absorption coefficient of CO₂. Numerical data show that the combined nongray and scattering effects are quite significant. For particles with moderate and large radius (say, ≥1 μm), ignoring the effect of scattering can lead to error in the prediction of total emittance by more than 20 percent. The no-scattering results also yield incorrect qualitative behavior of the total emittance in terms of its dependence on the mixture temperature and particle concentration. The accuracy of many of the existing predictions of total emittance of gas-particle mixtures that ignore the scattering effect is thus highly uncertain.