The radiative transfer in dispersed media in the geometric optic regime is investigated through two continuum-based approaches. The first one is the traditional treatment of dispersed media as continuous and homogeneous systems, referred here as the homogeneous phase approach (HPA). The second approach is based on a separate treatment of the radiative transfer in the continuous and dispersed phases, referred here as the multiphase approach (MPA). The effective radiative properties involved in the framework of the HPA are determined using the recent ray-tracing (RT) method, enabled to overcome the modeling difficulties such as the dependent scattering effects and the misunderstanding of the effective absorption coefficient. The two modeling approaches are compared with the direct Monte Carlo simulation. It is shown that (i) the HPA combined with effective radiative properties, such as those from the RT method, is satisfactory in analyzing the radiative transfer in dispersed media constituting of transparent, semitransparent, or opaque particles. Therefore, the use of more complex continuum models such as the dependence included discrete ordinate method (Singh, B. P., and Kaviany, M., 1992, “Modelling Radiative Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, 35, pp. 1397–1405) is not imperative anymore. (ii) The MPA, though a possible candidate to handle nonequilibrium problems, is suitable if the particle (geometric) backscattering is weak or absent. It is the case, for example, for dispersed media constituted of opaque particles or air bubbles. However, caution should be taken with the MPA when dealing with the radiative transfer in dispersed media constituted of nonopaque particles having refractive indexes greater than that of the continuous host medium.
Monte Carlo implementation of Schiff׳s approximation for estimating radiative properties of homogeneous, simple-shaped and optically soft particles: Application to photosynthetic micro-organisms
