Radiative characterization of random fibrous media with long cylindrical fibers: Comparison of single- and multi-RTE approaches

Radiative heat transfer is analyzed in participating media consisting of long cylindrical fibers with a diameter in the limit of geometrical optics. The absorption and scattering coefficients and the scattering phase function of the medium are determined based on the discrete-level medium geometry and optical properties of individual fibers. The fibers are assumed to be randomly oriented and positioned inside the medium. Two approaches are employed: a volume-averaged two-intensity approach referred to as multi-RTE approach and a homogenized single-intensity approach referred to as the single-RTE approach. Both approaches require effective properties, determined using direct Monte Carlo ray tracing techniques. The macroscopic radiative transfer equations (for single intensity or two volume-averaged intensities) with the corresponding effective properties are solved using Monte Carlo techniques and allow for the determination of the radiative flux distribution as well as overall transmittance and reflectance of the medium. The results are compared against predictions by the direct Monte Carlo simulation on the exact morphology. The effects of fiber volume fraction and optical properties on the effective radiative properties and the overall slab radiative characteristics are investigated. The single-RTE approach gives accurate predictions for high porosity fibrous media (porosity about 95%). The multi-RTE approach is recommended for isotropic fibrous media with porosity in the range of 79−95%.