We have studied radiative transfer through insulating materials made of fibres and slugs (modeled respectively as infinite cylinders and spheres) at elevated temperatures. The same theoretical analysis is used for both fibers and spheres: Kerker-Mie theory is applied to determine the radiative coefficients of each type of particle, from the bulk glass complex refractive index and the fiber and slug diameter spectrum. Average radiative coefficients are determined for both fibers and slugs. The independent scattering hypothesis enables us to derive the total radiative coefficients of the whole material using a mass weighted average.
The radiative transfer equation is solved for a one-dimensional problem, using the multiflux approximation. The conductive part is determined using a semi-empirical formula. The coupling between conduction and radiation is accounted for.
This radiative model is applied to mineral wool products at room and elevated temperatures (400°C). Materials made of glass or rock fibers are considered. Special attention is given to fibrous materials with slugs.
We show that radiative heat transfer reaches a minimum for given fiber and slug diameters. We study the respective contribution of fibers and slugs to radiative transfer as a function of the mean diameter and the amount of slugs present in the fibrous material.
Calculated fluxes are compared to experimental ones measured on industrial rock and glass wool products for temperatures ranging from 24 to 400°C. The calculations are performed using the diameter spectra of fibers and slugs measured for these products. The influence of fiber orientation is also studied to better fit experimental data.