Radiative heat transfer is important during high-temperature process because radiation emitted or absorbed by a porous solid or surface will determine temperature, which hence has great impact on both thermal and mechanical properties of high-temperature materials.

A multiple-scattering theory is developed that provides complementary upper and lower bounds of the effective emissivity ε_eff for semi-infinite fiber beds and fiber-matrix composites. The semi-infinite fiber beds are made up of randomly placed, freely overlapping cylinders for two possible bed edges—fibers all perpendicular or all parallel to the bed edge. In the fiber-matrix composites, matrix is parallel to the composite outside edge. The randomly placed, free overlapped fibers are either protruding from, or parallel to the matrix surface. Single scattering results for the fiber beds include analytical estimates of ε _eff with rigorous error bounds for different porosities, and local fiber surface emissivities. For the fiber-matrix composites, effect from the matrix is also considered. Rigorous variational upper bounds of ε _eff are presented for the fiber beds, and offer improved ε _eff estimates along with single scattering lower bounds. The fiber beds’ results compared favorably with an experimental correlation and Monte Carlo simulations. Parametric studies show the effective emissivity enhancement above the local fiber/matrix surface emissivities for all surface emissivity values and porosities. The structures with all fibers perpendicular to the edge offers better ε_eff enhancement than the parallel ones.

Knudsen diffusion occurs under low pressures, high temperatures, or in microporous film at normal pressures and temperatures. Single scattering lower bounds and variational upper bounds of the Knudsen diffusion transmission probability are obtained for a fibrous film with fibers all perpendicular or all parallel to the edge surface. Estimates and rigorous error bounds are generated for various film thicknesses. Insights into collision paths useful for thin film vapor deposition, etc., are obtained.

Characterization of a Honeywell carbon brake is performed by Optical Microscopy (OM) and Scanning Electron Microscopy (SEM). The fibers’ radius, orientation, and the porosity of the brake are obtained. The brake surfaces’ emissivities are measured under different temperatures in air. The results indicate that the effective emissivity follows our analytical predictions.