Analytical models of radiative transfer in fibrous insulation under collimated irradiation

• Reflectance and transmittance in fibrous insulation can be approximated using analytical expressions. • The transport and delta-Eddington approximations are useful for modeling the phase function in radiative transfer in fibrous materials. • Models based on deterministic properties can achieve results comparable to semi-empirical approaches and can be used for engineering materials with tailorable properties. Thermal insulation is essential for high temperature applications, where extreme operating conditions are found. Given its thermal, mechanical, optical and economical characteristics, refractory ceramic-based fibrous materials are widely used. In these materials, radiation is one of the most relevant mechanisms of heat transfer, making its modeling important for the design and optimization of thermal insulation systems. Although traditional techniques such as the Discrete Ordinate Method can be applied, the strong forward scattering found in fibrous materials limits the achievable accuracy due to the computing requirements and normalization issues associated with the phase function. Therefore, there is still a need for approximate but accurate methods to represent radiative transfer. This paper presents two analytical approaches based on the transport and delta-Eddington approximations, along with the Milne-Eddington method, for modeling the radiative transfer in low-density fibrous materials. Spectral transmittance and reflectance measurements on alumina and silica-based insulation were used for validation purposes. The model based on the transport approximation demonstrates good agreement with experimental measurements and can be used at wavelengths relevant to high-temperature applications. The model based on the delta-Eddington approximation extends the wavelength range of the transport approximation and can be used in applications at high and moderate temperatures. Since the models are based on deterministic properties, they can be used for engineering materials with tailorable properties and for improving their manufacturing process.