Applicable scope of the Rosseland model in predicting the radiative thermal conductivity of silica aerogel

Abstract

Silica aerogel, renowned for its exceptional insulation properties, exhibits extremely low thermal conductivity at room temperature, with radiative heat transfer contributing significantly to its overall thermal performance at higher temperature. Its radiative thermal conductivity is predicted by the extensively-employed Rosseland diffusion approximation model developed under the optically thick hypothesis. It is imperative to ascertain its applicability, as failing to determine the appropriate conditions for the Rosseland model can result in significant prediction discrepancy under varying optical thickness. A coupled radiative and conductive heat transfer model is developed in this study, where radiative heat transfer is solved by a spectral band method applicable at any optical thickness. The effects of temperature, Rosseland optical thickness, and boundary surface emissivity on the radiative thermal conductivity are systematically analyzed while comparing with predictions from the Rosseland model. Finally, the applicable scope of the Rosseland diffusion approximation model in silica aerogel is obtained.