An analytical model for combined radiative and conductive heat transfer in fiber-loaded silica aerogels

Abstract

An improved analytical model for the total thermal conductivity of fiber-loaded silica aerogels was developed based on the complex refractive index, size, orientation, volume fraction and morphology of the fibers and silica aerogel. A cubic array of spherical porous secondary nanoparticles and a modified parallel-series model were proposed to model the combined solid and gaseous thermal conductivities. An anomalous diffraction theory (ADT) was used to predict the fiber extinction coefficient. Five common fiber types in the composites were studied including amorphous SiO2 glass, silicon glass, common float glass, soda lime silica glass and borosilicate glass. The results show that the total extinction coefficient of the silica aerogel system is largest by loading with the common float glass fiber and lowest by loading with the soda lime silica glass among the five fiber types. The model provides theoretic guidelines for material designs with optimum parameters, such as the type, inclination angle, volume fraction and diameter of the fibers as well as the aerogel nanoparticle and pore sizes. The optimum fiber for improved thermal insulation should have a large spectral complex refractive index throughout the infrared region.