Analysis and modeling of the pore size effect on the thermal conductivity of alumina foams for high temperature applications

Analytical and finite element analyses were carried out to investigate the influence of the pore sizes on the effective thermal conductivity, which is the main physical property related to the ceramic microstructure insulating capacity at high temperatures. Thermal conductivity was estimated by analytical models using Litovsky's and Rosseland's approaches for a monodisperse pore distribution, whereas via finite element analysis a high porosity microstructure with three different pore sizes was investigated. Based on this, an ideal pore size range (0.5-3.0 µm) was found that optimizes the reduction of thermal energy transmission in the 1000-1700 °C range. Furthermore, the ideal pore size range seems to be independent of the ceramic foam material. When considering a pore size distribution, the ideal range is narrowed due to less effective thermal radiation scattering by sub-micron and large pores. The results obtained showed that nanopores (< 0.1 µm) are not the best option to reduce thermal conductivity at high temperatures. This statement is supported by experimental data on nanopore aerogels, which show a significant thermal conductivity increase at the high temperature range.