Hierarchically theoretical calculation and 3D reconstruction simulation of effective thermal conductivity for MTMS-based silica aerogels

Compared with nanoscale aerogels, the thermal conductivity of MTMS silica aerogel (MSA) is relatively large due to its micron-sized pore size, which hinders its popularization in the field of thermal insulation. In this study, the MSA samples with relatively low thermal conductivity (33.7 mW/m/K) and density (0.071 g/cm³) were prepared. Then, the theoretical mathematical models of thermal conductivity were discussed and selected. The three-dimensional model based on X-ray microscopic CT slices was reconstructed for their micrometer-scale structure and based on this physical reconstruction model, finite element numerical simulations were carried out. The two-hierarchy structure of MSA was found during scanning electron microscopy, and the stepwise prediction of its effective thermal conductivity was carried out using the equivalence method. The mathematical model applicable to MSA was also modified to propose hierarchically theoretical calculation (HTC) for thermal conductivity. The feasibility and accuracy of the mathematical modeling method were verified by the finite element numerical simulation method based on the high-reduction three-dimensional reconstruction model, and the prediction results of the two were in good agreement with the experimental test data, of which the error was within 5%.