A multi-level fractal model for the effective thermal conductivity of silica aerogel

• Considering the tortuosity and self-similarity of the solid heat transfer path
• Developing a multi-level fractal heat transfer model
• Deriving the expression of the effective thermal conductivity of the present model
• Analyzing the influences of the geometrical parameters and fractal dimensions

In the present paper, the fractal analysis on silica aerogel is performed based on the statistical self-similarity of porous media. A fractal model for the effective thermal conductivity of silica aerogel is proposed in consideration of the tortuosity of heat transfer path and the microstructure of secondary particle. The proposed model assumes that silica aerogel consists of two levels of microstructures: the secondary particles symbolized by improved 2-level Menger sponge and the cluster formed by secondary particles, which can be expressed as a function of density, the contact ratio, and the fractal dimensions. Validation with experimental data and predictions of other theoretical models shows that the present fractal model is reliable and accurate.