Mullite fibers/whiskers hierarchical porous materials: Experimental characterization and fractal model to predict thermal conductivity.

It is an effective method to predict thermal conductivity of porous materials by using fractal models. In this work, mullite fibers/whiskers hierarchical porous materials (MFWs) were prepared via in-situ growth method. The fractal dimension was obtained by calculating the microstructure photo after binarization according to the box-dimension method. Based on fractal theory and fractal dimension, improved Sierpinski carpet models were established. The models were then converted into electrical fractal patterns to solve the iterative formulas of effective thermal conductivity (K eff) and porosity. The results show that K eff decreases gradually with the increase of porosity. The thermal conductivity of the solid phase has a significant effect on K eff at low porosity. Pore size and its spatial distribution, especially the spatial distribution of the larger pore, have a substantial impact on K eff , and the smaller and uniformly distributed pore can reduce K eff , effectively. The calculated results are close to the experimental results, suggesting that the fractal model is suitable for predicting the thermal conductivity of MFWs. More crucially, the calculated results have guiding significance for the experimental preparation, and it is possible to reduce the thermal conductivity of MFWs by increasing whiskers length and growing efficiency. • The fractal model was linked with the hierarchical structure to forecast the thermal conductivity of MFWs. • Based on the fractal dimension and fractal theory, improved Sierpinski carpet models were created. • The results of thermal conductivity fractal model calculation are comparable to the experimental data. [ABSTRACT FROM AUTHOR]