Theoretical relation of the structure and thermal properties of gradient thermal insulator aerogels using fractal geometry

Abstract

This paper introduces a novel method to model gradient aerogels' structure and thermal properties (as for thermal insulators) with gradient porosity (or density) and thermal conductivity. To simplify and reduce the amount and complexity of calculation, we used fractal structures (Sierpinski carpet) and their properties (self-similarity) to model Functionally Gradient Materials (FGM). Hitherto, the Sierpinski carpet model was used to model the structure and properties of homogeneous media. But, in this paper, we used this method for modeling the structure and thermal properties of heterogeneous materials. For the first time, we modified the unit cell of the Sierpinski carpet model with binomial distribution probability function, which led to the heterogeneous and gradient structure. The effect of gradient structure on thermal conductivity showed the appropriate range of structural parameters of the gradient Sierpinski carpet model for the porosity of 25–93% is 0.3 < C/L < 0.93, t = 0 and n = 3. Also, we determined that considering the contact resistance of solid particles has no significant effect compared to ignoring the contact resistance condition (t = 0). This study's main challenge is modeling the structure and properties of heterogeneous materials by modifying the Sierpinski carpet model with binomial probability distribution function. We investigated the accuracy of the proposed model, which showed suitable matches comparing to experimental results.