Thermal modeling of two-dimensional periodic fractal patterns, an application to nanoporous media

Periodic patterns built with elementary Von Koch snowflakes have been found to be a good structural representation of nanoporous media (like monolithic silica aerogels) concerning the characterization of heat conduction. These geometries allow the modeling of different pore sizes, fractality and isotropy of the complex structure. A numerical model has been used to determine the effective thermal conductivity as a function of two parameters: density and tortuosity. The results—which match with an analytical model presented in the literature—are compared to simple periodic and random fractal geometries.