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

Abstract

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.

Thermal transport in nano-porous insulation of aerogel: Factors, models and outlook

“…Spagnol et al [112] established a numerical model based on two-dimensional fractal structure to simulate the heat transfer in silica aerogel. The method of Spagnol numerical model solves the coupled heat conduction in the solid and gas phases of aerogel based on the steady heat conduction equation, and then obtains the heat flux field and temperature distribution.…”

A 3-D numerical heat transfer model for silica aerogels based on the porous secondary nanoparticle aggregate structure

“…The third kind of thermal conductivity model is a numerical model using the Von Koch snowflake fractal structure or the random structure from the diffusion-limited cluster-cluster aggregation (DLCA) method to better represent the aerogel structure [22,23]. The DLCA method was usually used to describe the structural properties of materials obtained by sol-gel techniques [24][25][26][27][28][29].…”

“…To authors' knowledge, there is limited research in numerically modeling heat transfer in silica aerogels. Spagnol et al [23] developed a 2-D numerical model by translating the DLCA structure into a grid structure suitable for heat transfer calculations. However, their 2-D model neglected the radiative heat transfer, 3-D aggregate randomness, porosity of secondary nanoparticles, nanoparticle size and solid-gas coupling effect with no validation by experimental data.…”

“…However, their 2-D model neglected the radiative heat transfer, 3-D aggregate randomness, porosity of secondary nanoparticles, nanoparticle size and solid-gas coupling effect with no validation by experimental data. Besides, Spagnol et al [23] did not match the DLCA structural parameters with the material properties, leading to a too high silica aerogel density of 460 kg m − 3 .…”

Three-dimensional reconstruction of aerogels from TEM images

“…Presently, they are used for the building insulation, and in the past years they were synthesized in high purity or doped silica glasses, Cerenkov counters… Therefore, the modeling of the structure of such materials has been of main importance in order to understand their physical properties [1].…”