Thermal modeling of two-dimensional periodic fractal patterns, an application to nanoporous mediaS. Spagnol1, 2, B. Lartigue1, A. Trombe1, 2 and V. Gibiat1
1 Université Paul Sabatier, Laboratoire Physique de l'Homme Appliquée à Son Environnement, Bâtiment 3R1 118 route de Narbonne, 31062 Toulouse Cedex 9, France
2 Institut National des Sciences Appliquées de Toulouse - 135 av. de Rangueil, 31077 Toulouse Cedex 4, France
received 2 February 2007; accepted in final form 11 April 2007; published May 2007
published online 7 May 2007
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.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
65.90.+i - Other topics in thermal properties of condensed matter.
61.43.Gt - Powders, porous materials.
© Europhysics Letters Association 2007