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The conductive heat transfer in high-porosity cellular materials is generally treated by defining a homogeneous effective thermal conductivity. Numerous empirical and semiempirical models as well as numerical investigations have already been conducted to estimate this conductivity. These previous investigations were based on simplifications of the morphology of the cellular structure and/or of the method of solution of the heat transfer problem. Moreover, they were developed specifically for a type of foam, thus limiting their range of applicability. In order to improve the theoretical knowledge on this field, we have developed an innovative approach combining Voronoi methods for the generation of representative cellular materials and the finite element method (FEM) for solving the conductive heat transfer. The structures generated are able to reproduce the discriminating details of the microstructure and cover the whole range of open-cell or closed-cell foams commonly used in scientific or industrial applications. The influence of the structural parameters on the effective conductivity is analyzed. Based on this assessment, new simplified analytical relations are deduced accounting for the composition and structural parameters of the material. The validity of these laws has been verified by comparisons with “tomographic” results obtained from 3D tomographic data of real open-cell and closed-cell foams. The analytical correlations are potentially very useful for numerous applications.

In addition to the multiple actual or possible applications of metal and ceramic foams in various technological fields, their thermal properties make them a good candidate for utilization as fire barriers. Several studies have shown experimentally their exceptional fire retardance due to their low apparent thermal conductivity. However, while the thermal properties of this porous material have been widely studied at ambient temperature and are, at present, well-known, their thermal behaviour at fire temperatures remains relatively unexplored. Indeed, at such temperatures, the major difficulties are not only due to the fact that thermal measurements are rendered fussy since heavy equipments are required but also stem from the fact that a significant part of the heat transfer occurs by thermal radiation which is much more difficult to evaluate than conductive heat transfer. Therefore, the present chapter is written with a view to report progress on the knowledge of heat transfer in open cell foams and to enlighten the reader on the mechanisms of heat transfer at high temperatures. A first part is devoted to the review of the prior published works on the experimental or theoretical characterisations of radiative and conductive heat transfers from ambient to high temperatures. By taking inspiration from the concepts and models presented in these previous works, we propose, in a second part, a model of prediction of the conductive and radiative contributions to heat transfer at fire temperatures. This analytical model is based on numerical simulations applied to real foams and takes into account the structure of the foam and the optical and thermal properties of the constituents. In a third part, we propose an innovative experimental technique of characterization of heat transfer in foams at high temperatures which permit to evaluate independently the radiative and conductive contributions from a unique and simple measurement. The experimental results obtained on several metal and ceramic foams are compared to the results predicted by our numerical model. The good adequacy between experimental and theoretical results show the consistency of both approaches.

International audience; Superinsulating materials are currently of much interest because of the price of energy on the one hand and CO 2 emissions attributed to offices and houses cooling and heating on the other hand. In this work, we aim at understanding and modeling the radiative transfer within silica nanoporous matrices that are the principal components of nanoporous superinsulating materials. We first elaborate samples of various thicknesses from a pyrogenic silica powder. These samples are characterized using two spectrophotometers on the whole wavelength range [250 nm; 20 µm]. Using a parameter identification technique, we compute the radiative properties of the various samples. Then, our samples being made of packed quasi-spherical particles, we use the Mie theory to model the radiative properties of these materials. Due to the observed discrepancies between the experimental radiative properties and those computed from the Mie theory with a uniform value of 10 nm for the scatterer diameter (value derived from TEM images), we determine an effective scatterer diameter that allows a good agreement between the experimental radiative properties and the Mie results. Nevertheless, in the short wavelength range, the Mie theory gives results that significantly differ from the experimental radiative properties. This behavior is attributed to structure effects as the wavelength is of the same order of magnitude as the diameter of the scatterer that is now regarded as an aggregate of nanoparticles. Hence, to take into account these effects, we use the discrete dipole approximation (DDA). The DDA extinction coefficient spectra appear to be much closer to the experimental results than the Mie spectra, and these first results are quite encouraging.