Conductive and Radiative Heat Transfer in Ceramic and Metal Foams at Fire Temperatures

Abstract

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 12 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.

Numerical quantification of coupling effects for radiation-conduction heat transfer in participating macroporous media: Investigation of a model geometry

“…As the effective properties significantly depend on the geometry of the porous media, accurate computational approaches directly incorporate the exact morphology using, for example, computed tomography of the materials of interest [4][5][6][7][8]. There have been attempts to summarize effects of conduction and radiation into one single parameter sometimes referred to as ''phononic diffusivity" [9,10] or ''equivalent conductivity" [11]. This parameter must, by definition, heavily depend on temperature.…”

“…However, no quantification is given for a realistic case and the importance of the different terms under various conditions is not given in [14]. Coquard et al [11] stated that in the case of ''metal or ceramic open cell foams" they have ''checked from numerous results obtained on different cellular structures with various optical properties that this coupling is relatively weak". Their findings suggest that for some setups the superposition of the results obtained for the two modes separately is justified without giving more details.…”

The effective thermal conductivity of open cell replicated aluminium metal sponges

“…Three simplified models were used, one based on the assumption that conduction through the solid material can be either in series or parallel. A simple scaling expression was also used, along with D model [8,15,36], and an analytical model based on the numerical and 3D tomographic structure parameters in terms of ratio between the thickness of the struts and the nodes (referred to as lumps in the originating work, and preserved in the notation here, D st /d lu ) and the node shape [18]. Two empirical expressions for high porosity (> 90%) foams are also compared to our experimental measurements.…”

“…Strategies that go beyond simplified unit cell structures have been explored, for example, by analysing the real foam structure obtained from 3D computed tomography [12] to observe its effects on the ETC. This can support the development of more accurate generic correlations [10,12,18], but is limited by the small volumes of foams that can be investigated in this way. A review of the wide range of theoretical and empirical approaches for porous metals found that each model defines a specific morphology and is hence of limited applicability to other types [11,12,18].…”

“…Although it can be demonstrated that the pore size has little direct influence on ETC, the pore size will influence the foam fabrication process, and by establishing limits on what foams may actually be produced (there are usually upper and lower size limits). To this extent, pore size can affect the ETC [12,18]. The pore size itself is additionally not well defined as measures including both average pore diameters and Pores Per Inch (PPI) are presented in the literature.…”