Conductive Heat Transfer in Metallic/Ceramic Open‐Cell Foams

Abstract

During the last decade, solid foams which are characterized by a relatively high porosity (> 80 %), have known a strong development. Indeed, they allow to envisage a substantial improvement of the performance of standard materials in numerous technological fields. Notably, metallic and ceramic foams exhibit thermal, mechanical and exchange properties, which make them very interesting in lots of applications requiring multifunctionality. To illustrate this, we can cite a non-exhaustive list of functions for which they are usually used: ultra light panels, energy absorbing structures, heat dissipation media, electrodes for electric battery, ultrasound deflector, carrying structure for catalyst, medical prosthesis, heat exchanger _. In most of these applications, the knowledge of the thermal transport properties is of primary importance for the dimensioning of the structures. At ambient temperature, the heat transfer in solid foams is dominated by thermal conduction. To quantify the magnitude of heat conduction, one generally uses the effective conductivity k c which implies that the two-phase material behaves like a homogeneous conductive medium. This assumption is rigorously valid when the size of the pores is much lower than the dimensions of the materials, which is the case in solid foams. The effective conductivity depends on the porosity of the foam, the morphology of the material and on the properties of the two-phases. It is particularly difficult to estimate in solid foams due to the complexity of the geometry encountered and to the large difference between the thermal conductivity of fluid and solid phases.Numerous authors proposed empirical, analytical or numerical model depending on the porous morphology and on the conductivity of the phases to estimate the apparent conductivity of this type of materials. A study was conducted by Schuetz and Glicksmann. [2,3] They were interested in the conductivity of polymeric foams whose porous microstructure is very close to that of metallic and ceramic foams. Indeed, these foams are formed of closed or open cells made of cell struts and/or windows. The porosity of these foams is beyond 95 %. They modeled the foam as a network of thermal resistances and made several simplifications of the morphology and of the solution method to compute overestimating and underestimating values of the exact conductivity. These overestimating and underestimating values, given in, [2] are calculated analytically and are related to the conductivity of air and polymer and to morphological parameters:ek fluid 0:8 × 1 À e 2 À f s 3 k solid < k c

Experimental investigations of the coupled conductive and radiative heat transfer in metallic/ceramic foams

“…1 and 2 although its density is more important. This global increase of k c with the density is consistent with theoretical conclusions of previous studies [7] which underlined the substantial influence of the volume fraction of highly conductive solid phase on the conductive heat transfer. The surprising results evocated for sample No.…”

“…3 might be explained by a noticeable difference in the porous structure between this foam and the other samples. Indeed, Coquard et al [7] have already shown that the shape of the struts forming the cellular materials could have a noticeable influence on the magnitude of conductive heat transfer.…”

“…We can cite the work of Schuetz and Glicksmann [1,2], Boomsma and Poulikakos [3], or Battacharya et al [4]. More sophisticated numerical methods were also developed notably by Druma et al [5], Saadatfar et al [6] or, very recently, by Coquard et al [7]. Some of these models were applied to theoretical representations of the cellular morphology [5,7], permitting to investigate the influence of the structural parameters.…”

“…More sophisticated numerical methods were also developed notably by Druma et al [5], Saadatfar et al [6] or, very recently, by Coquard et al [7]. Some of these models were applied to theoretical representations of the cellular morphology [5,7], permitting to investigate the influence of the structural parameters. The methods developed were also applied to 3-D representations of the microstructures obtained from X-ray tomography [6].…”

Model of an integrated solar thermochemical reactor/reticulated ceramic foam heat exchanger for gas-phase heat recovery

“…The fluid phase effective thermal conductivity is given by k f,eff = /k f . Of the various correlations that were considered for k s,eff [46,[54][55][56], Coquard et al [57] and Kamuito [58] establish that the analytical expression obtained by Schuetz and Glicksman [56] for polyurethane foams is the most applicable, as it adequately (within 30% of experimental measurements) represents thermal conductivities of open cellular structures. The lower limit for k s,eff in Eq.…”