An appraisal of the heat transfer properties of metallic open-cell foams for strongly exo-/endo-thermic catalytic processes in tubular reactors

On the effective thermal conductivity of aluminum metal foams: Review and improvement of the available empirical and analytical models

“…The effective thermal conductivity was seen to depend, to varying degrees, on conduction in both the solid and fluid phase, convection and radiation [3]. Anyway, conduction in the solid phase proves to be the principal heat transfer modality, even in the case of less conducting matrices for which, as observed by Bianchi et al [1], both the dispersive and the radiative contributions may be significant. The contribution of thermal dispersion was analyzed by Calmidi and Mahajan [4], who modeled the dispersive conductivity as a fraction of eff k : thermal dispersion may be considerable for water-foam systems but extremely low in the case of air-foam media.…”

“…Metal foams are particularly effective for heat transfer augmentation in view of (i) the high surface area to volume ratio, (ii) the high conductivity of the solid struts and (iii) the enhanced flow mixing induced by their tortuous flow paths, which is sometimes referred to as thermal dispersion. As stated in [1], foam ligaments normal to the flow direction may induce the disruption of the boundary layer, while the thermal conduction in the solid phase is expected to augment axial and radial heat transfer. From a practical point of view, it is common to consider the foam as a homogeneous medium.…”

“…At the moment, a significant effort is devoted to describing the foam structure in a more realistic way: from this perspective, X-ray computed microtomography (μ-CT) appears a promising and appealing approach to be coupled to numerical simulations. The literature includes several works dealing with μ-CT, not only limited to metal foams or thermal conductivity estimations [1,3,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The literature offers a wide set of analytical and empirical correlations for the estimation of the effective thermal conductivity of metal foams.…”

“…The contribution of thermal dispersion was analyzed by Calmidi and Mahajan [4], who modeled the dispersive conductivity as a fraction of eff k : thermal dispersion may be considerable for water-foam systems but extremely low in the case of air-foam media. The radiative contribution, which is relevant only at high temperatures, can be derived from a modified diffusion approximation of the Rosseland equation, as reported in [1]. In view of the above considerations, only the conductive contribution to eff k will be taken into account hereafter.…”

“…Beside these, several papers provide relations designed specifically for metal foams, in which convection and thermal radiation are neglected. As summarized in [1], the existing works can be organized into three categories, depending on the methodology followed, as (1) asymptotic solutions, (2) empirical correlations and (3) unit cell approaches. The first group incorporates the theoretical correlations, corresponding to the limiting cases for the effective conductivity (upper and lower bounds), the second one embraces the relations deduced after a fitting of the experimental data [7,46,47], while the last one includes the theoretical models based on simplified descriptions of the foam geometries [5,7,8,12,46,[48][49][50][51].…”