On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam

A geometrical effective thermal conductivity model of a saturated porous metal foam was developed, based on the idealized three-dimensional basic cell geometry of a foam, the tetrakaidecahedron. This geometric shape results from filling a given space with cells of equal size yielding minimal surface energy [1]. The foam structure was represented with cylindrical ligaments which attach to cubic nodes at their centers. The relative geometrical lengths were calibrated with experiments [2]. It was found that the model estimated the effective thermal conductivity very well for these experimental configurations. It was shown that changing the fluid conductivity has a relatively small effect on increasing the effective thermal conductivity. For an aluminum foam ( k=218 W m −1 K −1) with 95% porosity in vacuum, the three-dimensional model predicted a k eff of 3.82 W m −1 K −1. Using air as the saturating fluid ( k=0.0265 W m −1 K −1) increased the thermal conductivity to 3.85 W m −1 K −1, and water ( k=0.613 W m −1 K −1) increased the thermal conductivity to 4.69 W m −1 K −1. This shows that despite the high porosity of the foam, the heat conductivity of the solid phase controls the overall effective thermal conductivity to a large extent, a fact that must be dealt with in the foam manufacturing process if specific ranges of the foam effective conductivity are desired. It also implies that an accurate representation of the contribution of the solid portion of the foam to the effective thermal conductivity is needed in effective conductivity models. Detailed expressions for the foam effective thermal conductivity were derived in the course of this work and are reported in this paper.