A Three-Dimensional Analytical Model for the Effective Thermal Conductivity and Porosity in High-Porosity Metal Foam Using a Nonisotropic Unit Cell

A comprehensive and precise analytical mesoscale model for effective thermal conductivity and porosity calculation for nonisotropic, open-cell metal foam are developed. These models are extended using an elongated nonisotropic tetrakaidecahedron as a representative unit cell. The unit cell consists of eight hexagons and six quadrilateral faces, with 36 edges and 24 vertices connecting them. The solid lump at the intersection of ligaments is represented as a spherical node and has a key role in effective thermal conductivity calculations. A general description of one unit cell is defined with five independent dimensions consisting of cell edge lengths L and b, inclination angle theta, diameter of fiber ligaments, and spherical node. The effect of porosity on the fiber cross-section shape was taken into consideration. It was found that the change in the cross-section shape affects strongly the porosity and k(eff) It was also confirmed that porosity increases with increasing b/L and decreasing theta. k(eff) is developed for two domains, high-porosity domain with a hypocycloid cross-section shape of ligaments and low-porosity domain with a circular cross-section shape. For both cases, conductivity decreases with increasing porosity and results are in very good agreement with experimental data. As aforementioned model was developed using a general nonisotropic representative elementary volume, then it is easily extended to a wide range of geometrical characteristics.