An image analysis method to obtain the effective thermal conductivity of metallic foams via a redefined concept of shape factor

In order to simulate the Effective Thermal Conductivity (ETC) of metallic foams, diverse geometries were discussed via different computational methods. However, the fundamental relation between the ETC and the structural parameters still remains vague in some extent. In this work, we found through derivation that the ETC is the product of the cell wall thermal conductivity, the relative density and a shape factor. The exact physical meaning of the shape factor was found to be the average of dimensionless temperature derivative weighted by volumes of cell walls. Furthermore, we expressed the shape factor with volumes and orientations of cell walls. Then we analyzed different geometries with an Image Analysis Method (IAM) developed by us. The shape factors obtained with the IAM are consistent with the results inversely deduced from reported ETCs. Furthermore, we applied the IAM to real closed-cell aluminum foams with different density. We found that the shape factor of the closed-cell aluminum foams is macroscopically isotropic, and the Voronoi geometries are appropriate for simulating the closed-cell aluminum foams, while the polyhedral geometries give overestimated shape factors. Without solving the temperature field, our IAM is promising in devising the structural parameters to obtain desired ETCs of metallic foams.