Resistance network-based thermal conductivity model for metal foams

A network model for the estimation of effective thermal conductivity of open-celled metal foams is presented. A nodal network representation of three aluminum foam samples from DUOCEL - 10 ppi, 20 ppi and 40 ppi - is constructed out of X-ray microtomography data obtained by computed tomography (CT) scanning of the samples using a commercial CT scanner. Image processing and 3D skeletonization are performed with commercially available image processing software. The effective thermal conductivity is estimated through a 1D conduction model, representing individual ligaments as an effective thermal resistance using the topological information from the scan data. The effective thermal conductivity data thus obtained are compared with the Lemlich theory and other pore-based models. Further, microstructural characterization of foam features - pore size, ligament thickness, ligament length and pore shapes - is performed. All the three foam samples are observed to have similar pore shapes and volumetric porosity, while the other features scale with the pore size. For a given porosity the computed permeability is found to scale as the square of the pore diameter, as also noted by previous researchers.