Prediction of directional effective thermal conductivity of anisotropic open-cell metal foam

In this work, the prediction of directional effective thermal conductivity (ETC) of anisotropic open-cell metal foam is addressed. First, the representative elementary volume (REV) of isotropic metal foam is numerically reconstructed from the Weaire-Phelan foam cell. Then the structural templates for the REV of anisotropic metal foam are obtained by applying directional scaling to the isotropic REVs. Through direct simulation of steadystate heat conduction at foam pore scale, the ETCs of metal foams under different anisotropy ratios (major-to-minor cell diameter ratios of elongated foam structure) and porosities are determined. Meanwhile, as an innovative contribution, the conduction shape factors for a series of anisotropic foam structures are characterized. Afterwards, a creative prediction model (simple in form, i.e., k(eff) = (0.48 + 0.55R(D))(0.91-0.59 epsilon)(1-epsilon)k(s) + [1-(0.48 +0.55R(D))(0.91-0.59 epsilon)(1-epsilon) ]k(f)) for the directional ETC of anisotropic metal foam porous media (MFPM) is proposed considering parallel conductive relation between distinct phases. This model not only considers the structure anisotropy, foam porosity and material properties but also avoids complicated characterization and computations. Experimental validation confirms that our ETC model reliably predicts the directional ETC of anisotropic MFPM with a deviation of less than 6 %, which remarkably reduces the deviation (14.0 % similar to 21.8 %) predicted by the ETC model based on isotropic assumption. This work also helps to input the anisotropic thermal conductivity tensor (or matrix) for practical macroscopic modeling.