Modeling heat conduction in open-cell metal foams by means of the Three-Dimensional Thermal Fin theory

Abstract

Their relatively high thermal conductivity makes metal open-cell foams promising heat transfer enhancers for lightweight applications. Conduction occurs through both solid and fluid phases, depending on the material and the microstructure. The effective conductivity of a foam is predicted by means of analytical and numerical methods, based on both idealized and realistic foam geometries, as well as by empirical correlations based on experiments. In this paper, a new model for the prediction of the effective thermal conductivity of foams is proposed. The proposed Three-Dimensional Thermal Fin (TTF) theory is based on the Electrochemical Fin (ECF) theory previously applied to the analysis of ion and electron transport through nanoporous materials. It has computational time two - three times shorter than those of current numerical techniques, such as finite-element methods. Starting from a tomography-reconstructed metallic open cell foam, the 3-D structure is modeled as a network. Conventional fin heat transfer scaled equations, applied to each part of the network, allow for the evaluation of the temperature distribution and heat rates. The effective thermal conductivity of the metal foam is then derived. The proposed model is validated by comparison with experimental results as well as with predictive models from the open literature and a finite-element based model.