Interfacial heat transfer in metal foam porous media (MFPM) under steady thermal conduction condition and extension of Lemlich foam conductivity theory

Abstract

In this work, interfacial heat transfer characteristic in metal foam porous media (MFPM) under a steady thermal conduction condition (usually employed to determine the effective thermal conductivity of MFPM) is firstly investigated. To this end, thermal conduction in metal foam unit cells (represented by Weaire-Phelan foam geometry of different foam porosities and pore densities) saturated with filling mediums is directly simulated considering a wide range of thermal conductivity ratio between foam skeleton and filling medium; and the corresponding key heat flux information is obtained and analyzed. It is revealed that the local interfacial heat conduction in MFPM can be significant; however, the net total interfacial conductive heat transfer is negligibly small. More importantly, the negligible net total interfacial conduction is found unaffected by the discrepancy in thermal conductivity between foam skeleton and filling medium, which in fact is due to the intrinsically symmetric characteristic of foam structure enabling a result that the heat flowing out of foam skeleton offsets the heat flowing in it. Therefore, the respective heat conduction in foam skeleton region and filling medium region of MFPM can be considered in parallel. Then based on this conclusion, the Lemlich foam conductivity theory is reasonably extended to incorporate the influence of filling medium for predicting the effective thermal conductivity (ETC) of MFPM. Further comparisons with previously reported experimental data and ETC models show that the extended Lemlich theory not only well improves the ETC prediction accuracy of MFPMs, but also keeps a simple and elegant form of expression. The findings in this work can correct the previous misleading cognition on interfacial heat transfer in MFPM under steady thermal conduction condition, and can provide crucial clue to derive more efficient ETC models of MFPM.