An Analytical Unit Cell Model for the Effective Thermal Conductivity of High Porosity Open-Cell Metal Foams

We present an analytical model for the effective thermal conductivity of fluid-saturated metal foams with open cells. For high porosity ranges (ε≥0.9)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varepsilon \ge 0.9)$$\end{document}, the model is derived based on a realistic representative unit cell (a tetrakaidecahedron with cuboid node) under the assumption of parallel heat conduction along the highly tortuous cell ligaments and the saturating fluid. Good agreement with existing experimental data as well as the present measurements of open-cell aluminum foams saturated with either air or water validates the present model. More realistic and reasonable node size is estimated and compared with other model predictions. Ligament shape and pore size (PPI) are found to have little influence upon the effective thermal conductivity of the bulk porous media. Further, the influence of the fluid phase as well as the interactive heat conduction between solid and fluid phase on the overall effective thermal conductivity is quantified.