Thermal conductivity correlations of open-cell foams: Extension of Hashin–Shtrikman model and introduction of effective solid phase tortuosity

Abstract

Open-cell foams have emerged as promising materials for use in heat sink and heat exchanger applications. The thermal behavior of open-cell foams depends on their microscopic structure. The effective thermal conductivity of open-cell porous foams can be measured using experimental techniques, predicted from the 3-D direct numerical simulations on reconstructed foam structures obtained from micro-computed tomography images or derived from idealized structure thermal analysis. Based on the tetrakaidecahedron unit cell and different strut morphologies, three dependent and interdependent empirical correlations for effective thermal conductivity were derived. They encompass all morphological parameters and ratios of constituent phases of foams of different materials.In this process, the Hashin–Shtrikman (HS) bounds model was first extended and applied to the resistor model. A correlation term, Ω was introduced to take into account the thermal conductivities of constituent phases and the morphological parameters of the foam structure. Secondly, a more complex effective model that is a combination of series and parallel models was derived by introducing effective solid phase tortuosity. Lastly, a simple model (KT-model) was derived that can be used to predict either effective thermal conductivity or intrinsic solid phase conductivity depending upon which one of these quantities is known. The present study clearly demonstrates that the proposed empirical correlations yield extremely accurate estimates of the effective thermal conductivity for all the experimental and numerical data of different foam materials reported in the literature.