Different arrangements of simplified models to predict effective thermal conductivity of open-cell foams

Abstract

It is often desirable to predict the effective thermal conductivity (ETC) of a homogenous material like open-cell foams based on its composition, particularly when variations in composition are expected. A combination of five fundamental simplified thermal conductivity bounds and models (series, parallel, Hashin–Shtrikman, effective medium theory, and reciprocity models) is proposed to predict ETC of open-cell foams. Usually, these models use a parameter as the weighted mean to account the proportion of each bound arranged in arithmetic and geometric schemes. Based on ETC data obtained on numerous virtual Kelvin-like foam samples, the dependence of this parameter has been deduced as a function of morphology and phase thermal conductivity ratio. Various effective thermal conductivity correlations are derived based on material properties and foam structure. This is valid for open-cell foams filled with any arbitrary working fluid over a solid conductivity of materials range ( $$\lambda_{s} /\lambda_{f}$$ = 10–30,000) and over a wide range of porosity (0.60 $$< \varepsilon_{o} <$$ 0.95). Arrangement of series and parallel models together using the simplest models for both, arithmetic and geometric schemes, is found to predict excellent results among all the generic combinations.