A three-cell effective thermal conductivity model of two-phase porous media

Effective thermal conductivity of porous media is of interest in many heat transfer applications. In this study, a new three-cell two-phase model is developed to calculate porous medium thermal conductivity. In the proposed three-cell model, each solid particle is enveloped by two concentric cells with one being fluid and the other solid. The outermost solid cell is proposed to conceptualize the interactions among the solid particles and fluid. The temperature distributions in the three cells are separately solved and the effective thermal conductivity is then determined. Quantitatively, a contact factor (z factor), which is equal to the solid volume faction that is in the outermost cell, is introduced to reflect the extent of phase contact among the two phases. Under special cases with z = 0 and z = 1 when the three-cell model collapses to two-cell models, the model can bridge the Hashin-Shtrikman (H.S.) lower and upper bounds (or the two forms of Maxwell-Eucken model). In more general cases, the model always predicts thermal conductivity between the H.S. bounds when the z factor is between 0 and 1. The proposed model can well capture the trend of published models and experimental data as well as the results from detailed pore-scale numerical simulations when the z factor decreases non-linearly as the porosity increases.