Numerical Study of Effective Thermal Conductivity for Periodic Closed-Cell Porous Media

The present investigation aims to evaluate the thermal conduction behavior of closed-cell porous media through micromechanical modeling. Numerical analyses were conducted using the finite element method. The overall thermal conductivity of the model structures, encompassing a range of porosity and pore geometry, was investigated. Attention is devoted to the effective response as a function of the two-dimensional (2D) and three-dimensional (3D) porous microstructures. The model geometries were generated based on non-overlapping pore topologies arranged in an orderly manner so the unit-cell modeling approach can be used. The sensitivity of the results to pore morphology was examined by comparing the normalized effective thermal conductivities, and by comparing the numerical results with available analytical models. It was found that the effective thermal conductivity, decreasing with the increasing porosity, is insensitive to the spatial arrangement, clustering, and size distribution of closed pores. The numerical predictions match the classical Maxwell and Rayleigh equations in both 2D and 3D. Elliptical pores with mixed orientations lead to nominally isotropic behavior, but the effective conductivity is lower compared to circular pores. An analytical expression used to convert 2D results to 3D is validated numerically, with its general applicability assessed and the adjusting parameter quantified in this study.