A 3D model to predict the influence of nanoscale pores or reduced gas pressures on the effective thermal conductivity of cellular porous building materials

Cellular porous materials are frequently applied in the construction industry, both for structural and insulation purposes. The progressively stringent energy regulations mandate the development of better performing insulation materials. Recently, novel porous materials with nanopores or reduced gas pressures have been shown to possess even lower thermal conductivities because of the Knudsen effect inside their pores. Further understanding of the relation between the pore structure and the effective thermal conductivity is needed to quantify the potential improvement and design new optimized materials. This article presents the extension of a 3D numerical framework simulating the heat transfer at the pore scale. A novel methodology to model the reduced gas-phase conductivity in nanopores or at low gas pressures is presented, accounting for the 3D pore geometry while remaining computationally efficient. Validation with experimental and numerical results from the literature indicates the accuracy of the methodology over the full range of pore sizes and gas pressures. Combined with an analytical model to account for thermal radiation, the framework is applied to predict the thermal conductivity of a nanocellular poly(methyl methacrylate) foam experimentally characterized in the literature. The simulation results show excellent agreement with less than 5% difference with the experimental results, validating the model's performance. Furthermore, results also indicate the potential improvements when decreasing the pore size from the micrometre to the nanometre range, mounting up to 40% reduction for such high-porosity low-matrix-conductivity materials. Future application of the model could assist the design of advanced materials, properly accounting for the effect of reduced pore sizes and gas pressures.