The stagnant thermal conductivity of porous media predicted by the random walk theory

Abstract

This study developed a predictive model based on the random walk theory to calculate the stagnant thermal conductivity of porous materials considering detailed pore geometries. This model can take the connectedness of solid matrix and filling fluid into consideration and simulate porous media with a wide range of porosities and geometries. The model was calibrated by comparing simulated thermal conductivities of simplified geometries proposed in literature with the corresponding experimental data. Results indicate that the stagnant thermal conductivities of porous media are very sensitive to the connectedness (or contact resistance) of the solid matrix, especially when the conductivity of the solid matrix (e.g. Al) is much higher than the conductivity of filling fluid (air). This study also imported reconstructed three-dimensional geometries (measured by micro computed tomography) of Al foams into the model and simulated their stagnant thermal conductivities. The measured Al foams have porosities around 0.9 and different pore sizes (5, 10, 20, and 40 parts per inch). The simulated stagnant thermal conductivities of Al foams slightly increased with decreased pore size at the porosity around 0.9.The model developed in this study is a powerful tool to predict stagnant thermal conductivity of porous media widely applied in a broad range of science and engineering disciplines. The low computational time of this model makes it a unique tool to provide real-time updates of material properties for on-site applications or other computational models. Furthermore, the solid matrix and the filling fluid in the porous medium could be multi-phase mixtures or composite materials due to the statistical nature of the random walk model.