An entropy-based random-walk model for predicting in-plane thermal conductivity of porous media

Abstract

In this study, we propose a random-walk model to estimate the in-plane thermal conductivity of porous media within a two-component, two-dimensional domain. An entropy-weighted procedure guides random walkers to explore a heterogeneous domain composed of distinct thermal properties by using independently injected thermal particles. This entropy-based random-walk (ERW) model was validated against several synthetic domains using numerical simulations and theoretical models. Our results demonstrate that the proposed model aligns with the Shannon–H theorem, exhibiting maximal entropy properties. The ERW model showed acceptable precision compared with the theoretical and numerical models. In some geometries, the model closely matched the numerical simulations, whereas in others, it aligned with the theoretical predictions. Connection between the ERW model and weighted harmonic mean model is discussed. Furthermore, the accuracy of the ERW model was tested using real applications with scanning electron microscopy (SEM) images and experimental measurements. A comparison between the ERW model and classical finite-volume method highlights the advantages of the proposed approach in heterogeneous domains with high conductance ratios, where finite-volume model convergence is hindered. To enhance the simulations, a multithreaded parallelized version of the ERW simulations was developed for the CPU platform, which is particularly effective for large numbers of particles.