Finite-size scaling and percolation behavior of the effective thermal conductivity in polydisperse porous media

Accurately predicting the effective thermal conductivity (ETC) of random porous media is critical for understanding heat and mass transfer in various engineering applications. Nevertheless, it remains challenging due to microstructural heterogeneity and finite-size effects, which increase the characterization difficulty and may lead to scale-dependent and non-representative predictions. To address these limitations, this study proposes a comprehensive finite-size scaling (FSS) framework. By coupling massive Monte Carlo 2D porous media generation with steady-state heat transfer simulations, considering various particle distribution patterns, a vast dataset of ETC results is obtained. Supported by the microstructural analysis of heat flux density distributions, the results demonstrate that ETC is highly sensitive to the finite-size effect, which is governed by the interplay between domain size and particle radius distributions. It is found that the thermal conductivity of the pore phase significantly lowers the macroscopic percolation threshold by allowing the fluid to act as the filler that bridges isolated solid clusters. Moreover, introducing contact thermal resistance reduces the magnitude of ETC but does not alter the percolation thresholds or the universal scaling behavior. Ultimately, by calculating the optimized critical exponent σ = 1.35 , the highly dispersive ETC data are successfully collapsed onto a single FSS curve. The proposed FSS framework eliminates the finite-size effect and proves that macroscopic thermal transport in polydisperse 2D porous media is fundamentally governed by a universal scaling law, providing a robust tool for porous media ETC determinations in practical engineering designs.