A Particle-Particle Heat Transfer Model Incorporating Conduction through Interparticle Contacts and the Interstitial Medium

Abstract Predicting the effective thermal conductivity of particulate systems is of critical importance for a wide range of applications, including powder-bed additive manufacturing, powder metallurgy, battery electrode manufacturing, thermal energy storage and thermal management materials. The inter-particle contacts significantly alter the heat-transfer pathways. Classical analytical models, such as the circular-contact solution of Batchelor & O'Brien, provide elegant formulations for particle-particle conduction but rely on the assumption that solid conduction overwhelmingly dominates over interstitial fluid heat transport. This assumption becomes invalid when heat transfer through the region outside the solid contact (the solid-fluid-solid pathway) is non-negligible. In this study, a corrected conduction model is developed to incorporate the contribution of interstitial fluid. The formulation introduces additional prescribed heat flux boundary conditions outside the solid-solid contact zone to account for the surrounding medium and yields results consistent with finite element analysis (FEA). Parametric studies demonstrate that the corrected model reduces the discrepancy between Batchelor & O'Brien's prediction and FEA prediction from several hundred percentages to within 10% across a wide range of solid-fluid conductivity ratios, compaction levels, and geometric parameters. The proposed model thus provides a unified and computationally efficient framework for evaluating effective thermal conductivity in particulate systems, which can be used in Discrete Element Method (DEM) simulation.