A Particle–Particle Heat Transfer Model Incorporating Conduction Through Interparticle Contacts and the Interstitial Medium

Abstract

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 interparticle contacts significantly alter the heat-transfer pathways. Classical analytical models, such as the circular-contact solution of Batchelor and O'Brien, provide elegant formulations for particle–particle conduction but rely on the assumption that solid conduction overwhelmingly dominates 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 the interstitial medium. 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 improves the agreement with FEA predictions compared with the original Batchelor and O'Brien model, the predicted total heat transfer ratio (qtotal,model/qtotal,FEA) remains close to unity over a wide range of (kS·rC)/(kF·rP) values and geometric conditions, with most deviations falling within 10%. In contrast, the original Batchelor & O'Brien model exhibits largest deviation of 30% under fluid-influenced conditions. The proposed model thus provides unified and computationally efficient formulations for computing particle–particle conduction, which can be used in discrete element method (DEM) simulation.