Prediction of effective thermal conductivity of a suspension of core-shell particles using asymptotic homogenization

This study presents the implementation of the asymptotic homogenization method (AHM) to predict the effective thermal conductivity of suspensions featuring core-shell particles. The AHM leverages the significant difference in scales between macroscopic and microscopic structures, making it possible to model the domain at multiple scales by capturing the influence of microscopic inclusions under macroscopic loading conditions on the domain. The study begins by deriving an analytical formulation for the thermal conductivity problem of core-shell composites, using a multiscale asymptotic expansion, followed by developing a finite element model to solve the unit cell problem. The results for core-shell inclusions are validated against known analytical solutions for different volume fractions. At low inclusion volume fractions, the numerical predictions closely match the effective medium approximations. However, at semi-dilute packing fractions, the AHM shows superior accuracy, aligning more closely with the experimental and analytical results. The study reveals that the effective thermal conductivity of the three-component composite is influenced by the volume fractions of the core and shell, the thermal conductivities of the core, shell, and matrix, as well as the spatial distribution of inclusions. The proposed AHM method coupled with finite element analysis offers a generalized approach to predict effective thermal or electrical conductivity.