Computational modelling of heat transfer in multi-sphere thermal energy storage composites

Graphene-enhanced phase-change materials offer a promising route to improve the thermal responsiveness of low-conductivity paraffin used in thermal energy storage. This study numerically investigates the effective thermal conductivity ( κ eff ) of a system of paraffin spheres coated with high-conductivity graphene shells. We use the conjugate heat transfer formulation of multi-inclusion representative volume elements (RVEs) and solve this problem using OpenFOAM. A mesh sensitivity analysis confirms that a spatial resolution of M = D / h ≥ 16 (corresponding to at least 16 computational cells across the sphere diameter) is required to reliably resolve thermal gradients. In coated configurations, the graphene shell is resolved by ensuring a minimum of two grid cells across its thickness. A planar formulation is introduced to compute the steady state effective thermal conductivity κ eff of the entire system. Configurations with 64 or more randomly placed inclusions are found adequate to closely approximate the thermodynamic limit. Comparisons between coated and uncoated systems show that graphene coating substantially enhances κ eff , with simulated values consistently falling between predictions from the Maxwell–Garnett and Bruggeman frameworks. Graphene-coated systems exhibit strong thermal homogenisation, resulting in low internal temperature gradients inside the spheres. In the high-volume fraction limit above ≈ 0 . 2 , the numerical model enables the onset of percolation in which all coating shells around the paraffin spheres combine into one conductive network that connects the high- and the low-temperature boundaries of the system. This illustrates how coating morphology shapes macroscopic heat transfer in structured PCM composites.