Effective thermal conductivity of graphene-coated paraffin spheres

We investigate the effective conjugate heat transfer in heterogeneous media consisting of graphene-coated paraffin spheres, designed as composite phase-change material for thermal batteries. We model the heterogeneous medium as a periodic system of spherical particles subjected to a temperature gradient. This system is described in terms of a lattice built using a unit cell with a configuration of spheres inside. Utilizing OpenFOAM, we develop a simulation platform to systematically determine resolution requirements for precise heat transfer predictions. The approach is demonstrated for unit cells containing a single coated sphere. The primary objective is to determine the required spatial resolution necessary to accurately predict the effective thermal conductivity (κ_eff). We establish convergence rates confirming the formal order of accuracy of the method when the grid resolution includes 8 or more grid cells per diameter D of the sphere and 4 grid cells or more to cover the thickness δ of the graphene coating. We examined the effective thermal conductivity varying the paraffin volume fraction, the graphene coating thickness, and the ratio of coating to paraffin thermal conductivity. We observed that the effective thermal conductivity increases rapidly with higher coating conductivity and thicker coatings. The effective thermal conductivity approaches a plateau value when the ratio between the conductivity of the coating and that of the paraffin exceeds approximately 100. Under such conditions κ_eff of the coated sphere is about 28% times higher than that of the pure paraffin sphere. We investigate this dependence of κ_eff for a range of graphene coating thicknesses and quantify the asymptotic regime for κ_eff.