Computational Requirements for Modeling Thermal Conduction in Polymeric Phase-Change Materials: Periodic Hard Spheres Case

Kevin A. Redosado Leon (Corresponding author), Alexey Lyulin, Bernard J. Geurts

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This research focuses on modeling heat transfer in heterogeneous media composed of stacked spheres of paraffin as a perspective polymeric phase-change material. The main goal is to study the requirements of the numerical scheme to correctly predict the thermal conductivity in a periodic system composed of an indefinitely repeated configuration of spherical particles subjected to a temperature gradient. Based on OpenFOAM, a simulation platform is created with which the resolution requirements for accurate heat transfer predictions were inferred systematically. The approach is illustrated for unit cells containing either a single sphere or a configuration of two spheres. Asymptotic convergence rates confirming the second-order accuracy of the method are established in case the grid is fine enough to have eight or more grid cells covering the distance of the diameter of a sphere. Configurations with two spheres can be created in which small gaps remain between these spheres. It was found that even the under-resolution of these small gaps does not yield inaccurate numerical solutions for the temperature field in the domain, as long as one adheres to using eight or more grid cells per sphere diameter. Overlapping and (barely) touching spheres in a configuration can be simulated with high fidelity and realistic computing costs. This study further extends to examine the effective thermal conductivity of the unit cell, particularly focusing on the volume fraction of paraffin in cases with unit cells containing a single sphere. Finally, we explore the dependence of the effective thermal conductivity for unit cells containing two spheres at different distances between them.

Original languageEnglish
Article number1015
Number of pages21
Issue number7
Publication statusPublished - 1 Apr 2024


This investigation is a part of the research initiative titled \u2018Nanofiller-enhanced wax for heat storage (Wax+)\u2019, identified by project number 18052 within the Open Technology Programme. The initiative receives (partial) funding from the Dutch Research Council (NWO), specifically under the Applied and Engineering Sciences (TTW) domain. Computations were performed at the Dutch national computing center Surf Sara, made possible by the \u2018Multiscale Modeling and Simulation\u2019 computing project, funded by NWO.

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek


    • conjugate heat transfer
    • effective thermal conductivity
    • high-fidelity simulation
    • OpenFOAM
    • periodic systems
    • resolution requirements


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