Boundary Condition Formulation and Validation in Finite Volume Modelling of Nano-Enhanced Phase Change Materials

Abstract: Nano-Enhanced Phase Change Materials (NePCMs) have become high-performance thermal energy storage media as a result of their augmented thermal conductivity and faster melting–solidification behaviour. However, despite a great development in numerical modelling on NePCMs, one important methodological problem is still unknown: the formulation, implementation and validation of boundary conditions in Finite Volume Method (FVM) based simulations for a systematic way. This gap has helped to feed numerical instability, inaccurate melt-front prediction, and unreliable thermal-fluids behaviour in past studies. The present study overcomes this limitation by merging and validating a complete boundary condition in the form of a Neumann, Dirichlet and Mixed formulation in control volume discretisation. Using coupled momentum and energy equations, nanoparticle enhanced thermophysical models and matrix inversion schemes, the simulations were run for x- and y- direction momentum carrying as well as heat distribution. The results have shown that the specification of proper boundary conditions is an important factor in heat-flux continuity, velocity-field development, thermal stratification and numerical stability. The model captures realistic buoyancy-driven convection, uniform heat diffusion and stable temperature gradients. The study concludes that boundary-condition modelling is very basic in correct NePCM simulations. Policy and future recommendations involve the use of validated numerical frameworks in thermal-storage system designs, expansion of the model to transient, 3D problems, and inclusion of experimental benchmarking for improved predictive reliability. Keywords: Boundary Condition Modelling, Finite Volume Method, Heat Transfer and Energy Storage, Nano-Enhanced Phase Change Materials, Numerical Stability Analysis, Thermophysical Property Enhancement. Title: Boundary Condition Formulation and Validation in Finite Volume Modelling of Nano-Enhanced Phase Change Materials Author: Florence Awuor Misawo, Onyango T. T. Mboya, Fredrick O. Nyamwala International Journal of Novel Research in Physics Chemistry & Mathematics ISSN 2394-9651 Vol. 12, Issue 3, September 2025 - December 2025 Page No: 8-28 Novelty Journals Website: www.noveltyjournals.com Published Date: 25-November-2025 DOI: https://doi.org/10.5281/zenodo.17710716 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Boundary%20Condition%20Formulation-25112025-1.pdf