Analyzing Stability of Nano-Enhanced PCM via Control Volume Method

Abstract: This work presents a rigorous numerical and theoretical investigation into the stability characteristics of nano-enhanced phase change materials (NEPCMs) subjected to control volume discretization. The governing energy conservation equation is discretized using a finite volume scheme, incorporating nonlinear thermophysical properties of NEPCMs, modeled via Maxwell-Garnett and mixture theory formulations for thermal conductivity and heat capacity, respectively. An explicit expression for the axial velocity component is derived from the energy balance, linking it to enthalpy evolution, spatial temperature gradients, and grid resolution. A generalized stability criterion is reformulated from the Courant-Friedrichs-Lewy (CFL) condition, parameterized by local thermophysical properties and mesh-dependent quantities. Stability number maps and phase-plane portraits are generated using MATLAB to define feasible computational domains under varying spatial variations. The impact of nanoparticle concentration, enthalpy flux, and thermal diffusion coefficients on the stability regime is systematically quantified. Results demonstrate that stability deteriorates nonlinearly with increasing nanoparticle concentration due to suppressed thermal diffusivity, and that finer spatial grids necessitate exponentially smaller time steps to maintain numerical fidelity. The analysis bridges the gap between physical modeling and numerical stability in NEPCM systems and establishes a robust framework for parameter selection in transient thermal simulations of latent heat storage media. Keywords: Control Volume Discretization, Enthalpy Evolution, Grid Resolution, Finite Volume Scheme, Nano-Enhanced Phase Change Material; Stability Characteristics. Title: Analyzing Stability of Nano-Enhanced PCM via Control Volume Method Author: Florence Awuor Misawo, Thomas T. O. Onyango, Fredrick O. Nyamwala International Journal of Novel Research in Physics Chemistry & Mathematics ISSN 2394-9651 Vol. 12, Issue 1, January 2025 - April 2025 Page No: 86-103 Novelty Journals Website: www.noveltyjournals.com Published Date: 26-April-2025 DOI: https://doi.org/10.5281/zenodo.15286312 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Analyzing%20Stability%20of%20Nano-26042025-3.pdf