CFD and Machine learning-based predictive modeling of natural convection in non-Newtonian nano-encapsulated phase change material within an Enclosure with a corrugated heated cylinder

Enhancing heat transfer and energy storage presents challenges in renewable energy applications. This study examines the thermal efficiency of power-law non-Newtonian nano-encapsulated phase change materials (NEPCM) in a cavity with a corrugated cylinder under natural convection. A non-dimensional framework was developed using the Galerkin finite element method (GFEM), with Polyethylene Glycol (PEG) as the base fluid. Machine learning-based predictive modeling was integrated with computational fluid dynamics (CFD) framework to provide a more reliable approach. The study numerically examined the effect of different non-dimensional parameters, including Rayleigh number $(Ra=10^4-10^6)$, Hartmann number $(Ha=0-90)$, power-law index $(n=0.7-1.4)$, Prandtl number $(Pr=200)$, Stefan number $(Ste=0.313)$, and fusion temperature $({\theta }_f=0.3-0.8)$. It examines streamline, isotherm, entropy generation, heat capacity ratio $\left(Cr\right)$, Nusselt number $\left(Nu\right)$, and Bejan number $\left(\overline{Be}\right)$. Five machine learning models-Decision Tree, Random Forest, KNN, XGBoost, and LightGBM-were used to predict fluid behavior. Results show that increasing $Ra$ reduces vortices, bringing NEPCM’s heat transient phase closer to the cylinder. Higher ${\theta }_f$ shrinks the melting region, and $Nu$ peaks at $Ra=10^6$, decreasing with higher $Ha$ due to the magnetic field. At $Ha=90$, $\overline{Nu}$ drops by 65.88% in the shear-thinning phase $(n=0.7)$. Additionally, $\overline{Nu}$ is reduced by 17.35% as the fluid transitions from the shear-thinning phase $(n=0.7)$ to the shear-thickening phase $(n=1.4)$. The power-law index increases $\overline{Be}$. Random Forest achieved the highest $R^2$ (0.9959) for $\overline{Nu}$, while Decision Tree, Random Forest, and LightGBM showed superior accuracy for $\overline{Be}$. These ML models guarantee quick and precise predictions and act as a roadmap for following fluid dynamics and thermal management research. The interdisciplinary nature of the study, combining GFEM, NEPCM, power-law fluids, and several machine learning models, establishes a benchmark for advancing computational and data-driven approaches to solving challenging engineering problems.