Finite Element Multigrid Simulation of Natural Convection in Hybrid Nanofluids Within Isolated Cavity for Solar Energy Systems: A Machine Learning-Levenberg-Marquardt Approach

Abstract

This study examines magnetoconvective heat transfer in an enclosure filled with a hybrid nanofluid consisting of Multi-Walled Carbon Nanotubes (MWCNTs) and iron oxide (Fe₃O₄) nanoparticles, a configuration with strong  relevance to solar thermal energy storage and management systems. The governing transport equations are solved using the Finite Element Method (FEM) implemented in COMSOL Multiphysics to analyze the coupled effects of buoyancy, magnetic field, and non-Newtonian rheology. The influence of key controlling parameters, namely the Rayleigh number (Ra), Hartmann number (Ha), and Casson parameter (β ), is systematically investigated. The results reveal that increasing Ra significantly intensifies buoyancy-driven flow circulation, leading to a 36.54% enhancement in convective heat transfer. In contrast, stronger magnetic fields (higher Ha) suppress fluid motion and thermal transport by up to 47.91% due to Lorentz-force-induced damping. Furthermore, an increase in the Casson parameter promotes Newtonian-like behavior, reducing viscous resistance and resulting in a 48.96% improvement in heat transfer performance. These findings provide clear physical insight into the competing roles of buoyancy, magnetic control, and rheological effects in hybrid nanofluid systems. To support rapid prediction and parametric analysis, an Artificial Neural Network (ANN) surrogate model is additionally developed and validated against FEM data, demonstrating high predictive accuracy. FEM simulations are carried out using COMSOL Multiphysics, while the ANN model is implemented in MATLAB. Overall, the study offers both fundamental physical understanding and practical guidance for optimizing magnetically controlled hybrid nanofluid systems in solar energy applications.