Asian Research Journal of Mathematics

This study presents an advanced artificial intelligence (AI) driven framework to model thermo-magnetic nanofluid convection within a wavy-top trapezoidal cavity containing internal obstacles of varying geometries. The study aims to develop an AI-enhanced model to analyze and optimize thermo-magnetic convection of nanofluids in a wavy-top trapezoidal cavity, focusing on the effects of magnetic field, nanoparticle concentration, and cavity geometry on heat transfer performance. The system is influenced by an external magnetic field, varying Rayleigh numbers (Ra), Hartmann numbers (Ha), nanoparticle volume fractions (ϕ), and obstacle shapes (square, star, triangle). Finite Element Method (FEM) simulations were conducted to generate high-fidelity datasets, capturing the variations in Nusselt number (Nu), entropy generation (S_T), and effective coefficient of performance (ECOP). These outputs were then predicted using three AI models: Support Vector Regression (SVR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost). Among the models, RF consistently demonstrated superior performance across all parameters. For Nu prediction, RF achieved a Mean Absolute Error (MAE) of 0.0193, Mean Squared Error (MSE) of 0.00069, and R² of 0.9989, outperforming SVR (MAE = 0.0247) and XGBoost (MAE = 0.0215). In entropy generation prediction, RF attained an MAE of 4.48×10⁻⁶, MSE of 4.35×10⁻¹¹, and R² of 0.9992. For ECOP, RF recorded an MAE of 15.201, MSE of 386.65, and R² of 0.9986, while SVR showed a higher error margin (MAE = 21.132). The strong alignment of AI-predicted values with FEM results confirms the reliability and generalizability of the models. This research highlights the feasibility of using machine learning as a computationally efficient surrogate to solve complex multiphysics problems in thermal engineering, offering a promising tool for real-time prediction and design optimization of advanced heat transfer systems. For future work, this research can be extended by exploring hybrid or non-Newtonian nanofluids, introducing transient and time-dependent thermal analyses, and applying more advanced AI techniques, such as deep learning or physics-informed neural networks.