Artificial Neural Network and Response Surface Methodology-Driven Optimization of Cu–Al 2 O 3 /Water Hybrid Nanofluid Flow in a Wavy Enclosure with Inclined Periodic Magnetohydrodynamic Effects

This study explores the optimization of a Cu–Al 2 O 3 /water hybrid nanofluid within an irregular wavy enclosure under inclined periodic MHD effects. Hybrid nanofluids, with different mixture ratios of copper (Cu) and alumina (Al 2 O 3 ) nanoparticles in water, are used in this study. Numerical simulations using the Galerkin residual-based finite-element method (FEM) are conducted to solve the governing PDEs. At the same time, artificial neural networks (ANNs) and response surface methodology (RSM) are employed to optimize thermal performance by maximizing the average Nusselt number ( Nu av ), the key indicator of thermal transport efficiency. Thermophysical properties such as viscosity and thermal conductivity are evaluated for validation against experimental data. The results include visual representations of heatlines, streamlines, and isotherms for various physical parameters. Additionally, Nu av , friction factors, and thermal efficiency index are analyzed using different nanoparticle ratios. The findings show that buoyancy and MHD parameters significantly influence heat transfer, friction, and thermal efficiency. The addition of Cu nanoparticles improves heat transport compared to Al 2 O 3 nanofluid, demonstrating the superior thermal conductivity of the Cu–Al 2 O 3 /water hybrid nanofluid. The results also indicate that adding Al 2 O 3 nanoparticles to the Cu/water nanofluid diminishes the heat transport rate. The waviness of the geometry shows a significant impact on thermal management as well. Moreover, the statistical RSM analysis indicates a high R 2 value of 98.88% for the response function, which suggests that the model is well suited for predicting Nu av . Furthermore, the ANN model demonstrates high accuracy with a mean squared error (MSE) of 0.00018, making it a strong alternative to RSM analysis. Finally, this study focuses on the interaction between the hybrid nanofluid, a wavy geometry, and MHD effects, which can optimize heat transfer and contribute to energy-efficient cooling or heating technologies.