Predictive modeling of unsteady mixed MHD nanofluid convection around a rotating wavy cylinder: a combined GFEM and neural network approach

This paper investigates the unsteady magneto-hydrodynamic mixed convection of Cu-water nanofluids within a square cavity featuring a centrally located rotating wavy cylinder. Unlike prior studies that focus on steady-state or smooth geometries, this research extends the field by exploring the synergistic effects of unsteady rotation and surface morphology. The study aims to bridge the gap between complex numerical simulations and real-time engineering applications by developing a high-precision Artificial Neural Network (ANN) surrogate model.

A hybrid computational approach is implemented, integrating the Galerkin Finite Element Method with machine learning. The investigation spans a wide range of parameters: Rayleigh number (⁠$103≤Ra≤106$⁠), Hartmann number (⁠$0≤Ha≤60$⁠) and rotational speed (⁠$−500≤Ωrot≤500$⁠). A dataset of 960 high-fidelity samples was generated to train a multilayer feed-forward ANN, optimized with 9 hidden neurons and the Levenberg–Marquardt algorithm.

The results quantify the significant impact of the governing parameters on thermal performance. Increasing Ra from $103$ to $106$ enhances the average Nusselt number (⁠$Nuavg$⁠) by 180.5%, while the magnetic field (⁠$Ha=60$⁠) exerts a damping effect that reduces heat transfer by 38.2%. Notably, the interaction between surface waviness and rotation reveals that high rotational speeds can mitigate magnetic damping, providing an additional 8.7% thermal boost. The ANN model achieved an exceptional $R2$ of 0.9836 and an mean squared error of $1.3719×10−6$⁠, effectively reducing computational overhead from several minutes to milliseconds.

This study distinguishes itself by establishing a robust framework that captures nonlinear thermal transients in complex wavy geometries – a configuration often overlooked in standard computational fluid dynamics literature. The implications of this study are significant for the thermal management of high-power density systems, such as electric motor cooling and solar thermal receivers. By providing a highly efficient surrogate tool, this research establishes a foundational framework for rapid parametric screening and design optimization in advanced thermal systems, bypassing the computational bottlenecks associated with traditional iterative solvers.