Numerical and Intelligent Modeling of MHD Casson Nanofluid Heat Transfer in Fractal Porous Cavities for Energy Systems

Abstract

This study investigates the enhancement of convective heat transfer in magnetohydrodynamic (MHD) nanofluid systems containing complex internal structures. Although fractal geometries have recently attracted attention for improving thermal transport, their interaction with porous media, non-Newtonian fluid behavior, and magnetic effects remains insufficiently understood. In particular, the combined influence of fractal barriers and Casson nanofluids on flow structure and heat transfer performance has not been systematically explored. To address this gap, the present work develops a computational framework that integrates the Finite Element Method (FEM) with Artificial Neural Networks (ANN) to analyze and predict thermal behavior in porous enclosures containing fractal internal barriers. Numerical simulations are performed using COMSOL Multiphysics to examine MHD Cu–H₂O nanofluid flow under varying Rayleigh numbers, Darcy numbers, nanoparticle volume fractions, and geometric configurations. The results reveal that the geometric complexity of fractal barriers significantly modifies flow circulation, disrupts symmetry, and generates secondary vortices, leading to a 35%–48% enhancement in the local Nusselt number. Increasing the Rayleigh number intensifies buoyancy-driven convection and fluid mixing, while larger Darcy numbers improve permeability and strengthen convective transport. The application of a transverse magnetic field introduces Lorentz damping, reducing convection by up to 13% and shifting the heat transfer mechanism toward conduction-dominant regimes. To accelerate prediction and optimization, a data-driven ANN model based on Bayesian Regularization Training (BRT-ANN) is developed using the FEM simulation dataset. The trained network demonstrates excellent predictive capability with regression coefficients of R = 1 for training, validation, and testing datasets, rapid mean squared error convergence over 238 epochs, and very small gradient values (9.8894 × 10⁻⁸). The strong agreement between FEM and ANN predictions highlights the effectiveness of the proposed hybrid FEM–ANN framework for rapid thermal performance estimation in complex thermal systems. This integrated approach provides a reliable tool for the design and optimization of advanced heat transfer devices in aerothermal and energy engineering applications.