Computational Analysis of Magnetohydrodynamic Jeffery–Hamel Flow for Couple Stress Fluids in Stretching/Shrinking Channels via Artificial Neural Network

ABSTRACT The Jeffery–Hamel flow, a classic benchmark in fluid dynamics, describes the motion of an incompressible viscous fluid within convergent or divergent channels. Although extensively studied for Newtonian fluids, the dynamics of such flows in channels with stretching or shrinking walls, especially for couple‐stress fluids, remain largely unexplored. In this study, we pioneer the use of artificial neural networks (ANNs) to solve a fifth‐order nonlinear differential equation arising from the two‐dimensional Jeffery–Hamel flow of couple‐stress fluids within stretching/shrinking channels, addressing a complex, nonlinear fluid dynamics problem. By capturing microstructural effects and the unique rheology of couple‐stress fluids, our approach enables high‐accuracy solutions for complex flow behaviour influenced by wall deformation. We focus exclusively on fluid flow behaviour, analysing the influence of key parameters such as Reynolds number, magnetic parameter, channel angle, stretching parameter, and couple stress parameter on velocity distribution and flow structure. Our results reveal new flow topologies and response patterns that are unattainable with traditional analytical or numerical methods. The proposed ANN‐based methodology bridges significant gaps in the literature and provides a powerful tool for modelling biological, industrial, and microfluidic flows in adaptive geometries. This work advances the understanding of the dynamics of Jeffery–Hamel flow in couple‐stress fluids within magnetically influenced stretching/shrinking channels, demonstrating unprecedented microstructural interactions absent in prior Newtonian or non‐Newtonian studies, and unveiling the effectiveness of intelligent methods for solving problems in computational fluid mechanics.