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<p>This study investigates the Jeffery–Hamel flow of a couple-stress fluid under the influence of a magnetic field using an artificial neural network (ANN) approach. While extensively studied for Newtonian fluids, the dynamics of such flows in converging/diverging channels, especially for couple-stress fluids, remain largely unexplored. We pioneer the use of ANNs to solve a fifth-order nonlinear differential equation arising from the Jeffery–Hamel flow, 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 velocity profiles influenced by magnetic fields. We focus on fluid flow behaviour, analysing the effects of key parameters<b>:</b> Reynolds number (<i>Re</i>), magnetic parameter (<i>M</i>), channel angle (<i>α</i>), and couple-stress parameter (<i>S</i>)<b>,</b> on velocity distribution and flow structure. Results show that increasing <i>M</i> reduces fluid velocity for both low (<i>S</i> = 5) and high (<i>S</i> = 1000) values of the couple-stress parameter. In contrast, this behaviour is opposite in the case of Newtonian fluids, where increasing <i>M</i> enhances the velocity of the fluid. We also observe that at low <i>S</i>, the velocity profiles are tightly clustered due to the dominant couple-stress viscosity. In contrast, at high <i>S</i>, the profiles show noticeable variation as the influence of couple-stress viscosity decreases. Larger channel angles <i>α</i> and higher <i>S</i> values increase fluid velocity, whereas increasing <i>Re</i> also elevates velocity, revealing deviations from Newtonian fluid behaviour. The proposed ANN-based methodology bridges gaps in the literature and provides a powerful tool for modelling biological, industrial, and microfluidic flows in magnetically influenced channels, demonstrating unprecedented microstructural interactions absent in prior Newtonian or non-Newtonian studies. These insights can guide the optimisation of fluid dynamics in applications involving couple-stress fluids under magnetic fields.</p>

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Analysis of Magnetohydrodynamic Jeffery–Hamel Flow of a Couple-Stress Fluid Using an Artificial Neural Network Model

  • 期刊论文

  • 发表日期：

    2026年7月19日

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  • Atul Kaushik,
  • J. V. Ramana Murthy

摘要

This study investigates the Jeffery–Hamel flow of a couple-stress fluid under the influence of a magnetic field using an artificial neural network (ANN) approach. While extensively studied for Newtonian fluids, the dynamics of such flows in converging/diverging channels, especially for couple-stress fluids, remain largely unexplored. We pioneer the use of ANNs to solve a fifth-order nonlinear differential equation arising from the Jeffery–Hamel flow, 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 velocity profiles influenced by magnetic fields. We focus on fluid flow behaviour, analysing the effects of key parameters: Reynolds number (Re), magnetic parameter (M), channel angle (α), and couple-stress parameter (S), on velocity distribution and flow structure. Results show that increasing M reduces fluid velocity for both low (S = 5) and high (S = 1000) values of the couple-stress parameter. In contrast, this behaviour is opposite in the case of Newtonian fluids, where increasing M enhances the velocity of the fluid. We also observe that at low S, the velocity profiles are tightly clustered due to the dominant couple-stress viscosity. In contrast, at high S, the profiles show noticeable variation as the influence of couple-stress viscosity decreases. Larger channel angles α and higher S values increase fluid velocity, whereas increasing Re also elevates velocity, revealing deviations from Newtonian fluid behaviour. The proposed ANN-based methodology bridges gaps in the literature and provides a powerful tool for modelling biological, industrial, and microfluidic flows in magnetically influenced channels, demonstrating unprecedented microstructural interactions absent in prior Newtonian or non-Newtonian studies. These insights can guide the optimisation of fluid dynamics in applications involving couple-stress fluids under magnetic fields.