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<p>This study explores the magnetohydrodynamic (MHD) Jeffery–Hamel flow and heat transfer of a viscous hybrid nanofluid (Cu–Al<sub>2</sub>O<sub>3</sub>/water) between two rigidly inclined, non-parallel plates using fuzzy logic and Artificial Neural Networks (ANN). A core novelty is the incorporation of fuzzy logic with the volume fraction of nanoparticles described as triangular fuzzy numbers (TFNs) (0, 0.05, 0.1), reflecting intrinsic uncertainties in the model. The numerical data obtained from the governing equations are used to train ANN models based on the Bayesian Regularization and Levenberg–Marquardt algorithms for accurately predicting the Nusselt number and flow parameters. Most importantly, the incorporation of alpha-cut methods (α in [0,1]) on the fuzzy differential equations enables effective investigation of the system's dynamic behavior with minimal computing cost. The results reveal that the growth of Hartmann numbers accelerates fluid velocity, whereas the influence of channel angle and Reynolds number vary distinctly between divergent and convergent flow configurations. Fuzzy α-cut analysis reveals noticeable spreads in the velocity, Nusselt number, temperature and skin-friction responses, demonstrating clear sensitivity of the system to uncertainty in nanoparticle concentrations. The hybrid nanofluid exhibits lower skin friction but decreased Nusselt number compared to mono nanofluids. The ANN predictions accomplished an exceptional correlation (R = 1) and minimal mean squared error (~<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(10^{ - 8}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>), confirming the validity of the model.</p>

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Fuzzy-ANN integrated modeling of magnetohydrodynamic Jeffery–Hamel hybrid nanofluid flow in convergent–divergent channels

  • 期刊论文

  • 发表日期：

    2025年12月26日

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  • Rabia Zetoon,
  • Azad Hussain

摘要

This study explores the magnetohydrodynamic (MHD) Jeffery–Hamel flow and heat transfer of a viscous hybrid nanofluid (Cu–Al2O3/water) between two rigidly inclined, non-parallel plates using fuzzy logic and Artificial Neural Networks (ANN). A core novelty is the incorporation of fuzzy logic with the volume fraction of nanoparticles described as triangular fuzzy numbers (TFNs) (0, 0.05, 0.1), reflecting intrinsic uncertainties in the model. The numerical data obtained from the governing equations are used to train ANN models based on the Bayesian Regularization and Levenberg–Marquardt algorithms for accurately predicting the Nusselt number and flow parameters. Most importantly, the incorporation of alpha-cut methods (α in [0,1]) on the fuzzy differential equations enables effective investigation of the system's dynamic behavior with minimal computing cost. The results reveal that the growth of Hartmann numbers accelerates fluid velocity, whereas the influence of channel angle and Reynolds number vary distinctly between divergent and convergent flow configurations. Fuzzy α-cut analysis reveals noticeable spreads in the velocity, Nusselt number, temperature and skin-friction responses, demonstrating clear sensitivity of the system to uncertainty in nanoparticle concentrations. The hybrid nanofluid exhibits lower skin friction but decreased Nusselt number compared to mono nanofluids. The ANN predictions accomplished an exceptional correlation (R = 1) and minimal mean squared error (~ \(10^{ - 8}\) 10 - 8 ), confirming the validity of the model.