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<p>This study presents a comprehensive analysis of Cu–Al<sub>2</sub>O<sub>3</sub>/water hybrid nanofluid over a stretched cylinder surface, including microscale effects in terms of velocity slip and thermal jump conditions. An unsupervised deep learning framework called unsupervised deep learning physics-informed neural networks (UDL-PINN) was used in modeling the nonlinear system governing the momentum and energy transport processes. The physical effects for magnetohydrodynamics (MHD), viscous dissipation, curvature, and radiative heat transfer were incorporated, and the governing equations were transformed into a coupled system of dimensionless ordinary differential equations through similarity transformations. These differential equations were solved in a physics-informed neural network framework with automatic differentiation. A number of parametric studies in the regime of slip and jump conditions, Prandtl number, Eckert number, curvature, and magnetic field strength were investigated in order to determine the effect on the velocity and temperature distributions. The results benchmarked well to already existing numerical solutions, confirming the accuracy and convergence of the model. The results confirmed that hybrid nanofluids has optimal heat transfer enhancement given the same conditions, and reduced skin friction compared to classical nanofluids. The model was also a consistent operating framework for future deep learning integration into real-time digital twin systems, which could optimize thermal processes in engineering, biomedical, and bioenergy applications.</p>

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Unsupervised deep learning for enhancement in Cu–Al2O3/water hybrid nanofluid flow over a stretched cylinder with slip and thermal jump effects

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Hanen Louati,
  • Zahoor Shah,
  • Hamza Iqbal,
  • Maryam Jawaid,
  • Mohammed M. A. Almazah

摘要

This study presents a comprehensive analysis of Cu–Al2O3/water hybrid nanofluid over a stretched cylinder surface, including microscale effects in terms of velocity slip and thermal jump conditions. An unsupervised deep learning framework called unsupervised deep learning physics-informed neural networks (UDL-PINN) was used in modeling the nonlinear system governing the momentum and energy transport processes. The physical effects for magnetohydrodynamics (MHD), viscous dissipation, curvature, and radiative heat transfer were incorporated, and the governing equations were transformed into a coupled system of dimensionless ordinary differential equations through similarity transformations. These differential equations were solved in a physics-informed neural network framework with automatic differentiation. A number of parametric studies in the regime of slip and jump conditions, Prandtl number, Eckert number, curvature, and magnetic field strength were investigated in order to determine the effect on the velocity and temperature distributions. The results benchmarked well to already existing numerical solutions, confirming the accuracy and convergence of the model. The results confirmed that hybrid nanofluids has optimal heat transfer enhancement given the same conditions, and reduced skin friction compared to classical nanofluids. The model was also a consistent operating framework for future deep learning integration into real-time digital twin systems, which could optimize thermal processes in engineering, biomedical, and bioenergy applications.