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<p>Advanced thermal management systems likely microchannel cooling, biomedical transport, and coating processes depends upon various nanofluids due to their superior heat and mass transfer properties. Motivated by these applications, the present study examines the predictive capability of data-driven approaches with numerical modelling on steady MHD Casson nanofluid flow past an extending elastic cylinder. The analysis incorporates significant physical effects including thermophoretic force, Brownian motion, velocity slip, Darcy resistance, and thermal and concentration Biot numbers. The governing nonlinear PDEs of momentum, energy, and concentration transport are transformed into a coupled system of similarity ODEs using suitable similarity transformations. The reference numerical solutions are obtained using the MATLAB <i>bvp4c</i> solver. Methodologically, the study develops and validates a hybrid computational framework by integrating MATLAB bvp4c solutions with physics-informed neural networks (PINNs) and Levenberg–Marquardt artificial neural networks (LM-ANNs). The learning-based models exhibit excellent agreement with the reference numerical solutions, with prediction errors remaining below 0.7% for all transport variables. Physically, the results demonstrate that thermophoretic and Brownian diffusion mechanisms enhance thermal and mass transport, whereas increasing Biot numbers intensify surface convection. The magnetic field suppresses momentum transport while promoting thermal and concentration boundary-layer growth. These findings establish both the reliability of physics-informed machine learning approaches for nonlinear transport problems and new perceptions into MHD Casson nanofluid behaviour in elastic cylindrical systems. The study confirms that PINN and LM-ANN provide reliable alternatives for modelling difficult nanofluid transport phenomena.</p>

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Predictive design using PINN and ANN integrating bvp4c for MHD Casson nanofluid flow over an extending cylinder: microchannel coating and biomedical systems

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Subrata Ghosh,
  • Silpi Hazarika,
  • Sahin Ahmed,
  • S. R. Mishra

摘要

Advanced thermal management systems likely microchannel cooling, biomedical transport, and coating processes depends upon various nanofluids due to their superior heat and mass transfer properties. Motivated by these applications, the present study examines the predictive capability of data-driven approaches with numerical modelling on steady MHD Casson nanofluid flow past an extending elastic cylinder. The analysis incorporates significant physical effects including thermophoretic force, Brownian motion, velocity slip, Darcy resistance, and thermal and concentration Biot numbers. The governing nonlinear PDEs of momentum, energy, and concentration transport are transformed into a coupled system of similarity ODEs using suitable similarity transformations. The reference numerical solutions are obtained using the MATLAB bvp4c solver. Methodologically, the study develops and validates a hybrid computational framework by integrating MATLAB bvp4c solutions with physics-informed neural networks (PINNs) and Levenberg–Marquardt artificial neural networks (LM-ANNs). The learning-based models exhibit excellent agreement with the reference numerical solutions, with prediction errors remaining below 0.7% for all transport variables. Physically, the results demonstrate that thermophoretic and Brownian diffusion mechanisms enhance thermal and mass transport, whereas increasing Biot numbers intensify surface convection. The magnetic field suppresses momentum transport while promoting thermal and concentration boundary-layer growth. These findings establish both the reliability of physics-informed machine learning approaches for nonlinear transport problems and new perceptions into MHD Casson nanofluid behaviour in elastic cylindrical systems. The study confirms that PINN and LM-ANN provide reliable alternatives for modelling difficult nanofluid transport phenomena.