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<p>In a recent era, artificial intelligence (AI) has become a wonderful tool to deal with nonlinear problem in fluid dynamic fields. We utilize an advanced AI-based computational algorithm known as Levenberg–Marquardt algorithm (LMA) to study a highly nonlinear magnetohydrodynamics (MHD) flow of Carreau nanofluid in a porous medium. Some of the key physical effects incorporated in the present study are viscous dissipation, thermal radiation, mixed convection, Joule heating, and two-component chemical reaction. Assuming unsteady 2D-laminar flow over the surface of a porous circular disk stretching radially with time. The governing partial differential equations (PDEs) are first transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformations, and then solved numerically using Mathematica to obtain high, precision benchmark solutions. Synthetic databases are generated by varying the porosity parameter, magnetic parameter, Weissenberg number, Eckert number, radiation parameter, unsteady parameter, and Schmidt number one at a time, while keeping all other parameters fixed. The referred velocity, temperature, and concentration profiles are taken as the input data to train the LMA-based neural network model with a data split of 70% for training, 15% for validation, and 15% for testing. The method proposed in this paper can be a very accurate tool since it is demonstrated by steadily decreasing absolute errors and very low mean squared error values obtained in all phases of learning. Further stability tests show strong convergence and confirm numerical stability. The parametric study shows that velocity is responsive to the Weissenberg number by going up but under the influence of stronger magnetism and porous effects it goes down, on the other hand, the temperature is changed in the same direction as the viscous dissipation, radiation, and unsteadiness. The concentration goes up with thermal radiation and goes down with the increment of Schmidt and Weissenberg numbers.</p> Graphical Abstract <p></p>

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AI-driven modeling of Carreau nanofluid dynamics with Joule heating and viscous dissipation

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Lin Zhang,
  • Zahoor Shah,
  • Wajeeha Naeem,
  • Amina magdich,
  • Hafedh Mahmoud Zayani

摘要

In a recent era, artificial intelligence (AI) has become a wonderful tool to deal with nonlinear problem in fluid dynamic fields. We utilize an advanced AI-based computational algorithm known as Levenberg–Marquardt algorithm (LMA) to study a highly nonlinear magnetohydrodynamics (MHD) flow of Carreau nanofluid in a porous medium. Some of the key physical effects incorporated in the present study are viscous dissipation, thermal radiation, mixed convection, Joule heating, and two-component chemical reaction. Assuming unsteady 2D-laminar flow over the surface of a porous circular disk stretching radially with time. The governing partial differential equations (PDEs) are first transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformations, and then solved numerically using Mathematica to obtain high, precision benchmark solutions. Synthetic databases are generated by varying the porosity parameter, magnetic parameter, Weissenberg number, Eckert number, radiation parameter, unsteady parameter, and Schmidt number one at a time, while keeping all other parameters fixed. The referred velocity, temperature, and concentration profiles are taken as the input data to train the LMA-based neural network model with a data split of 70% for training, 15% for validation, and 15% for testing. The method proposed in this paper can be a very accurate tool since it is demonstrated by steadily decreasing absolute errors and very low mean squared error values obtained in all phases of learning. Further stability tests show strong convergence and confirm numerical stability. The parametric study shows that velocity is responsive to the Weissenberg number by going up but under the influence of stronger magnetism and porous effects it goes down, on the other hand, the temperature is changed in the same direction as the viscous dissipation, radiation, and unsteadiness. The concentration goes up with thermal radiation and goes down with the increment of Schmidt and Weissenberg numbers.

Graphical Abstract