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Modeling and simulation of Maxwell nanofluid flows in the presence of Lorentz and Darcy–Forchheimer forces: toward a new approach on Buongiorno’s model using artificial neural network (ANN)

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Abstract

The current work explores the intelligent computational strength of neural networks based on the Levenberg–Marquardt backpropagation (LMBP-NNs) neural networks technique for simulation of Maxwell nanofluid flow past a linear stretchable surface model. The fluid flow is incorporated Rosseland’s thermal radiation, and Darcy’s Forchheimer law. The Maxwell nanofluid model gives more relaxing time to momentum boundary layer. For the nanofluid phenomena that concentrate on thermophoresis and Brownian motion, Buongiorno’s model is used. The procedure transforms partial differential equations arising in nanofluidics systems with an appropriate degree of similarity into nonlinear differential equation systems. For the nonlinear nanofluid problem with accuracy having order 4–5, the (FDM) finite difference method (Lobatto IIIA) is implemented via various selections of collocation points. The strong aspect of Lobatto IIIA is its ability to handle very nonlinear couple differential equations in an easy manner. The precise results of (FDM) are used to build the reference datasets for LMBP-NNs technique for the various factors of fluid problem. The design scheme for various factors of fluid problem carries out a series of operations based on training, testing, and authentication on reference dataset. The accuracy of LMBP-NNs is checked through statistical based neural network tools such that mean square error, regression plot, curve fitting graphs, and error histogram. Furthermore, the investigation of flow model parameters for momentum, energy, and concentration profiles is described via visual representation.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available within the article.]

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, 23200, Pakistan

    Zeeshan Khan, Saeed Islam & Aatif Ali

  2. Department of Computing and Technology, Abasyn University, Peshawar, 25000, Pakistan

    Samina Zuhra

  3. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC

    Muhammad Asif Zahoor Raja

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  1. Zeeshan Khan
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Khan, Z., Zuhra, S., Islam, S. et al. Modeling and simulation of Maxwell nanofluid flows in the presence of Lorentz and Darcy–Forchheimer forces: toward a new approach on Buongiorno’s model using artificial neural network (ANN). Eur. Phys. J. Plus 138, 107 (2023). https://doi.org/10.1140/epjp/s13360-022-03583-w

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