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<p>The proposed study is to examine the application of blood flow in a 2D Non-Newtonian magnetic dipole over a stretching sheet incorporating ferrofluid nanoparticles. By employing appropriate similarity transformations, the system of PDEs is transformed into a set of coupled nonlinear ODEs. The results were obtained using artificial neural networks (ANNs) in conjunction with the Levenberg–Marquardt backpropagation method (ANNs-LMBM). The Levenberg–Marquardt backpropagation method is a widely used optimization algorithm for training neural networks, specifically designed to effectively minimize the loss function that measures the difference between the neural network’s predicted output (based on a given input vector) and the true target output (the true value obtained from the numerical solution). Additionally, the Runge–Kutta shooting technique was employed to compare the results. Graphical representations were generated to illustrate the relevant parameters such as velocity, temperature, and concentration. Numerical outcomes for the local Nusselt number and local skin friction number were calculated under various parametric scenarios to reveal interesting features of the investigation. Replications using regression/correlation, state transitions, and error histograms were also discussed to validate the capability, validity, consistency, and accuracy of the ANNs-LMBM method.</p>

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Simulation of magnetized ferric oxide nanoparticle flow over a stretching surface using a Levenberg–Marquardt backpropagation approach

  • 期刊论文

  • 发表日期：

    2025年8月2日

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  • Iftikhar Ahmed,
  • Ehtsham Azhar,
  • Hashmat Ali,
  • Muhammad Jamal,
  • Harsa Afaq

摘要

The proposed study is to examine the application of blood flow in a 2D Non-Newtonian magnetic dipole over a stretching sheet incorporating ferrofluid nanoparticles. By employing appropriate similarity transformations, the system of PDEs is transformed into a set of coupled nonlinear ODEs. The results were obtained using artificial neural networks (ANNs) in conjunction with the Levenberg–Marquardt backpropagation method (ANNs-LMBM). The Levenberg–Marquardt backpropagation method is a widely used optimization algorithm for training neural networks, specifically designed to effectively minimize the loss function that measures the difference between the neural network’s predicted output (based on a given input vector) and the true target output (the true value obtained from the numerical solution). Additionally, the Runge–Kutta shooting technique was employed to compare the results. Graphical representations were generated to illustrate the relevant parameters such as velocity, temperature, and concentration. Numerical outcomes for the local Nusselt number and local skin friction number were calculated under various parametric scenarios to reveal interesting features of the investigation. Replications using regression/correlation, state transitions, and error histograms were also discussed to validate the capability, validity, consistency, and accuracy of the ANNs-LMBM method.