Simulation of magnetized ferric oxide nanoparticle flow over a stretching surface using a Levenberg–Marquardt backpropagation approach
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 result...
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| Vydané v: | Journal of the Brazilian Society of Mechanical Sciences and Engineering Ročník 47; číslo 10; s. 464 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2025
Springer Nature B.V |
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| ISSN: | 1678-5878, 1806-3691 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 464 |
| Author | Azhar, Ehtsham Ahmed, Iftikhar Ali, Hashmat Jamal, Muhammad Afaq, Harsa |
| Author_xml | – sequence: 1 givenname: Iftikhar surname: Ahmed fullname: Ahmed, Iftikhar organization: Department of Mathematics, COMSATS University – sequence: 2 givenname: Ehtsham surname: Azhar fullname: Azhar, Ehtsham organization: Department of Mathematics, PMAS Arid Agriculture University – sequence: 3 givenname: Hashmat surname: Ali fullname: Ali, Hashmat organization: Department of Mathematics, PMAS Arid Agriculture University – sequence: 4 givenname: Muhammad surname: Jamal fullname: Jamal, Muhammad organization: Department of Mathematics, PMAS Arid Agriculture University – sequence: 5 givenname: Harsa orcidid: 0009-0000-4580-7447 surname: Afaq fullname: Afaq, Harsa email: harsaafaq357@gmail.com organization: Department of Mathematics, PMAS Arid Agriculture University |
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| SubjectTerms | Artificial neural networks Back propagation networks Blood flow Boundary conditions Charged particles Engineering Ferric oxide Ferrofluids Fluid flow Graphical representations Heat transfer Investigations Magnetic dipoles Magnetic fields Mechanical Engineering Nanoparticles Nusselt number Ordinary differential equations Partial differential equations Radiation Runge-Kutta method Skin friction Stretching Technical Paper Two dimensional flow Velocity |
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| Title | Simulation of magnetized ferric oxide nanoparticle flow over a stretching surface using a Levenberg–Marquardt backpropagation approach |
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