Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions
In this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects a...
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024227?viewType=HTML |
| _version_ | 1797323838116069376 |
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| author | Khalil Ur Rehman Wasfi Shatanawi Zead Mustafa |
| author_facet | Khalil Ur Rehman Wasfi Shatanawi Zead Mustafa |
| author_sort | Khalil Ur Rehman |
| collection | DOAJ |
| description | In this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects at the surface. The problem is modelled in terms of a non-linear differential system and Lie symmetry is used to get the scaling group of transformation. The order reduction of differential equations is done by using Lie transformation. The reduced system is solved by the shooting method. The surface quantity, namely skin friction, is evaluated at the surface for the absence and presence of an externally applied magnetic field. A total of 88 sample values are estimated for developing an artificial neural network model to predict skin friction coefficient (SFC). Weissenberg number, magnetic field parameter, and power law index are considered three inputs in the first layer, while 10 neurons are taken in the hidden layer. 62 (70%), 13 (15%), and 13 (15%) samples are used for training, validation, and testing, respectively. The Levenberg-Marquardt backpropagation is used to train the network by entertaining the random 62 sample values. Both mean square error and regression analysis are used to check the performance of the developed neural networking model. The SFC is noticed to be high at a magnetized surface for power law index and Weissenberg number. |
| first_indexed | 2024-03-08T05:33:54Z |
| format | Article |
| id | doaj.art-597a35a5979e4a6ea1d2b460e7fb3308 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:33:54Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-597a35a5979e4a6ea1d2b460e7fb33082024-02-06T01:36:53ZengAIMS PressAIMS Mathematics2473-69882024-01-01924707472810.3934/math.2024227Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditionsKhalil Ur Rehman 0Wasfi Shatanawi1Zead Mustafa 21. Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia1. Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia 2. Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan2. Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, JordanIn this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects at the surface. The problem is modelled in terms of a non-linear differential system and Lie symmetry is used to get the scaling group of transformation. The order reduction of differential equations is done by using Lie transformation. The reduced system is solved by the shooting method. The surface quantity, namely skin friction, is evaluated at the surface for the absence and presence of an externally applied magnetic field. A total of 88 sample values are estimated for developing an artificial neural network model to predict skin friction coefficient (SFC). Weissenberg number, magnetic field parameter, and power law index are considered three inputs in the first layer, while 10 neurons are taken in the hidden layer. 62 (70%), 13 (15%), and 13 (15%) samples are used for training, validation, and testing, respectively. The Levenberg-Marquardt backpropagation is used to train the network by entertaining the random 62 sample values. Both mean square error and regression analysis are used to check the performance of the developed neural networking model. The SFC is noticed to be high at a magnetized surface for power law index and Weissenberg number.https://www.aimspress.com/article/doi/10.3934/math.2024227?viewType=HTMLartificial intelligenceneural networkstangent hyperbolic fluidlie symmetryheat generation |
| spellingShingle | Khalil Ur Rehman Wasfi Shatanawi Zead Mustafa Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions AIMS Mathematics artificial intelligence neural networks tangent hyperbolic fluid lie symmetry heat generation |
| title | Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| title_full | Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| title_fullStr | Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| title_full_unstemmed | Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| title_short | Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| title_sort | artificial intelligence ai based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions |
| topic | artificial intelligence neural networks tangent hyperbolic fluid lie symmetry heat generation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024227?viewType=HTML |
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