A predictive neuro-computing approach for micro-polar nanofluid flow along rotating disk in the presence of magnetic field and partial slip

Muhammad Asif Zahoor Raja; Kottakkaran Sooppy Nisar; Muhammad Shoaib; Ajed Akbar; Hakeem Ullah; Saeed Islam; Muhammad Asif Zahoor Raja; Kottakkaran Sooppy Nisar; Muhammad Shoaib; Ajed Akbar; Hakeem Ullah; Saeed Islam

doi:10.3934/math.2023608

AIMS Mathematics

2023, Volume 8, Issue 5: 12062-12092. doi: 10.3934/math.2023608

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A predictive neuro-computing approach for micro-polar nanofluid flow along rotating disk in the presence of magnetic field and partial slip

1.
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Douliou, Yunlin 64002, Taiwan
2.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
3.
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India
4.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
5.
Yuan Ze University, AI Center, Taoyuan 320, Taiwan
6.
Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan

Received: 01 September 2022 Revised: 28 December 2022 Accepted: 23 January 2023 Published: 21 March 2023
MSC : 35Qxx, 76Nxx

The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation.
- neural network,
- Levenberg-Marquard backpropagation,
- Adams method,
- micro-polar nanofluid,
- magnetohydrodynamics,
- rotating disk,
- slip effects
Citation: Muhammad Asif Zahoor Raja, Kottakkaran Sooppy Nisar, Muhammad Shoaib, Ajed Akbar, Hakeem Ullah, Saeed Islam. A predictive neuro-computing approach for micro-polar nanofluid flow along rotating disk in the presence of magnetic field and partial slip[J]. AIMS Mathematics, 2023, 8(5): 12062-12092. doi: 10.3934/math.2023608

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Abstract

The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation.

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