Neural networking analysis for MHD mixed convection Casson flow past a multiple surfaces: A numerical solution

Khalil Ur Rehman; Wasfi Shatanawi; Zeeshan Asghar; Haitham M. S. Bahaidarah; Khalil Ur Rehman; Wasfi Shatanawi; Zeeshan Asghar; Haitham M. S. Bahaidarah

doi:10.3934/math.2023807

AIMS Mathematics

2023, Volume 8, Issue 7: 15805-15823. doi: 10.3934/math.2023807

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Neural networking analysis for MHD mixed convection Casson flow past a multiple surfaces: A numerical solution

1.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
4.
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
5.
NUTECH, School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan
6.
Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
7.
Interdisciplinary Research Center for Renewable Energy and Power Systems, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received: 22 March 2023 Revised: 18 April 2023 Accepted: 19 April 2023 Published: 04 May 2023
MSC : 35A25, 65MO6, 76D05

The heat and mass transfer within non-Newtonian fluid flow results in complex mathematical equations and solution in this regard remains a challenging task for researchers. The present paper offers a numerical solution for the non-Newtonian flow field by using Artificial neural networking (ANN) model with the Levenberg Marquardt training technique. To be more specific, we considered thermally magnetized non-Newtonian flow headed for inclined heated surfaces. The flow is carried with viscous dissipation, stagnation point, heat generation, mixed convection, and thermal radiation effects. The concentration aspects are entertained by the owing concentration equation. The shooting method is used to solve the mathematical flow equations. The quantity of interest includes the temperature and heat transfer coefficient. Two different artificial neural networking models have been built. The training of networks is done by use of the Levenberg Marquardt technique. The values of the coefficient of determination suggest artificial neural networks as the best method for predicting the Nusselt number at both surfaces. The thermal radiation parameter and Prandtl number admit a direct relationship to the Nusselt number while the differing is the case for variable thermal conductivity and Casson parameters. Further, by using Nusselt number (NN)-ANN models, we found that for cylindrical surface, the strength of the NN is greater than the flat surface.
- neural networking,
- Levenberg-Marquardt algorithm,
- shooting method,
- heat transfer,
- thermal radiations,
- mixed convection
Citation: Khalil Ur Rehman, Wasfi Shatanawi, Zeeshan Asghar, Haitham M. S. Bahaidarah. Neural networking analysis for MHD mixed convection Casson flow past a multiple surfaces: A numerical solution[J]. AIMS Mathematics, 2023, 8(7): 15805-15823. doi: 10.3934/math.2023807

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Abstract

The heat and mass transfer within non-Newtonian fluid flow results in complex mathematical equations and solution in this regard remains a challenging task for researchers. The present paper offers a numerical solution for the non-Newtonian flow field by using Artificial neural networking (ANN) model with the Levenberg Marquardt training technique. To be more specific, we considered thermally magnetized non-Newtonian flow headed for inclined heated surfaces. The flow is carried with viscous dissipation, stagnation point, heat generation, mixed convection, and thermal radiation effects. The concentration aspects are entertained by the owing concentration equation. The shooting method is used to solve the mathematical flow equations. The quantity of interest includes the temperature and heat transfer coefficient. Two different artificial neural networking models have been built. The training of networks is done by use of the Levenberg Marquardt technique. The values of the coefficient of determination suggest artificial neural networks as the best method for predicting the Nusselt number at both surfaces. The thermal radiation parameter and Prandtl number admit a direct relationship to the Nusselt number while the differing is the case for variable thermal conductivity and Casson parameters. Further, by using Nusselt number (NN)-ANN models, we found that for cylindrical surface, the strength of the NN is greater than the flat surface.

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