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Effect of Thermal Radiation on Electrically Conducting Nanofluid with Slip Conditions and Heat Source Using Artificial Neural Networks

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A Correction to this article was published on 31 August 2023

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Abstract

In science and engineering, analytical and numerical methods have been utilized to compute the solutions of partial differential equations. Mathematicians are now employing artificial neural network (ANN) to investigate complex problem involving highly nonlinear partial differential equations. The aim of current study is to implement the Bayesian regularization methodology (BRM) to investigate the heat generation/absorption in thermally radiative nanofluid flow over stretched surface embedded in a porous medium with slip conditions. The flow governing equations have been obtained through boundary layer approximation theory. Reference data has been accumulated using the simplified form of equations with the help of “ND Solver” in Mathematica. Different scenarios have been created, and for each scenario, three different cases have been developed. Additionally, the reference data has been trained, tested, and validated using Bayesian regularization methodology in MATLAB. The reference data has been distributed in the following portions, training 71% and testing and validation 15% each, during simulation of each scenario. The proposed methodology’s effectiveness and accuracy have been validated through generated mean square error (MSE), error histograms (EH), proposed solutions, absolute errors (AE) comparative comparison plots, and regression plots. It has been observed that maximum absolute error 10−08 found for mass suction effect. Convergence of proposed methodology has been validated with mean square error. It has been observed that with high applied magnetization force and permeability motion of fluid declines whereas opposite behavior has been observed for non uniform inertial force. It has been noted that when slip mechanism is significant, contraction has been observed in thermal boundary layer of fluid. Present outcomes of drag coefficient and heat transfer coefficient show good agreement with already published results.

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Data Availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R236), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan

    Qusain Haider, Ali Hassan & Mubashar Arsahd

  2. Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Fahima Hajjej

  3. Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia

    Fahad M. Alharbi

  4. Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

    Abdulkafi Mohammed Saeed

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  1. Qusain Haider
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Contributions

Qusain Haider: conceptualization, formal analysis, and data curation. Ali Hassan: conceptualization, writing original draft, writing—review and editing, and formal analysis. Fahima Hajjej: methodology, source, supervisions, and validation, Fahad M. Alharbi: sources and validation. Abdulkafi Mohammed Saeed: re-validation, investigation, and sources, Mubashar Arsahd: sources and formal analysis

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Haider, Q., Hassan, A., Hajjej, F. et al. Effect of Thermal Radiation on Electrically Conducting Nanofluid with Slip Conditions and Heat Source Using Artificial Neural Networks. BioNanoSci. 13, 2483–2506 (2023). https://doi.org/10.1007/s12668-023-01171-5

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