Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy
Abstract This study is the application of a recurrent neural networks with Bayesian regularization optimizer (RNNs-BRO) to analyze the effect of various physical parameters on fluid velocity, temperature, and mass concentration profiles in the Darcy–Forchheimer flow of propylene glycol mixed with ca...
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Nature Portfolio
2024-12-01
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| Online Access: | https://doi.org/10.1038/s41598-024-82569-3 |
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| author | Hafiz Muhammad Shahbaz Iftikhar Ahmad |
| author_facet | Hafiz Muhammad Shahbaz Iftikhar Ahmad |
| author_sort | Hafiz Muhammad Shahbaz |
| collection | DOAJ |
| description | Abstract This study is the application of a recurrent neural networks with Bayesian regularization optimizer (RNNs-BRO) to analyze the effect of various physical parameters on fluid velocity, temperature, and mass concentration profiles in the Darcy–Forchheimer flow of propylene glycol mixed with carbon nanotubes model across a stretched cylinder. This model has significant applications in thermal systems such as in heat exchangers, chemical processing, and medical cooling devices. The data-set of the proposed model has been generated with variation of various parameters such as, curvature parameter, inertia coefficient, Hartmann number, porosity parameter, Eckert number, Prandtl number, radiation parameter, activation energy variable, Schmidt number and reaction rate parameter for different scenarios. The refinement of each data-set is processed through RNNs-BRO for attestation of the proposed scheme. The outcomes are provided through graphical interpretation. The increment of curvature parameter results in the acceleration of the velocity profile, while an opposite behavior is noticed for higher values of inertia coefficient, Hartmann number, porosity parameter for single wall carbon nanotubes (SWCNTs) as well as multi wall carbon nanotubes (MWCNTs). The temperature of fluid increases for both SWCNTs and MWCNTs as the curvature parameter, radiation parameter, Eckert number, and Hartmann number are increased. However, an opposite trend is noticed for Prandtl number. The concentration profile is enhanced for higher values of activation energy variable and curvature parameter for both SWCNTs and MWCNTs, whereas opposite trend is observed for reaction rate parameter, and Schmidt number. The effectiveness of scheme is endorsed through various statistical measures like regression index, error histograms, correlation analysis and convergence analysis showing a minimum level of mean square error (E-12 to E-04) for the comprehensive simulation of the proposed model. |
| format | Article |
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| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-940832cfd6cf4c4ca22512e73e371bc32025-08-20T02:43:32ZengNature PortfolioScientific Reports2045-23222024-12-0114113610.1038/s41598-024-82569-3Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energyHafiz Muhammad Shahbaz0Iftikhar Ahmad1Department of Mathematics, University of GujratDepartment of Mathematics, University of GujratAbstract This study is the application of a recurrent neural networks with Bayesian regularization optimizer (RNNs-BRO) to analyze the effect of various physical parameters on fluid velocity, temperature, and mass concentration profiles in the Darcy–Forchheimer flow of propylene glycol mixed with carbon nanotubes model across a stretched cylinder. This model has significant applications in thermal systems such as in heat exchangers, chemical processing, and medical cooling devices. The data-set of the proposed model has been generated with variation of various parameters such as, curvature parameter, inertia coefficient, Hartmann number, porosity parameter, Eckert number, Prandtl number, radiation parameter, activation energy variable, Schmidt number and reaction rate parameter for different scenarios. The refinement of each data-set is processed through RNNs-BRO for attestation of the proposed scheme. The outcomes are provided through graphical interpretation. The increment of curvature parameter results in the acceleration of the velocity profile, while an opposite behavior is noticed for higher values of inertia coefficient, Hartmann number, porosity parameter for single wall carbon nanotubes (SWCNTs) as well as multi wall carbon nanotubes (MWCNTs). The temperature of fluid increases for both SWCNTs and MWCNTs as the curvature parameter, radiation parameter, Eckert number, and Hartmann number are increased. However, an opposite trend is noticed for Prandtl number. The concentration profile is enhanced for higher values of activation energy variable and curvature parameter for both SWCNTs and MWCNTs, whereas opposite trend is observed for reaction rate parameter, and Schmidt number. The effectiveness of scheme is endorsed through various statistical measures like regression index, error histograms, correlation analysis and convergence analysis showing a minimum level of mean square error (E-12 to E-04) for the comprehensive simulation of the proposed model.https://doi.org/10.1038/s41598-024-82569-3Activation energyPropylene glycolCarbon nanotubesRecurrent neural networksBayesian regularization |
| spellingShingle | Hafiz Muhammad Shahbaz Iftikhar Ahmad Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy Scientific Reports Activation energy Propylene glycol Carbon nanotubes Recurrent neural networks Bayesian regularization |
| title | Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy |
| title_full | Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy |
| title_fullStr | Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy |
| title_full_unstemmed | Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy |
| title_short | Numerical treatment for Darcy–Forchheimer flow of propylene glycol with carbon nanotubes under the impacts of MHD and activation energy |
| title_sort | numerical treatment for darcy forchheimer flow of propylene glycol with carbon nanotubes under the impacts of mhd and activation energy |
| topic | Activation energy Propylene glycol Carbon nanotubes Recurrent neural networks Bayesian regularization |
| url | https://doi.org/10.1038/s41598-024-82569-3 |
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