Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects
The non-linear ordinary differential equations (NODEs) in this article are estimated and analyzed numerically using the capability of the Quartic Splines Method (QSM) for mathematical modeling of the Falkner-Skan fluidic system and its optimization through global search Genetic Algorithms (GAs) and...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-01-01
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| Series: | Case Studies in Thermal Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214157X23011930 |
| _version_ | 1797356920639586304 |
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| author | Fazle Subhan Kottakkaran Sooppy Nisar Muhammad Asif Zahoor Raja Iftikhar Uddin Muhammad Shoaib Kashif Ullah Saeed Islam Shankar Rao Munjam |
| author_facet | Fazle Subhan Kottakkaran Sooppy Nisar Muhammad Asif Zahoor Raja Iftikhar Uddin Muhammad Shoaib Kashif Ullah Saeed Islam Shankar Rao Munjam |
| author_sort | Fazle Subhan |
| collection | DOAJ |
| description | The non-linear ordinary differential equations (NODEs) in this article are estimated and analyzed numerically using the capability of the Quartic Splines Method (QSM) for mathematical modeling of the Falkner-Skan fluidic system and its optimization through global search Genetic Algorithms (GAs) and local search Active-Set (AS) techniques. The concept of hybridization is used to optimize the obtained results and provide a boost to the suggested method, QSM, which allows for rapid iteration. Falkner-Skan fluid model (FSFM) is solved by the proposed technique QSM-GAs-AS. The FSFM is solved for three, seven, and twelve splines successfully. The problem is analyzed for three scenarios, in which each scenario is based on the variation of a parameter out of the three involved parameters, namely the wall mass transfer parameter (γ), the wall movement parameter (λ), and the stream-wise pressure gradient parameter (β), appearing in FSFM. The QSM-GAs-AS produces an interpolated function that is continuous up to its fourth derivative. The solution outcomes of FSFM, treated by the designed scheme QSM-GAs-AS, are presented graphically. The evaluation of the planned solution is done with a deterministic numerical solver, the Homotopy Analysis Method (HAM). Statistical analysis for multiple runs is used to examine the proposed scheme's convergence, exactness, and accuracy. |
| first_indexed | 2024-03-08T14:36:48Z |
| format | Article |
| id | doaj.art-f42ba24739e04776b4abffa32c5990ed |
| institution | Directory Open Access Journal |
| issn | 2214-157X |
| language | English |
| last_indexed | 2024-03-08T14:36:48Z |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Case Studies in Thermal Engineering |
| spelling | doaj.art-f42ba24739e04776b4abffa32c5990ed2024-01-12T04:56:49ZengElsevierCase Studies in Thermal Engineering2214-157X2024-01-0153103887Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effectsFazle Subhan0Kottakkaran Sooppy Nisar1Muhammad Asif Zahoor Raja2Iftikhar Uddin3Muhammad Shoaib4Kashif Ullah5Saeed Islam6Shankar Rao Munjam7Department of Mathematics, Abdul Wali Khan University Mardan (KP), 23200, PakistanDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al Kharj, 11942, Saudi Arabia; School of Technology, Woxsen University, Hyderabad, 502345, Telangana State, India; Corresponding author. Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, 16278, Saudi Arabia.Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC; Corresponding author.Department of Mathematics, Abdul Wali Khan University Mardan (KP), 23200, PakistanYuan Ze University, AI Centre, Taoyuan, 320, Taiwan, ROCDepartment of Mathematics, Abdul Wali Khan University Mardan (KP), 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan (KP), 23200, PakistanSchool of Technology, Woxsen University, Hyderabad, 502345, Telangana State, IndiaThe non-linear ordinary differential equations (NODEs) in this article are estimated and analyzed numerically using the capability of the Quartic Splines Method (QSM) for mathematical modeling of the Falkner-Skan fluidic system and its optimization through global search Genetic Algorithms (GAs) and local search Active-Set (AS) techniques. The concept of hybridization is used to optimize the obtained results and provide a boost to the suggested method, QSM, which allows for rapid iteration. Falkner-Skan fluid model (FSFM) is solved by the proposed technique QSM-GAs-AS. The FSFM is solved for three, seven, and twelve splines successfully. The problem is analyzed for three scenarios, in which each scenario is based on the variation of a parameter out of the three involved parameters, namely the wall mass transfer parameter (γ), the wall movement parameter (λ), and the stream-wise pressure gradient parameter (β), appearing in FSFM. The QSM-GAs-AS produces an interpolated function that is continuous up to its fourth derivative. The solution outcomes of FSFM, treated by the designed scheme QSM-GAs-AS, are presented graphically. The evaluation of the planned solution is done with a deterministic numerical solver, the Homotopy Analysis Method (HAM). Statistical analysis for multiple runs is used to examine the proposed scheme's convergence, exactness, and accuracy.http://www.sciencedirect.com/science/article/pii/S2214157X23011930Quartic splines methodActive-Set algorithmsGenetic-AlgorithmFSFM Hybrid computingBio-inspired computationHAM |
| spellingShingle | Fazle Subhan Kottakkaran Sooppy Nisar Muhammad Asif Zahoor Raja Iftikhar Uddin Muhammad Shoaib Kashif Ullah Saeed Islam Shankar Rao Munjam Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects Case Studies in Thermal Engineering Quartic splines method Active-Set algorithms Genetic-Algorithm FSFM Hybrid computing Bio-inspired computation HAM |
| title | Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects |
| title_full | Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects |
| title_fullStr | Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects |
| title_full_unstemmed | Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects |
| title_short | Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects |
| title_sort | novel quartic spline method for boundary layer fluid flow problem of falkner skan model with wall stretching and transfer of mass effects |
| topic | Quartic splines method Active-Set algorithms Genetic-Algorithm FSFM Hybrid computing Bio-inspired computation HAM |
| url | http://www.sciencedirect.com/science/article/pii/S2214157X23011930 |
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