New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach
The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier’s law were converted into n...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/13/11/1963 |
| _version_ | 1797464504064278528 |
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| author | Muhammad Imran Asjad Ayesha Riaz Abeer S. Alnahdi Sayed M. Eldin |
| author_facet | Muhammad Imran Asjad Ayesha Riaz Abeer S. Alnahdi Sayed M. Eldin |
| author_sort | Muhammad Imran Asjad |
| collection | DOAJ |
| description | The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier’s law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system. |
| first_indexed | 2024-03-09T18:09:04Z |
| format | Article |
| id | doaj.art-93ec85a7ffc14f0aa6cf04a328f17bfc |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-09T18:09:04Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-93ec85a7ffc14f0aa6cf04a328f17bfc2023-11-24T09:15:32ZengMDPI AGMicromachines2072-666X2022-11-011311196310.3390/mi13111963New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles ApproachMuhammad Imran Asjad0Ayesha Riaz1Abeer S. Alnahdi2Sayed M. Eldin3Department of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi ArabiaCenter of Research, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, EgyptThe existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier’s law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system.https://www.mdpi.com/2072-666X/13/11/1963ternary nanoparticleshybrid nanoparticlesmono nanoparticlesJeffrey fluidPrabhakar fractional operator |
| spellingShingle | Muhammad Imran Asjad Ayesha Riaz Abeer S. Alnahdi Sayed M. Eldin New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach Micromachines ternary nanoparticles hybrid nanoparticles mono nanoparticles Jeffrey fluid Prabhakar fractional operator |
| title | New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach |
| title_full | New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach |
| title_fullStr | New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach |
| title_full_unstemmed | New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach |
| title_short | New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach |
| title_sort | new solutions of fractional jeffrey fluid with ternary nanoparticles approach |
| topic | ternary nanoparticles hybrid nanoparticles mono nanoparticles Jeffrey fluid Prabhakar fractional operator |
| url | https://www.mdpi.com/2072-666X/13/11/1963 |
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