Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform
In this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy for...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023004176 |
| _version_ | 1811161878899982336 |
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| author | Salah Uddin Obaid Ullah Mehmood Mahathir Mohamad Rozaini Roslan Ilyas Khan Abdullah Mohamed |
| author_facet | Salah Uddin Obaid Ullah Mehmood Mahathir Mohamad Rozaini Roslan Ilyas Khan Abdullah Mohamed |
| author_sort | Salah Uddin |
| collection | DOAJ |
| description | In this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy force. Here, the MHD flow is modeled using the Caputo-Fabrizio non-integer derivative approach. The exact solution of the governing continuity, momentum and energy equations is obtained by means of Laplace and finite Hankel transforms. The commercial simulation software, Mathematica is used for calculating the roots of the Bessel function. The effects of dimensionless parameters such as Grashof and Prandtl numbers, magnetic field and fractional parameters on the second-grade fluid flow are analyzed. Heat transfer is high at a small Prandtl number. Velocity correlates positively with Grashof number and magnetic field, and negatively with Prandtl number. The heat and mass transfer results obtained from both conventional and fractional models are compared as well. |
| first_indexed | 2024-04-10T06:21:07Z |
| format | Article |
| id | doaj.art-e3427f00b5594915ad4ddc47ad193e06 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-10T06:21:07Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-e3427f00b5594915ad4ddc47ad193e062023-03-02T05:00:29ZengElsevierHeliyon2405-84402023-02-0192e13210Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transformSalah Uddin0Obaid Ullah Mehmood1Mahathir Mohamad2Rozaini Roslan3Ilyas Khan4Abdullah Mohamed5Department of Humanities & Science, College of Aeronautical Engineering, National University of Sciences & Technology, Risalpur, 23200, PakistanDeprartment of Mathematics, Comsats University Islamabad, Wah Campus, 47040, PakistanDepartment of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, 84600, Pagoh, Johor, MalaysiaDepartment of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, 84600, Pagoh, Johor, MalaysiaDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia; Corresponding author.Research Centre, Future University in Egypt, New Cairo, 11835, EgyptIn this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy force. Here, the MHD flow is modeled using the Caputo-Fabrizio non-integer derivative approach. The exact solution of the governing continuity, momentum and energy equations is obtained by means of Laplace and finite Hankel transforms. The commercial simulation software, Mathematica is used for calculating the roots of the Bessel function. The effects of dimensionless parameters such as Grashof and Prandtl numbers, magnetic field and fractional parameters on the second-grade fluid flow are analyzed. Heat transfer is high at a small Prandtl number. Velocity correlates positively with Grashof number and magnetic field, and negatively with Prandtl number. The heat and mass transfer results obtained from both conventional and fractional models are compared as well.http://www.sciencedirect.com/science/article/pii/S2405844023004176Magnetized solutionBuoyancy forcesNon-integer derivativeConventional fluidFractional fluid |
| spellingShingle | Salah Uddin Obaid Ullah Mehmood Mahathir Mohamad Rozaini Roslan Ilyas Khan Abdullah Mohamed Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform Heliyon Magnetized solution Buoyancy forces Non-integer derivative Conventional fluid Fractional fluid |
| title | Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform |
| title_full | Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform |
| title_fullStr | Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform |
| title_full_unstemmed | Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform |
| title_short | Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform |
| title_sort | effect of natural heat convection on fractional mhd second grade fluid in an infinite vertically oscillating cylinder with hankel transform |
| topic | Magnetized solution Buoyancy forces Non-integer derivative Conventional fluid Fractional fluid |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023004176 |
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