Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature
This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alg...
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| Format: | Article |
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MDPI AG
2020-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/4/401 |
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| author | Talha Anwar Poom Kumam Ilyas Khan Wiboonsak Watthayu |
| author_facet | Talha Anwar Poom Kumam Ilyas Khan Wiboonsak Watthayu |
| author_sort | Talha Anwar |
| collection | DOAJ |
| description | This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alginate. The flow is restricted to an infinite vertical plate saturated in a porous material incorporating the generalized Darcy’s law and heat suction/injection. The governing equations for momentum, shear stress and energy are modelled in the form of partial differential equations along with ramped wall temperature and ramped wall velocity boundary conditions. Laplace transformation is applied to convert principal partial differential equations to ordinary differential equations first and, later, complex multivalued functions of Laplace parameter are handled with numerical inversion to obtain the solutions in real time domain. Expression for Nusselt number is also obtained to clearly examine the difference in rate of heat transfer. A comparison for isothermal wall condition and ramped wall condition is also made to analyze the difference in both profiles. A graphical study is conducted to analyze how the fluid profiles are significantly affected by several pertinent parameters. Rate of heat transfer increases with increasing volume fraction of nanoparticle while shear stress reduces with elevation in retardation time. Moreover, flow gets accelerated with increase in Grashof number and Porosity parameter. For every parameter, a comparison between solutions of SWCNTs and MWCNTs is also presented. |
| first_indexed | 2024-03-10T20:45:38Z |
| format | Article |
| id | doaj.art-1bac299ef21e4fc1bc4ec8ae8566ad0c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T20:45:38Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-1bac299ef21e4fc1bc4ec8ae8566ad0c2023-11-19T20:17:34ZengMDPI AGEntropy1099-43002020-03-0122440110.3390/e22040401Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall TemperatureTalha Anwar0Poom Kumam1Ilyas Khan2Wiboonsak Watthayu3Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandKMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandThis article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alginate. The flow is restricted to an infinite vertical plate saturated in a porous material incorporating the generalized Darcy’s law and heat suction/injection. The governing equations for momentum, shear stress and energy are modelled in the form of partial differential equations along with ramped wall temperature and ramped wall velocity boundary conditions. Laplace transformation is applied to convert principal partial differential equations to ordinary differential equations first and, later, complex multivalued functions of Laplace parameter are handled with numerical inversion to obtain the solutions in real time domain. Expression for Nusselt number is also obtained to clearly examine the difference in rate of heat transfer. A comparison for isothermal wall condition and ramped wall condition is also made to analyze the difference in both profiles. A graphical study is conducted to analyze how the fluid profiles are significantly affected by several pertinent parameters. Rate of heat transfer increases with increasing volume fraction of nanoparticle while shear stress reduces with elevation in retardation time. Moreover, flow gets accelerated with increase in Grashof number and Porosity parameter. For every parameter, a comparison between solutions of SWCNTs and MWCNTs is also presented.https://www.mdpi.com/1099-4300/22/4/401carbon nanotubesLaplace transformramped wallMHDheat transferOldroyd-B nanofluid |
| spellingShingle | Talha Anwar Poom Kumam Ilyas Khan Wiboonsak Watthayu Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature Entropy carbon nanotubes Laplace transform ramped wall MHD heat transfer Oldroyd-B nanofluid |
| title | Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature |
| title_full | Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature |
| title_fullStr | Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature |
| title_full_unstemmed | Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature |
| title_short | Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature |
| title_sort | heat transfer enhancement in unsteady mhd natural convective flow of cnts oldroyd b nanofluid under ramped wall velocity and ramped wall temperature |
| topic | carbon nanotubes Laplace transform ramped wall MHD heat transfer Oldroyd-B nanofluid |
| url | https://www.mdpi.com/1099-4300/22/4/401 |
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