Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis
Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darc...
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MDPI AG
2022-12-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/14/1/106 |
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| author | Liaquat Ali Lund Abdul Fattah Chandio Narcisa Vrinceanu Ubaidullah Yashkun Zahir Shah Ahmed Alshehri |
| author_facet | Liaquat Ali Lund Abdul Fattah Chandio Narcisa Vrinceanu Ubaidullah Yashkun Zahir Shah Ahmed Alshehri |
| author_sort | Liaquat Ali Lund |
| collection | DOAJ |
| description | Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darcy–Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is quantitatively solved using the three-step Lobatto-three formula. This research studied the effects of the dimensionlessness, magnetic field, ratio of rates, porosity, Eckert number, Prandtl number, and coefficient of inertia characteristics on fluid flow. Multiple solutions were observed. In the first solution, the increased magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters reduce the velocity field along the η-direction. In the second solution, the magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters increase the η-direction velocity field. For engineering purposes, the graphs show the impacts of factors on the Nusselt number and skin friction. Finally, the stability analysis was performed to determine which solution was the more stable of the two. |
| first_indexed | 2024-03-09T11:40:15Z |
| format | Article |
| id | doaj.art-6416a5b1439441d4a234234763db0885 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-09T11:40:15Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-6416a5b1439441d4a234234763db08852023-11-30T23:33:17ZengMDPI AGMicromachines2072-666X2022-12-0114110610.3390/mi14010106Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability AnalysisLiaquat Ali Lund0Abdul Fattah Chandio1Narcisa Vrinceanu2Ubaidullah Yashkun3Zahir Shah4Ahmed Alshehri5KCAET Khairpur Mirs, Sindh Agriculture University, Tandojam 70060, Sindh, PakistanDepartment of Electronic Engineering, Quaid-E-Awam University of Engineering, Science & Technology Nawabshah, Nawabshah 67480, Sindh, PakistanFaculty of Engineering, Department of Industrial Machines and Equipments, “Lucian Blaga” University of Sibiu, 10 Victoriei Boulevard, 550024 Sibiu, RomaniaDepartment of Mathematics and Social Sciences, Sukkur IBA University, Sukkur 79165, Sindh, PakistanDepartment of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi ArabiaNanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darcy–Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is quantitatively solved using the three-step Lobatto-three formula. This research studied the effects of the dimensionlessness, magnetic field, ratio of rates, porosity, Eckert number, Prandtl number, and coefficient of inertia characteristics on fluid flow. Multiple solutions were observed. In the first solution, the increased magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters reduce the velocity field along the η-direction. In the second solution, the magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters increase the η-direction velocity field. For engineering purposes, the graphs show the impacts of factors on the Nusselt number and skin friction. Finally, the stability analysis was performed to determine which solution was the more stable of the two.https://www.mdpi.com/2072-666X/14/1/106Darcy–Forchheimernanofluidviscous dissipationjoule heatingdualitystability |
| spellingShingle | Liaquat Ali Lund Abdul Fattah Chandio Narcisa Vrinceanu Ubaidullah Yashkun Zahir Shah Ahmed Alshehri Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis Micromachines Darcy–Forchheimer nanofluid viscous dissipation joule heating duality stability |
| title | Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis |
| title_full | Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis |
| title_fullStr | Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis |
| title_full_unstemmed | Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis |
| title_short | Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis |
| title_sort | darcy forchheimer magnetized nanofluid flow along with heating and dissipation effects over a shrinking exponential sheet with stability analysis |
| topic | Darcy–Forchheimer nanofluid viscous dissipation joule heating duality stability |
| url | https://www.mdpi.com/2072-666X/14/1/106 |
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