Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet
In this work, the combined effects of velocity slip and convective heat boundary conditions on a hybrid nano-fluid over a nonlinear curved stretching surface were considered. Two kinds of fluids, namely, hybrid nano-fluid and aluminum oxide (<inline-formula><math xmlns="http://www.w3.o...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/12/7/1152 |
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| author | Asifa Ashraf Zhiyue Zhang Tareq Saeed Hussan Zeb Taj Munir |
| author_facet | Asifa Ashraf Zhiyue Zhang Tareq Saeed Hussan Zeb Taj Munir |
| author_sort | Asifa Ashraf |
| collection | DOAJ |
| description | In this work, the combined effects of velocity slip and convective heat boundary conditions on a hybrid nano-fluid over a nonlinear curved stretching surface were considered. Two kinds of fluids, namely, hybrid nano-fluid and aluminum oxide (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>)- and iron oxide (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mi>e</mi><mn>3</mn></msub><msub><mi>O</mi><mn>4</mn></msub></mrow></semantics></math></inline-formula>)-based nano-fluid, were also taken into account. We transformed the governing model into a nonlinear system of ordinary differential equations (ODEs). For this we used the similarity transformation method. The solution of the transformed ODE system was computed via a higher-order numerical approximation scheme known as the shooting method with the Runge–Kutta method of order four (RK-4). It is noticed that the fluid velocity was reduced for the magnetic parameter, curvature parameter, and slip parameters, while the temperature declined with higher values of the magnetic parameter, Prandtl number, and convective heat transfer. Furthermore, the physical quantities of engineering interest, i.e., the behavior of the skin fraction and the Nusselt number, are presented. These behaviors are also illustrated graphically along with the numerical values in a comparison with previous work in numerical tabular form. |
| first_indexed | 2024-03-09T11:35:06Z |
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| language | English |
| last_indexed | 2024-03-09T11:35:06Z |
| publishDate | 2022-03-01 |
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| series | Nanomaterials |
| spelling | doaj.art-8e6a5e02851b4e63bdd26291482be4072023-11-30T23:45:13ZengMDPI AGNanomaterials2079-49912022-03-01127115210.3390/nano12071152Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching SheetAsifa Ashraf0Zhiyue Zhang1Tareq Saeed2Hussan Zeb3Taj Munir4Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics & Statistics, Hazara University, Mansehra 21120, PakistanAbdus Salam School of Mathematical Sciences, Government College University Lahore, Lahore 54600, PakistanIn this work, the combined effects of velocity slip and convective heat boundary conditions on a hybrid nano-fluid over a nonlinear curved stretching surface were considered. Two kinds of fluids, namely, hybrid nano-fluid and aluminum oxide (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>)- and iron oxide (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mi>e</mi><mn>3</mn></msub><msub><mi>O</mi><mn>4</mn></msub></mrow></semantics></math></inline-formula>)-based nano-fluid, were also taken into account. We transformed the governing model into a nonlinear system of ordinary differential equations (ODEs). For this we used the similarity transformation method. The solution of the transformed ODE system was computed via a higher-order numerical approximation scheme known as the shooting method with the Runge–Kutta method of order four (RK-4). It is noticed that the fluid velocity was reduced for the magnetic parameter, curvature parameter, and slip parameters, while the temperature declined with higher values of the magnetic parameter, Prandtl number, and convective heat transfer. Furthermore, the physical quantities of engineering interest, i.e., the behavior of the skin fraction and the Nusselt number, are presented. These behaviors are also illustrated graphically along with the numerical values in a comparison with previous work in numerical tabular form.https://www.mdpi.com/2079-4991/12/7/1152<i>Al</i><sub>2</sub><i>O</i><sub>3</sub> aluminum oxide and ferro <i>Fe</i><sub>3</sub><i>O</i><sub>4</sub> nano-particlesnon-linear curved sheetconvective heat transfervelocity slip boundary condition |
| spellingShingle | Asifa Ashraf Zhiyue Zhang Tareq Saeed Hussan Zeb Taj Munir Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet Nanomaterials <i>Al</i><sub>2</sub><i>O</i><sub>3</sub> aluminum oxide and ferro <i>Fe</i><sub>3</sub><i>O</i><sub>4</sub> nano-particles non-linear curved sheet convective heat transfer velocity slip boundary condition |
| title | Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet |
| title_full | Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet |
| title_fullStr | Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet |
| title_full_unstemmed | Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet |
| title_short | Convective Heat Transfer Analysis for Aluminum Oxide (<i>Al</i><sub>2</sub><i>O</i><sub>3</sub>)- and Ferro (<i>Fe</i><sub>3</sub><i>O</i><sub>4</sub>)-Based Nano-Fluid over a Curved Stretching Sheet |
| title_sort | convective heat transfer analysis for aluminum oxide i al i sub 2 sub i o i sub 3 sub and ferro i fe i sub 3 sub i o i sub 4 sub based nano fluid over a curved stretching sheet |
| topic | <i>Al</i><sub>2</sub><i>O</i><sub>3</sub> aluminum oxide and ferro <i>Fe</i><sub>3</sub><i>O</i><sub>4</sub> nano-particles non-linear curved sheet convective heat transfer velocity slip boundary condition |
| url | https://www.mdpi.com/2079-4991/12/7/1152 |
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