Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid
This study investigates the three-dimensional, steady, laminar boundary-layer equations of a non-Newtonian fluid over a flat plate in the absence of body forces. The classical boundary-layer theory, introduced by Prandtl in 1904, suggests that fluid flows past a solid surface can be divided into two...
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2024-12-01
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| author | Ali El Saheli Bashar Zogheib |
| author_facet | Ali El Saheli Bashar Zogheib |
| author_sort | Ali El Saheli |
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| description | This study investigates the three-dimensional, steady, laminar boundary-layer equations of a non-Newtonian fluid over a flat plate in the absence of body forces. The classical boundary-layer theory, introduced by Prandtl in 1904, suggests that fluid flows past a solid surface can be divided into two regions: a thin boundary layer near the surface, where steep velocity gradients and significant frictional effects dominate, and the outer region, where friction is negligible. Within the boundary layer, the velocity increases sharply from zero at the surface to the freestream value at the outer edge. The boundary-layer approximation significantly simplifies the Navier–Stokes equations within the boundary layer, while outside this layer, the flow is considered inviscid, resulting in even simpler equations. The viscoelastic properties of the fluid are modeled using the Rivlin–Ericksen tensors. Lie group analysis is applied to reduce the resulting third-order nonlinear system of partial differential equations to a system of ordinary differential equations. Finally, we determine the admissible forms of the freestream velocities in the x- and z-directions. |
| format | Article |
| id | doaj-art-ebd0a8f706394fd5a2c92ec7c049027c |
| institution | Kabale University |
| issn | 2673-9909 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-ebd0a8f706394fd5a2c92ec7c049027c2024-12-27T14:07:10ZengMDPI AGAppliedMath2673-99092024-12-01441588159910.3390/appliedmath4040084Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian FluidAli El Saheli0Bashar Zogheib1Department of Mathematics and Natural Sciences, American University of Kuwait, Salmiya 13034, KuwaitDepartment of Mathematics and Natural Sciences, American University of Kuwait, Salmiya 13034, KuwaitThis study investigates the three-dimensional, steady, laminar boundary-layer equations of a non-Newtonian fluid over a flat plate in the absence of body forces. The classical boundary-layer theory, introduced by Prandtl in 1904, suggests that fluid flows past a solid surface can be divided into two regions: a thin boundary layer near the surface, where steep velocity gradients and significant frictional effects dominate, and the outer region, where friction is negligible. Within the boundary layer, the velocity increases sharply from zero at the surface to the freestream value at the outer edge. The boundary-layer approximation significantly simplifies the Navier–Stokes equations within the boundary layer, while outside this layer, the flow is considered inviscid, resulting in even simpler equations. The viscoelastic properties of the fluid are modeled using the Rivlin–Ericksen tensors. Lie group analysis is applied to reduce the resulting third-order nonlinear system of partial differential equations to a system of ordinary differential equations. Finally, we determine the admissible forms of the freestream velocities in the x- and z-directions.https://www.mdpi.com/2673-9909/4/4/84laminar boundary layersnon-Newtonian fluidsymmetry analysis |
| spellingShingle | Ali El Saheli Bashar Zogheib Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid AppliedMath laminar boundary layers non-Newtonian fluid symmetry analysis |
| title | Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid |
| title_full | Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid |
| title_fullStr | Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid |
| title_full_unstemmed | Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid |
| title_short | Symmetry Analysis of the 3D Boundary-Layer Flow of a Non-Newtonian Fluid |
| title_sort | symmetry analysis of the 3d boundary layer flow of a non newtonian fluid |
| topic | laminar boundary layers non-Newtonian fluid symmetry analysis |
| url | https://www.mdpi.com/2673-9909/4/4/84 |
| work_keys_str_mv | AT alielsaheli symmetryanalysisofthe3dboundarylayerflowofanonnewtonianfluid AT basharzogheib symmetryanalysisofthe3dboundarylayerflowofanonnewtonianfluid |