Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate
The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigate...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/6/1269 |
| _version_ | 1797592489595502592 |
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| author | Constantin Fetecau Costică Moroşanu |
| author_facet | Constantin Fetecau Costică Moroşanu |
| author_sort | Constantin Fetecau |
| collection | DOAJ |
| description | The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium. |
| first_indexed | 2024-03-11T01:52:53Z |
| format | Article |
| id | doaj.art-3612b65a8bbf4c1db6de6f4486012324 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:52:53Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3612b65a8bbf4c1db6de6f44860123242023-11-18T12:51:50ZengMDPI AGSymmetry2073-89942023-06-01156126910.3390/sym15061269Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite PlateConstantin Fetecau0Costică Moroşanu1Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, RomaniaDepartment of Mathematics, “Alexandru Ioan Cuza” University, 700506 Iasi, RomaniaThe main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium.https://www.mdpi.com/2073-8994/15/6/1269second grade fluidsMHD motionsporous mediumgeneral solutionsinfinite plateflow resistance of fluid |
| spellingShingle | Constantin Fetecau Costică Moroşanu Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate Symmetry second grade fluids MHD motions porous medium general solutions infinite plate flow resistance of fluid |
| title | Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate |
| title_full | Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate |
| title_fullStr | Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate |
| title_full_unstemmed | Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate |
| title_short | Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate |
| title_sort | influence of magnetic field and porous medium on the steady state and flow resistance of second grade fluids over an infinite plate |
| topic | second grade fluids MHD motions porous medium general solutions infinite plate flow resistance of fluid |
| url | https://www.mdpi.com/2073-8994/15/6/1269 |
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