Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions
In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/10/582 |
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| author | Abdellah Bouchendouka Zine El Abiddine Fellah Zakaria Larbi Nicholas O. Ongwen Erick Ogam Mohamed Fellah Claude Depollier |
| author_facet | Abdellah Bouchendouka Zine El Abiddine Fellah Zakaria Larbi Nicholas O. Ongwen Erick Ogam Mohamed Fellah Claude Depollier |
| author_sort | Abdellah Bouchendouka |
| collection | DOAJ |
| description | In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology. |
| first_indexed | 2024-03-09T20:11:29Z |
| format | Article |
| id | doaj.art-3e9d3de732214dbcafaa2a92df7bde0d |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:29Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-3e9d3de732214dbcafaa2a92df7bde0d2023-11-24T00:12:01ZengMDPI AGFractal and Fractional2504-31102022-10-0161058210.3390/fractalfract6100582Flow of a Self-Similar Non-Newtonian Fluid Using Fractal DimensionsAbdellah Bouchendouka0Zine El Abiddine Fellah1Zakaria Larbi2Nicholas O. Ongwen3Erick Ogam4Mohamed Fellah5Claude Depollier6Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, 4 Impasse Nikola Tesla CS 40006, CEDEX 13, 13453 Marseille, FranceAix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, 4 Impasse Nikola Tesla CS 40006, CEDEX 13, 13453 Marseille, FranceLaboratory of Theoretical and Applied Fluid Mechanics, Physics’ Faculty, University of Sciences and Technology Houari Boumediene USTHB, LMFTA BP 32 El Alia, Bab Ezzouar 16111, AlgeriaDepartment of Physics and Materials Science, Maseno University, Maseno 40105, KenyaAix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, 4 Impasse Nikola Tesla CS 40006, CEDEX 13, 13453 Marseille, FranceLaboratory of Theoretical Physics, Faculty of Physics USTHB, BP 32 El Alia, Bab Ezzouar 16111, AlgeriaLaboratoire d’Acoustique de l’Université du Mans (LAUM), UMR 6613, Institut d’Acoustique, CNRS, Le Mans Université, France, Avenue O. Messiaen, CEDEX 09, F-72085 Le Mans, FranceIn this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.https://www.mdpi.com/2504-3110/6/10/582fractal dimensionspower-law fluidnon-Newtonian fluidself-similar fluidnoninteger dimensional space |
| spellingShingle | Abdellah Bouchendouka Zine El Abiddine Fellah Zakaria Larbi Nicholas O. Ongwen Erick Ogam Mohamed Fellah Claude Depollier Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions Fractal and Fractional fractal dimensions power-law fluid non-Newtonian fluid self-similar fluid noninteger dimensional space |
| title | Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions |
| title_full | Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions |
| title_fullStr | Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions |
| title_full_unstemmed | Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions |
| title_short | Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions |
| title_sort | flow of a self similar non newtonian fluid using fractal dimensions |
| topic | fractal dimensions power-law fluid non-Newtonian fluid self-similar fluid noninteger dimensional space |
| url | https://www.mdpi.com/2504-3110/6/10/582 |
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