Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media
This theoretical study analyses the effects of geometrical and fluid parameters on the flow metrics in the Hagen-Poiseuille and plane-Poiseuille flows of Herschel-Bulkley fluid through porous medium which is considered as (i) single pipe/single channel and (ii) multi–pipes/multi-channels when the di...
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| Format: | Article |
| Language: | English |
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Shahid Chamran University of Ahvaz
2022-10-01
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| Series: | Journal of Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | https://jacm.scu.ac.ir/article_16840_39277d65173045e342bc8310d166a88c.pdf |
| _version_ | 1818000265535553536 |
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| author | D.S. Sankar K.K. Viswanathan Atulya K. Nagar Nurul Aini Binti Jaafar A. Vanav Kumar |
| author_facet | D.S. Sankar K.K. Viswanathan Atulya K. Nagar Nurul Aini Binti Jaafar A. Vanav Kumar |
| author_sort | D.S. Sankar |
| collection | DOAJ |
| description | This theoretical study analyses the effects of geometrical and fluid parameters on the flow metrics in the Hagen-Poiseuille and plane-Poiseuille flows of Herschel-Bulkley fluid through porous medium which is considered as (i) single pipe/single channel and (ii) multi–pipes/multi-channels when the distribution of pores size in the flow medium are represented by each one of the four probability density functions: (i) Uniform distribution, (ii) Linear distribution of Type-I, (iii) Linear distribution of Type-II and (iv) Quadratic distribution. It is found that in Hagen-Poiseuille and plane-Poiseuille flows, Buckingham-Reiner function increases linearly when the pressure gradient increases in the range 1 - 2.5 and then it ascends slowly with the raise of pressure gradient in the range 2.5 - 5.In all of the four kinds of pores size distribution, the fluid’s mean velocity, flow medium’s porosity and permeability are substantially higher in Hagen-Poiseuille fluid rheology than in plane-Poiseuille fluid rheology and, these flow quantitiesascend considerably with the raise of pipe radius/channel width and a reverse characteristic is noted for these rheological measures when the power law index parameter increases.The flow medium’s porosity decreases rapidly when the period of the pipes/channels distribution rises from 1 to 2 and it drops very slowly when the period of the pipes/channels rises from 2 to 11. |
| first_indexed | 2024-04-14T03:19:41Z |
| format | Article |
| id | doaj.art-17b12471462446b2b9165f8edca89548 |
| institution | Directory Open Access Journal |
| issn | 2383-4536 |
| language | English |
| last_indexed | 2024-04-14T03:19:41Z |
| publishDate | 2022-10-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-17b12471462446b2b9165f8edca895482022-12-22T02:15:20ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362022-10-01841246126910.22055/jacm.2021.36921.292816840Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous MediaD.S. Sankar0K.K. Viswanathan1Atulya K. Nagar2Nurul Aini Binti Jaafar3A. Vanav Kumar4Applied Mathematics and Economics Programme, School of Applied Sciences and Mathematics, Universiti Teknologi Brunei, Jalan Tungku Link, Bandar Seri Begawan, BE1410, Brunei DarussalamUTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scienntific and Industrial Research, Universiti Teknologi Malaysia, 81310 Johor Bharu, Johor, MalaysiaSchool of Mathematics, Computer Science and Engineering, Liverpool Hope University, Hope Park, Liverpool L16 9JD, United KingdomDepartment of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 Johor Bharu, Johor, MalaysiaDepartment of Mathematics, National Institute of Technology, Yupia – 791112, Arunachal Pradesh, IndiaThis theoretical study analyses the effects of geometrical and fluid parameters on the flow metrics in the Hagen-Poiseuille and plane-Poiseuille flows of Herschel-Bulkley fluid through porous medium which is considered as (i) single pipe/single channel and (ii) multi–pipes/multi-channels when the distribution of pores size in the flow medium are represented by each one of the four probability density functions: (i) Uniform distribution, (ii) Linear distribution of Type-I, (iii) Linear distribution of Type-II and (iv) Quadratic distribution. It is found that in Hagen-Poiseuille and plane-Poiseuille flows, Buckingham-Reiner function increases linearly when the pressure gradient increases in the range 1 - 2.5 and then it ascends slowly with the raise of pressure gradient in the range 2.5 - 5.In all of the four kinds of pores size distribution, the fluid’s mean velocity, flow medium’s porosity and permeability are substantially higher in Hagen-Poiseuille fluid rheology than in plane-Poiseuille fluid rheology and, these flow quantitiesascend considerably with the raise of pipe radius/channel width and a reverse characteristic is noted for these rheological measures when the power law index parameter increases.The flow medium’s porosity decreases rapidly when the period of the pipes/channels distribution rises from 1 to 2 and it drops very slowly when the period of the pipes/channels rises from 2 to 11.https://jacm.scu.ac.ir/article_16840_39277d65173045e342bc8310d166a88c.pdfmathematical analysisporous mediumpermeabilityporositymean velocity. |
| spellingShingle | D.S. Sankar K.K. Viswanathan Atulya K. Nagar Nurul Aini Binti Jaafar A. Vanav Kumar Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media Journal of Applied and Computational Mechanics mathematical analysis porous medium permeability porosity mean velocity. |
| title | Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media |
| title_full | Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media |
| title_fullStr | Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media |
| title_full_unstemmed | Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media |
| title_short | Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media |
| title_sort | theoretical study on poiseuille flow of herschel bulkley fluid in porous media |
| topic | mathematical analysis porous medium permeability porosity mean velocity. |
| url | https://jacm.scu.ac.ir/article_16840_39277d65173045e342bc8310d166a88c.pdf |
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