Transient Dean flow in an annulus: a semi-analytical approach
The mathematical model of a fully developed laminar transient flow formation between the gaps of two horizontally stationary concentric tubes forming concentric annulus due to the impact of sudden application of azimuthal pressure gradient is analysed. Analytical and numerical solutions of the momen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2018.1549529 |
| _version_ | 1828169682167791616 |
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| author | Basant Kumar Jha Jibrin Danjuma Yahaya |
| author_facet | Basant Kumar Jha Jibrin Danjuma Yahaya |
| author_sort | Basant Kumar Jha |
| collection | DOAJ |
| description | The mathematical model of a fully developed laminar transient flow formation between the gaps of two horizontally stationary concentric tubes forming concentric annulus due to the impact of sudden application of azimuthal pressure gradient is analysed. Analytical and numerical solutions of the momentum equations are obtained by the aid of two-step process. The first step is by solving the governing partial differential equation analytically by using Laplace transform technique in the Laplace domain. Using Riemann–sum approximation of Laplace inversion, the velocity and skin friction are then inverted to time domain. Expressions for steady-state velocity and skin friction are obtained for the validations of the method employed. In the course of numerical computations, it is observed that increase in dimensionless time $ (T ) $ leads to increase in velocity as well as skin friction at the surfaces of tubes. It is also found that at large values of dimensionless time $ (T ) $ , the velocity and skin friction reach steady state. |
| first_indexed | 2024-04-12T02:56:12Z |
| format | Article |
| id | doaj.art-8198533b3cc14ab68d7df601d87ad69a |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-12T02:56:12Z |
| publishDate | 2019-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-8198533b3cc14ab68d7df601d87ad69a2022-12-22T03:50:49ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552019-12-0113116917610.1080/16583655.2018.15495291549529Transient Dean flow in an annulus: a semi-analytical approachBasant Kumar Jha0Jibrin Danjuma Yahaya1Ahmadu Bello UniversityAhmadu Bello UniversityThe mathematical model of a fully developed laminar transient flow formation between the gaps of two horizontally stationary concentric tubes forming concentric annulus due to the impact of sudden application of azimuthal pressure gradient is analysed. Analytical and numerical solutions of the momentum equations are obtained by the aid of two-step process. The first step is by solving the governing partial differential equation analytically by using Laplace transform technique in the Laplace domain. Using Riemann–sum approximation of Laplace inversion, the velocity and skin friction are then inverted to time domain. Expressions for steady-state velocity and skin friction are obtained for the validations of the method employed. In the course of numerical computations, it is observed that increase in dimensionless time $ (T ) $ leads to increase in velocity as well as skin friction at the surfaces of tubes. It is also found that at large values of dimensionless time $ (T ) $ , the velocity and skin friction reach steady state.http://dx.doi.org/10.1080/16583655.2018.1549529transientdean flowannulusriemann–sum approximation |
| spellingShingle | Basant Kumar Jha Jibrin Danjuma Yahaya Transient Dean flow in an annulus: a semi-analytical approach Journal of Taibah University for Science transient dean flow annulus riemann–sum approximation |
| title | Transient Dean flow in an annulus: a semi-analytical approach |
| title_full | Transient Dean flow in an annulus: a semi-analytical approach |
| title_fullStr | Transient Dean flow in an annulus: a semi-analytical approach |
| title_full_unstemmed | Transient Dean flow in an annulus: a semi-analytical approach |
| title_short | Transient Dean flow in an annulus: a semi-analytical approach |
| title_sort | transient dean flow in an annulus a semi analytical approach |
| topic | transient dean flow annulus riemann–sum approximation |
| url | http://dx.doi.org/10.1080/16583655.2018.1549529 |
| work_keys_str_mv | AT basantkumarjha transientdeanflowinanannulusasemianalyticalapproach AT jibrindanjumayahaya transientdeanflowinanannulusasemianalyticalapproach |