A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube
A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindric...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/487819 |
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| author | A. M. Siddiqui A. A. Farooq M. A. Rana |
| author_facet | A. M. Siddiqui A. A. Farooq M. A. Rana |
| author_sort | A. M. Siddiqui |
| collection | DOAJ |
| description | A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region Hp as well as the cilia length parameter ε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract. |
| format | Article |
| id | doaj-art-84dc418c9c1541bd983df8e0667ceec2 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-84dc418c9c1541bd983df8e0667ceec22025-02-03T06:12:28ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/487819487819A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a TubeA. M. Siddiqui0A. A. Farooq1M. A. Rana2Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17403, USADepartment of Basic Sciences, Riphah International University, Islamabad 44000, PakistanDepartment of Basic Sciences, Riphah International University, Islamabad 44000, PakistanA mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region Hp as well as the cilia length parameter ε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.http://dx.doi.org/10.1155/2015/487819 |
| spellingShingle | A. M. Siddiqui A. A. Farooq M. A. Rana A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube The Scientific World Journal |
| title | A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube |
| title_full | A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube |
| title_fullStr | A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube |
| title_full_unstemmed | A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube |
| title_short | A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube |
| title_sort | mathematical model for the flow of a casson fluid due to metachronal beating of cilia in a tube |
| url | http://dx.doi.org/10.1155/2015/487819 |
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