### Abstract

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.

Original language | English (US) |
---|---|

Article number | 487819 |

Journal | Scientific World Journal |

Volume | 2015 |

DOIs | |

State | Published - 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)

### Cite this

*Scientific World Journal*,

*2015*, [487819]. https://doi.org/10.1155/2015/487819

}

*Scientific World Journal*, vol. 2015, 487819. https://doi.org/10.1155/2015/487819

**A mathematical model for the flow of a casson fluid due to metachronal beating of cilia in a tube.** / Siddiqui, A. M.; Farooq, A. A.; Rana, M. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A mathematical model for the flow of a casson fluid due to metachronal beating of cilia in a tube

AU - Siddiqui, A. M.

AU - Farooq, A. A.

AU - Rana, M. A.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84924251485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924251485&partnerID=8YFLogxK

U2 - 10.1155/2015/487819

DO - 10.1155/2015/487819

M3 - Article

C2 - 25789334

AN - SCOPUS:84924251485

VL - 2015

JO - The Scientific World Journal

JF - The Scientific World Journal

SN - 2356-6140

M1 - 487819

ER -