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Khan WU, Imran A, Raja MAZ, Shoaib M, Awan SE, Kausar K, He Y. A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel. Sci Rep 2021; 11:20601. [PMID: 34663851 PMCID: PMC8523557 DOI: 10.1038/s41598-021-00039-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 10/05/2021] [Indexed: 11/25/2022] Open
Abstract
In the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.
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Affiliation(s)
- Wasim Ullah Khan
- School of Electrical Engineering and Automation, Wuhan University, Wuhan, 430072, China.
| | - Ali Imran
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC
| | - Muhammad Shoaib
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan
| | - Saeed Ehsan Awan
- Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Kamra road, Attock, Pakistan
| | - Khadija Kausar
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan
| | - Yigang He
- School of Electrical Engineering and Automation, Wuhan University, Wuhan, 430072, China
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Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: fertilization and implantation. Biomech Model Mechanobiol 2021; 20:609-630. [PMID: 33389240 DOI: 10.1007/s10237-020-01405-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2020] [Accepted: 11/24/2020] [Indexed: 10/22/2022]
Abstract
The monitoring of the ciliated walls in the uterine tube has supreme importance in enhancing the sperm to reach the egg (capacitation processes), and at peristaltic ciliary flow has a more favorable residual time along the canal when compared to the peristaltic flow. Based on the importance of this study, a mathematical simulation of this process has been carried out by studying the behavior of a non-Newtonian magnetized fluid with a Darcy flow model with an oscillating wall having an internal ciliated surface. The governing equation is formed with Eyring-Powell fluid (tubal fallopian fluid) without using any approximations and solved using the Adomian analysis method. Using the vorticity formula, the components of the velocity function, pressure gradient, and stream function are obtained. The influence of relevant parameters is explained through diagramming and discussion. We also analyzed the residue time effects on the flow parameters. The results indicate that peristaltic ciliary flow has a more favorable residual time along the canal when compared to peristaltic flow.
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Mann AB, Shaheen S, Maqbool K, Poncet S. Fractional Burgers Fluid Flow Due to Metachronal Ciliary Motion in an Inclined Tube. Front Physiol 2019; 10:588. [PMID: 31156463 PMCID: PMC6532758 DOI: 10.3389/fphys.2019.00588] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2018] [Accepted: 04/26/2019] [Indexed: 11/23/2022] Open
Abstract
Cilia-induced flow of fractional Burgers fluid is studied in an inclined tube for both symplectic and antiplectic wave patterns. The solution of the problem is persued under the long wave length limitation. The fractional Adomian decomposition method is employed to evaluate the pressure gradient. Mathematical expressions for the axial velocity, frictional force, pressure gradient, and stream function are obtained and the influence of the main operating parameters is discussed in detail. It is noted that the velocity profile is more dominant in the case of antiplectic metachronal waves compared to symplectic ones, which confirms former results on the better capability of antiplectic waves to transport mucus, obtained with more complex numerical solvers.
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Affiliation(s)
- Amer Bilal Mann
- Department of Mathematical Sciences, Federal Urdu University of Arts Science & Technology, Islamabad, Pakistan
| | - Sidra Shaheen
- Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan
| | - Khadija Maqbool
- Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan
| | - Sébastien Poncet
- Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, Canada
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Manzoor N, Maqbool K, Bég OA, Shaheen S. Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer. ACTA ACUST UNITED AC 2018. [DOI: 10.1002/htj.21394] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Naeema Manzoor
- Department of Mathematics and Statistics; International Islamic University; Islamabad Pakistan
| | - Khadija Maqbool
- Department of Mathematics and Statistics; International Islamic University; Islamabad Pakistan
| | - Osman Anwar Bég
- Aeronautical and Mechanical Engineering Department; University of Salford; Manchester UK
| | - Sidra Shaheen
- Department of Mathematics and Statistics; International Islamic University; Islamabad Pakistan
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Maqbool K, Shaheen S, Mann AB. Exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube. SPRINGERPLUS 2016; 5:1379. [PMID: 27610298 PMCID: PMC4993733 DOI: 10.1186/s40064-016-3021-8] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/12/2016] [Accepted: 08/08/2016] [Indexed: 11/17/2022]
Abstract
The present study investigated the cilia induced flow of MHD Jeffrey fluid through an inclined tube. This study is carried out under the assumptions of long wavelength and low Reynolds number approximations. Exact solutions for the velocity profile, pressure rise, pressure gradient, volume flow rate and stream function are obtained. Effects of pertinent physical parameters on the computational results are presented graphically.
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Affiliation(s)
- K. Maqbool
- Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000 Pakistan
| | - S. Shaheen
- Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000 Pakistan
| | - A. B. Mann
- Department of Mathematical Sciences, Federal Urdu University of Arts, Science and Technology, Near Zero Point, G-7/1, Islamabad, 44000 Pakistan
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Siddiqui AM, Farooq AA, Rana MA. An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube. INT J BIOMATH 2015. [DOI: 10.1142/s1793524515500163] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.
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Affiliation(s)
- A. M. Siddiqui
- Department of Mathematics, Pennsylvania State University, York Campus, York PA 17403-3398, USA
| | - A. A. Farooq
- Department of Basic Sciences, Riphah International University, Islamabad 44000, Pakistan
- Department of Mathematics, COMSATS Institute of Information Technology, Tobe Camp, Abbottabad, Pakistan
| | - M. A. Rana
- Department of Basic Sciences, Riphah International University, Islamabad 44000, Pakistan
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Siddiqui AM, Farooq AA, Rana MA. A mathematical model for the flow of a Casson fluid due to metachronal beating of cilia in a tube. ScientificWorldJournal 2015; 2015:487819. [PMID: 25789334 PMCID: PMC4350871 DOI: 10.1155/2015/487819] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Accepted: 12/14/2014] [Indexed: 11/17/2022] Open
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 H p 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.
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Affiliation(s)
- A. M. Siddiqui
- Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17403, USA
| | - A. A. Farooq
- Department of Basic Sciences, Riphah International University, Islamabad 44000, Pakistan
- COMSATS Institute of Information Technology, Tobe Camp, Abbottabad 22010, Pakistan
| | - M. A. Rana
- Department of Basic Sciences, Riphah International University, Islamabad 44000, Pakistan
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