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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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Gudekote M, Choudhari R, Vaidya H, K.V. P, J.U. V. Influence of convective conditions on the peristaltic mechanism of power-law fluid through a slippery elastic porous tube with different waveforms. ACTA ACUST UNITED AC 2019. [DOI: 10.1108/mmms-01-2019-0006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Purpose
The purpose of this paper is to emphasize the peristaltic mechanism of power-law fluid in an elastic porous tube under the influence of slip and convective conditions. The effects of different waveforms on the peristaltic mechanism are taken into account.
Design/methodology/approach
The governing equations are rendered dimensionless using the suitable similarity transformations. The analytical solutions are obtained by using the long wavelength and small Reynold’s number approximations. The expressions for velocity, flow rate, temperature and streamlines are obtained and analyzed graphically. Furthermore, an application to flow through an artery is determined by using a tensile expression given by Rubinow and Keller.
Findings
The principal findings from the present model are as follows. The axial velocity increases with an expansion in the estimation of velocity slip parameter and fluid behavior index, and it diminishes for a larger value of the porous parameter. The magnitude of temperature diminishes with an expansion in the Biot number. The flux is maximum for trapezoidal wave and minimum for the triangular wave when compared with other considered waveforms. The flow rate in an elastic tube increases with an expansion in the porous parameter, and it diminishes with an increment in the slip parameter. The volume of tapered bolus enhances with increasing values of the porous parameter.
Originality/value
The current study finds the application in designing the heart-lung machine and dialysis machine. The investigation further gives a superior comprehension of the peristaltic system associated with the gastrointestinal tract and the stream of blood in small or microvessels.
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Impact of Thermal Radiation and Heat Source/Sink on MHD Time-Dependent Thin-Film Flow of Oldroyed-B, Maxwell, and Jeffry Fluids over a Stretching Surface. Processes (Basel) 2019. [DOI: 10.3390/pr7040191] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this study paper, we examined the magnetohydrodynamic (MHD) flow of three combined fluids, Maxwell, Jeffry, and Oldroyed- B fluids, with variable heat transmission under the influence of thermal radiation embedded in a permeable medium over a time-dependent stretching sheet. The fluid flow of liquid films was assumed in two dimensions. The fundamental leading equations were changed to a set of differential nonlinear and coupled equations. For this conversion, suitable similarity variables were used. An optimal tactic was used to acquire the solution of the modeled problems. The convergence of the technique has been shown numerically. The obtained analytical and numerical consequences are associated graphically and tabulated. An excellent agreement was obtained between the homotropy analysis method (HAM) and numerical methods. The variation of the skin friction and Nusslet number and their influence on the temperature and concentration profiles were scrutinized. The influence of the thermal radiation, unsteadiness effect, and MHD were the main focus of this study. Furthermore, for conception to be physically demonstrated, the entrenched parameters are discussed graphically in detail along with their effect on liquid film flow.
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Computer modelling of electro-osmotically augmented three-layered microvascular peristaltic blood flow. Microvasc Res 2017; 114:65-83. [DOI: 10.1016/j.mvr.2017.06.004] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Revised: 06/08/2017] [Accepted: 06/09/2017] [Indexed: 11/20/2022]
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Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model. Biomech Model Mechanobiol 2017; 17:71-86. [DOI: 10.1007/s10237-017-0945-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Accepted: 07/25/2017] [Indexed: 10/19/2022]
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Vajravelu K, Sreenadh S, Sucharitha G, Lakshminarayana P. Peristaltic transport of a conducting Jeffrey fluid in an inclined asymmetric channel. INT J BIOMATH 2014. [DOI: 10.1142/s1793524514500648] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter δ, the angle of inclination θ and the phase difference ϕ. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.
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Affiliation(s)
- K. Vajravelu
- Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, Florida 32816-1364, USA
| | - S. Sreenadh
- Department of Mathematics, Sri Venkateswara University, Tirupati 517 502, India
| | - G. Sucharitha
- Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati 517 102, India
| | - P. Lakshminarayana
- Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati 517 102, India
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Hayat T, Saleem N, Abd elmaboud Y, Asghar S. Peristaltic flow of a second-order fluid in the presence of an induced magnetic field. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2011; 67:537-558. [DOI: 10.1002/fld.2371] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Abd elmaboud Y, Mekheimer K. Non-linear peristaltic transport of a second-order fluid through a porous medium. APPLIED MATHEMATICAL MODELLING 2011; 35:2695-2710. [DOI: 10.1016/j.apm.2010.11.031] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Hariharan P, Seshadri V, Banerjee RK. Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/j.mcm.2007.10.018] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Nagarani P, Sarojamma G. Peristaltic transport of small particles — power law fluid suspension in a channel. ACTA ACUST UNITED AC 2007; 30:185-93. [DOI: 10.1007/bf03178425] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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