Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number

Tithi Sikdar; Nusrat Jahan Pinky; Avijit Roy; Shahid Shafayet Hossain; Nazmul Islam

doi:doi:10.11648/j.ijfmts.20200601.12

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Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number

Tithi Sikdar, Nusrat Jahan Pinky, Avijit Roy, Shahid Shafayet Hossain, Nazmul Islam

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 1)

Received: 28 October 2019 Accepted: 28 November 2019 Published: 7 January 2020

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Abstract

The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 1)
DOI	10.11648/j.ijfmts.20200601.12
Page(s)	9-18
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Oscillating Flow, Low Reynolds Number, Boundary Element Method, Sinusoidal Periodic Tube

References

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[2]	Jawadzadegan, A., Esmaeili, M., Majidi, S. and Fakhimghanbarzadeh, B. (2009) Pulsatile flow of viscous and viscoelastic fluids in constricted tubes, J. Mech. Sci. Technol 23, 2456–2467.
[3]	Hewitt, G. F. and Marshall, J. S. (2010) Particle focusing in a suspension flow through a corrugated tube, J. Fluid Mech. 660, 258–281.
[4]	Fedkiw, P. and Newman, J. (1977) Mass-transferathighPecletnumbersforcreepingflow in a packed-bed reactor, AIChE J. 23, 255–263.
[5]	Kettner, C., Reimann, P., Hanggi, P. and Muller, F. (2000) Drift ratchet, Phys. Rev. E 61, 312–323.
[6]	Matthias, S. and Muller, F. (2003) Asymmetric pores in a silicon membrane acting as massively parallel Brownian ratchets, Lett. Nat. 424, 53–57.
[7]	Bellhouse, B. J., Bellhouse, F. H., Curl, C. M., MacMillan, T. I., Gunning, A. J., Spratt, E. H., MacMurray, S. B. and Nelems, J. M. (1973) A high efficiency membrane oxygenator and pulsatile pumping system and its application to animal trials, Trans. Am. Soc. Artif. Intern. Organs 19, 72.
[8]	Sobey, I. J. (1980) On flow through furrowed channels. Part 1. Calculated flow patterns, J. Fluid Mech. 96, 1.
[9]	Sobey, I. J. (1983) The occurrence of separation in oscillatory flow, J. Fluid Mech. 134, 247.
[10]	Stephanoff, K. D., Sobey, I. J. and Bellhouse, B. J. (1980) On flow through furrowed channels. Part 2. Observed flow patterns, J. Fluid Mech. 96, 27.
[11]	Nishimura, T., Ohori, Y. and Kawamura, Y. (1984) Flow characteristics in a channel with symmetric wavy wall for steady flow, J Chem Eng Japan, 17, 466-471.
[12]	Nishimura, T. and Kojima, N. (1995) Mass transfer enhancement in a symmetric sinusoidal wavy-walled channel for pulsatile flow, Int. J. Heat Mass Transfer 38, 1719-1731.
[13]	Ralph, M. E. (1986) Oscillatory flows in wavy-walled tubes, J. Fluid Mech. 168, 515.
[14]	Lee, B. S., Kang, I. S. and Lim, H. C. (199) Chaotic mixing and mass transfer enhancement by pulsatile laminar flow in an axisymmetric wavy channel, International Journal of Heat and Mass Transfer 42, 2571-2581.
[15]	Nishimura, T., Bian, Y. N., Kunitsugu, K. and Morega, A. M. (2003) Fluid flow and mass transfer in a sinusoidal wavy-walled tube at moderate Reynold numbers, Heat Transfer—Asian Research 7, 650-661.
[16]	Chakravarty, S. and Sen, S. (2006) A mathematical model of blood flow and convective diffusion processes in constricted bifurcated arteries, Korea-Australia Rheology Journal 18, 51-65.
[17]	Islam, N., Bradshaw-Hajek, B. H., Miklavcic, S. J. and White, L. R. (2015) The onset of recirculation flow in periodic capillaries: Geometric effects, European Journal of Mechanics B/Fluids 53, 119-128.
[18]	Pozrikidis, C. (1992) Boundary Integral and singularity Methods for Linearised Viscous Flow, Cambridge University Press, Cambridge, U. K.

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APA Style

Tithi Sikdar, Nusrat Jahan Pinky, Avijit Roy, Shahid Shafayet Hossain, Nazmul Islam. (2020). Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. International Journal of Fluid Mechanics & Thermal Sciences, 6(1), 9-18. https://doi.org/10.11648/j.ijfmts.20200601.12

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ACS Style

Tithi Sikdar; Nusrat Jahan Pinky; Avijit Roy; Shahid Shafayet Hossain; Nazmul Islam. Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. Int. J. Fluid Mech. Therm. Sci. 2020, 6(1), 9-18. doi: 10.11648/j.ijfmts.20200601.12

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AMA Style

Tithi Sikdar, Nusrat Jahan Pinky, Avijit Roy, Shahid Shafayet Hossain, Nazmul Islam. Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. Int J Fluid Mech Therm Sci. 2020;6(1):9-18. doi: 10.11648/j.ijfmts.20200601.12

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@article{10.11648/j.ijfmts.20200601.12,
  author = {Tithi Sikdar and Nusrat Jahan Pinky and Avijit Roy and Shahid Shafayet Hossain and Nazmul Islam},
  title = {Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {1},
  pages = {9-18},
  doi = {10.11648/j.ijfmts.20200601.12},
  url = {https://doi.org/10.11648/j.ijfmts.20200601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200601.12},
  abstract = {The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.},
 year = {2020}
}

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TY  - JOUR
T1  - Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number
AU  - Tithi Sikdar
AU  - Nusrat Jahan Pinky
AU  - Avijit Roy
AU  - Shahid Shafayet Hossain
AU  - Nazmul Islam
Y1  - 2020/01/07
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200601.12
DO  - 10.11648/j.ijfmts.20200601.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 9
EP  - 18
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200601.12
AB  - The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.
VL  - 6
IS  - 1
ER  -

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Author Information

Tithi Sikdar

Mathematics Discipline, Khulna University, Khulna, Bangladesh
Nusrat Jahan Pinky

Mathematics Discipline, Khulna University, Khulna, Bangladesh
Avijit Roy

Mathematics Discipline, Khulna University, Khulna, Bangladesh
Shahid Shafayet Hossain

Mathematics Department, Govt. K. C. College, Jhenaidah, Bangladesh
Nazmul Islam

Mathematics Discipline, Khulna University, Khulna, Bangladesh

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APA Style

Tithi Sikdar, Nusrat Jahan Pinky, Avijit Roy, Shahid Shafayet Hossain, Nazmul Islam. (2020). Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. International Journal of Fluid Mechanics & Thermal Sciences, 6(1), 9-18. https://doi.org/10.11648/j.ijfmts.20200601.12

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ACS Style

Tithi Sikdar; Nusrat Jahan Pinky; Avijit Roy; Shahid Shafayet Hossain; Nazmul Islam. Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. Int. J. Fluid Mech. Therm. Sci. 2020, 6(1), 9-18. doi: 10.11648/j.ijfmts.20200601.12

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AMA Style

Tithi Sikdar, Nusrat Jahan Pinky, Avijit Roy, Shahid Shafayet Hossain, Nazmul Islam. Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number. Int J Fluid Mech Therm Sci. 2020;6(1):9-18. doi: 10.11648/j.ijfmts.20200601.12

Copy | Download

@article{10.11648/j.ijfmts.20200601.12,
  author = {Tithi Sikdar and Nusrat Jahan Pinky and Avijit Roy and Shahid Shafayet Hossain and Nazmul Islam},
  title = {Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {1},
  pages = {9-18},
  doi = {10.11648/j.ijfmts.20200601.12},
  url = {https://doi.org/10.11648/j.ijfmts.20200601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200601.12},
  abstract = {The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number
AU  - Tithi Sikdar
AU  - Nusrat Jahan Pinky
AU  - Avijit Roy
AU  - Shahid Shafayet Hossain
AU  - Nazmul Islam
Y1  - 2020/01/07
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200601.12
DO  - 10.11648/j.ijfmts.20200601.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 9
EP  - 18
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200601.12
AB  - The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.
VL  - 6
IS  - 1
ER  -

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