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Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number
International Journal of Fluid Mechanics & Thermal Sciences
Volume 6, Issue 1, March 2020, Pages: 9-18
Received: Oct. 28, 2019; Accepted: Nov. 28, 2019; Published: Jan. 7, 2020
Authors
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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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.
Keywords
Oscillating Flow, Low Reynolds Number, Boundary Element Method, Sinusoidal Periodic Tube
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, International Journal of Fluid Mechanics & Thermal Sciences. Vol. 6, No. 1, 2020, pp. 9-18. doi: 10.11648/j.ijfmts.20200601.12
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