International Journal of Fluid Mechanics & Thermal Sciences 2020; 6(1): 9-18 http://www.sciencepublishinggroup.com/j/ijfmts doi: 10.11648/j.ijfmts.20200601.12 ISSN: 2469-8105 (Print); ISSN: 2469-8113 (Online) Oscillating Flow of Viscous Incompressible Fluid Through Sinusoidal Periodic Tube at Low Reynolds Number Tithi Sikdar 1 , Nusrat Jahan Pinky 1 , Avijit Roy 1 , Shahid Shafayet Hossain 2 , Nazmul Islam 1, * 1 Mathematics Discipline, Khulna University, Khulna, Bangladesh 2 Mathematics Department, Govt. K. C. College, Jhenaidah, Bangladesh Email address: * Corresponding author To cite this article: 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 Received: October 28, 2019; Accepted: November 28, 2019; Published: January 7, 2020 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 1. Introduction The study of flow in tubes with periodic variations has attracted much attention of researchers due to its various physiological and engineering applications. It helps us to understand the characteristics of the blood flow through arteries or the transport of intestinal fluid through the colon [1-3]. Other applications include the investigation of transport processes in porous media and separate particle dispersions within micro fluidic devices and nano porous membranes [4-6]. A number of authors have investigated oscillating flow through different periodic tubes. Previous studies on the oscillatory flow in nonuniform channels and tubes with smooth constrictions began with Bellhouse et al. [7] who studied oscillatory flow in a furrowed channel and reported that the oscillatory flow could improve the mass transfer rate in a blood oxygenator. They confirmed that the combination of a large laminar oscillation with a much smaller mean flow through a wavy-walled channel could achieve a higher mass transfer rate. Sobey [8, 9] simulated the flow patterns using a two-dimensional numerical simulation for the oscillatory flow in the furrowed channel and showed that vortex formation and ejection were responsible for the enhanced mixing and mass transfer. This simulation was supported by experimental observations by Stephanoff et al. [10]. Nishimura et al. [11] conducted an experiment about the flow characteristics in wavy-walled channels for steady flow and indicated that the diverse flow structures in this geometry depended on both oscillatory Reynolds number and Strouhal number. They got the