Volume 5, Issue 3, September 2019, Page: 72-81
Numerical Study of Creeping Flow Through Sinusoidally Periodic Tube
Asif Mahmud, Mathematics Discipline, Khulna University, Khulna, Bangladesh
Suhana Perveen, Mathematics Discipline, Khulna University, Khulna, Bangladesh
Md. Nazmul Hasan, Mathematics Discipline, Khulna University, Khulna, Bangladesh
Md. Samsuzzoha, Department of Mathematics, Swinburne University of Technology, Victoria, Australia
Nazmul Islam, Mathematics Discipline, Khulna University, Khulna, Bangladesh
Received: Apr. 29, 2019;       Accepted: Sep. 4, 2019;       Published: Sep. 19, 2019
DOI: 10.11648/j.ijamtp.20190503.14      View  480      Downloads  139
There has been renewed interest in the flow behaviour within tubes with periodically varying cross-section with the recognition that they can be used as particle separation devices. In this paper, we present a numerical study of the effect of tube geometry on creeping flow of viscous incompressible fluid through sinusoidally constricted periodic tube which is axisymmetric but longitudinally asymmetric. The boundary element method is used to solve for the flow in the tube by specifying the pressure drop across the ends of the tube. The boundary element equations have been formulated for ­an infinite periodic tube by writing the velocity in terms of the integrals over the tube boundary and is used to calculate the force on the tube boundary, to obtain the detailed velocity distribution within the tube and to determine the effect of amplitude and wavelength of corrugation on the structure of the flow. We have found that the highest axial velocity is at throat region and lowest axial velocity is at expansion region. Also, we have discovered that the maximum radial velocity occurs at diverging cross-section and minimum radial velocity occurs at converging cross-section. The tangential force on the tube wall is examined for different amplitudes and wavelengths of corrugation and observed that the tangential force is greater in the constricted region than in the expansion region. The physical quantities (such as velocity and force) increase with increasing amplitude and decrease with increasing wavelength. Finally, we have compared our results with the work of Hemmat and Borhan [3] and have found good agreement with them.
Creeping Flow, Numerical Study, Periodic Tube, Sinusoidal Cross-Section, Boundary Element Method
To cite this article
Asif Mahmud, Suhana Perveen, Md. Nazmul Hasan, Md. Samsuzzoha, Nazmul Islam, Numerical Study of Creeping Flow Through Sinusoidally Periodic Tube, International Journal of Applied Mathematics and Theoretical Physics. Vol. 5, No. 3, 2019, pp. 72-81. doi: 10.11648/j.ijamtp.20190503.14
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