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Chin. Phys. B, 2014, Vol. 23(6): 064701    DOI: 10.1088/1674-1056/23/6/064701
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

Z. Asghar, N. Ali
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Abstract  We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.
Keywords:  viscous fluid      slip condition      streamline topologies      bifurcation  
Received:  05 September 2013      Revised:  30 October 2013      Published:  15 June 2014
PACS:  47.15.-x (Laminar flows)  
  47.10.ad (Navier-Stokes equations)  
  47.15.G-  
  05.45.-a (Nonlinear dynamics and chaos)  
Corresponding Authors:  Z. Asghar     E-mail:  zaheer_asghar@yahoo.com

Cite this article: 

Z. Asghar, N. Ali Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid 2014 Chin. Phys. B 23 064701

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