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Chin. Phys. B, 2014, Vol. 23(6): 064701    DOI: 10.1088/1674-1056/23/6/064701

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) (Navier-Stokes equations)  
  05.45.-a (Nonlinear dynamics and chaos)  
Corresponding Authors:  Z. Asghar     E-mail:

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

[1] Shapiro A H 1967 National Academy of Science Natural Research Council 1 109
[2] Shapiro A H and Latham T W 1966 Proc. Ann. Conf. Engng. Med. Bio., San Francisco, California 8 147
[3] Weinberg S L 1970 Ph. D. Thesis, MIT, Cambridge MA, USA
[4] Shapiro A H, Jaffrin M Y and Weinberg S L 1969 J. Fluid Mech. 37 799
[5] Ebaid A 2008 Phys. Lett. A 372 4493
[6] Elshahed M and Haroun M H 2005 Math. Probs. Engng. 6 663
[7] Hayat T, Ali N and Asghar S 2007 Phys. Lett. A 363 397
[8] Hayat T, Ahmed N and Ali N 2008 Commun. Nonlinear Sci. Numer. Simul. 13 1581
[9] Hayat T, Javed M and Ali N 2008 Transp. Porous Med. 74 259
[10] Hayat T, Qureshi M U and Ali N 2009 Appl. Math. Model. 33 1862
[11] Hayat T, Noreen S, Asghar S and Hendi A A 2011 Chem. Engng. Commun. 198 609
[12] Hayat T and Noreen S 2012 Chem. Engng. Commun. 199 512
[13] Mekheimer Kh S 2008 Phys. Lett. A 372 4271
[14] Mekheimer Kh S and Elmaboud Y A 2008 Phys. Lett. A 372 1657
[15] Nadeem S and Akram S 2010 Commun. Nonlinear Sci. Numer. Simul. 15 312
[16] Vajravelu K, Sreenadh S and Babu V R 2005 Appl. Math. Comput. 169 726
[17] Vajravelu K, Radhakrishnamacharya G and Radhakrishnamurty V 2007 Non-Linear Mech. 42 754
[18] Srinivas S and Muthuraj R 2010 Chem. Engng. Commun. 197 1387
[19] Abd-Alla A M, Abo-Dahab S M and Al-Shahrany 2013 Chin. Phys. B 22 074702
[20] Akbar N S and Nadeem S 2013 Chin. Phys. B 22 014703
[21] Ali N, Sajid M and Javed T 2011 Chin. Phys. Lett. 28 014704
[22] Mehmood O U, Mustapha N and Shafie S 2012 Appl. Math. Mech.: Engl. Ed. 33 1313
[23] Oswatitsch K 1958 IUTAM Symposium on Boundary Layer Research (Berlin: Springer-Verlag) p. 357
[24] Davey A 1961 J. Fluid Mech. 10 593
[25] Lighthill M J 1963 Laminar Boundary Layers 2 72
[26] Hunt J C R, Abell C J, Peterka J A and Woo H 1978 J. Fluid Mech. 86 179
[27] Tobak M and Peake D J 1982 Ann. Rev. Fluid Mech. 14 61
[28] Perry A E and Chong M S 1987 Ann. Rev. Fluid Mech. 19 125
[29] Brons M and Hartnack J N 1999 Phys. Fluids 11 314
[30] Gurcan F, Deliceoglu A and Bakker P G 2005 J. Fluid Mech. 539 299
[31] Jimenez J and Sen M 2010 Chem. Engng. Process. 49 704
[32] Bakker P G 1991 Bifurcations in Flow Patterns (Dordrecht: Kluwer Academic Publishers)
[33] Seydel R 1988 From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis (New York: Elsevier)
[34] Perko L 2000 Differential Equations and Dynamical Systems, 3rd edn. (Los Alamitos: Springer-Verlag)
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