Circular flow around a turning point in an annular area between two coaxial porous cylinders

  • Médard Marcus NganbeII
  • Jacques HonaEmail author
  • Elisabeth Ngo Nyobe
  • Elkana Pemha
Regular Article


In order to investigate a suction-driven circular flow within an annular tube formed by two coaxial porous cylinders, a mathematical model expressed as a nonlinear two-point boundary-value problem is achieved. In seeking solutions of the problem, the results obtained reveal the existence of a hydrodynamic turning point among the main physical settings of the study. The dynamics of the fluid is examined through three solution branches Fr, S1 and S2 that form this turning point. By increasing the Reynolds number above the turning point, regions where the fluid moves in the counterclockwise direction are observed through the first branch Fr and the secondary branch of type S2 near the inner and the outer cylinders, respectively. Due to this described behavior, solutions of types Fr and S2 seem to be mirror images of each other. A flow of the boundary layer type takes place through the secondary branch of type S1 for great values of the Reynolds number. This boundary layer causes the radial velocity to approach a linear profile at the same constant curve for different Reynolds numbers.


  1. 1.
    J. Rahimi, D.D. Ganji, M. Khaki, Kh. Hosseinzadeh, Alex. Eng. J. 56, 621 (2017)CrossRefGoogle Scholar
  2. 2.
    S.S. Ghadikolaei, Kh. Hosseinzadeh, M. Yassari, H. Sadeghi, D.D. Ganji, Therm. Sci. Eng. Prog. 5, 309 (2018)CrossRefGoogle Scholar
  3. 3.
    C.E. Dauenhauer, J. Majdalani, Phys. Fluids 15, 1485 (2003)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edition (Wiley, NY, 2002)Google Scholar
  5. 5.
    R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Fluids, Vol. 1, Fluid Mechanics (Wiley, NY, 1987)Google Scholar
  6. 6.
    M. Hatami, Kh. Hosseinzadeh, G. Damairry, M.T. Behnamfar, J. Taiwan Inst. Chem. Eng. 45, 2238 (2014)CrossRefGoogle Scholar
  7. 7.
    Kh. Hosseinzadeh, A. Jafarian Amiri, S. Saedi Ardahaie, D.D. Ganji, Case Stud. Therm. Eng. 10, 595 (2017)CrossRefGoogle Scholar
  8. 8.
    E. Magyari, B. Keller, Eur. J. Mech. B-Fluids 19, 109 (2000)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    G. Damairry, M. Hatami, J. Mol. Liq. 193, 37 (2014)CrossRefGoogle Scholar
  10. 10.
    P. Watson, W.H.H. Banks, M.B. Zaturska, P.G. Drazin, Eur. J. Appl. Math. 2, 359 (1991)CrossRefGoogle Scholar
  11. 11.
    V. Nyemb Nsoga, J. Hona, E. Pemha, Int. J. Nonlinear Sci. Numer. Simul. 18, 507 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    M.L. Martins-Costa, R.M. Saldanha Da Gama, S. Frey, Mech. Res. Commun. 27, 707 (2000)CrossRefGoogle Scholar
  13. 13.
    M.B. Zaturska, P.G. Drazin, W.H.H. Banks, Fluid Dyn. Res. 4, 151 (1988)ADSCrossRefGoogle Scholar
  14. 14.
    G.J. Hwang, Y.C. Cheng, M.L. Ng, Int. J. Heat Mass Transfer 36, 2429 (1993)ADSCrossRefGoogle Scholar
  15. 15.
    S.M. Cox, J. Fluid Mech. 27, 1 (1991)ADSCrossRefGoogle Scholar
  16. 16.
    J.F. Brady, A. Acrivos, J. Fluid Mech. 112, 127 (1981)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    P. Watson, W.H.H. Banks, M.B. Zaturska, P.G. Drazin, Eur. J. Appl. Math. 2, 359 (1991)CrossRefGoogle Scholar
  18. 18.
    S. Dinarvand, M.M. Rashidi, Nonlinear Anal. 11, 1502 (2010)CrossRefGoogle Scholar
  19. 19.
    J. Hona, M.M. Nganbe II, Int. J. Eng. Syst. Model. Simul. 9, 177 (2017)Google Scholar
  20. 20.
    E.B.B. Watson, W.H.H. Banks, M.B. Zaturska, P.G. Drazin, J. Fluid Mech. 212, 451 (1990)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    J. Majdalani, C. Zhou, J. Appl. Math. Mech. 83, 181 (2003)Google Scholar
  22. 22.
    C. Zhou, J. Majdalani, J. Prop. Power 18, 703 (2002)CrossRefGoogle Scholar
  23. 23.
    O.D. Makinde, Eur. Phys. J. Plus 129, 270 (2014)CrossRefGoogle Scholar
  24. 24.
    W.H.H. Banks, M.B. Zaturska, Phys. Fluids A 4, 1131 (1992)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    J. Hona, E. Ngo Nyobe, E. Pemha, Int. J. Bifurc. Chaos Appl. Sci. Eng. 19, 2939 (2009)CrossRefGoogle Scholar
  26. 26.
    T. Saad, J. Majdalani, AIAA J. 55, 3868 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    J.F. Brady, Phys. Fluids 27, 1061 (1984)ADSCrossRefGoogle Scholar
  28. 28.
    J. Majdalani, G.A. Flandro, Proc. R. Soc. London Ser. A 458, 1621 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    A.S. Berman, J. Appl. Phys. 24, 1232 (1953)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    E. Pemha, J. Hona, E. Ngo Nyobe, Int. J. Flow Control 6, 119 (2014)CrossRefGoogle Scholar
  31. 31.
    J. Hona, E. Ngo Nyobe, E. Pemha, Int. J. Eng. Syst. Model. Simul. 7, 192 (2015)Google Scholar
  32. 32.
    J. Hona, E. Ngo Nyobe, E. Pemha, Int. J. Eng. Syst. Model. Simul. 8, 183 (2016)Google Scholar
  33. 33.
    G.I. Taylor, Proc. R. Soc. London 234, 456 (1956)ADSCrossRefGoogle Scholar
  34. 34.
    R.M. Terrill, Aeronaut. Quart. 15, 299 (1964)MathSciNetCrossRefGoogle Scholar
  35. 35.
    J.R. Sellars, J. Appl. Phys. 26, 489 (1955)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Médard Marcus NganbeII
    • 1
  • Jacques Hona
    • 1
    Email author
  • Elisabeth Ngo Nyobe
    • 2
  • Elkana Pemha
    • 1
  1. 1.Applied Mechanics Laboratory, Faculty of ScienceUniversity of Yaoundé IYaoundéCameroon
  2. 2.Department of Mathematics and Physical Science, National Advanced School of EngineeringUniversity of Yaoundé IYaoundéCameroon

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