Three-dimensional Couette flow of a Jeffrey fluid along periodic injection/suction

Open Access
Article

Abstract

Three-dimensional Couette flow of an incompressible Jeffrey fluid is formulated and discussed analytically and graphically. The suction is applied over uniformly moving upper plate and its equivalent deduction by injection at the lower stationary plate. Because of this type of suction/injection, this flow turns into three-dimensional. An analytical method is applied to get main flow velocity, secondary flows velocities and pressure components. Also skin friction components along the main and secondary flow directions have been calculated. The effects of different physical parameters, for example, the Deborah number, suction/injection parameter, the ratio of relaxation time to the retardation time and Reynolds number have been discussed graphically. It is witnessed that the Deborah number plays vital role to control the main flow velocity.

Mathematics Subject Classification

76A05 

Notes

References

  1. 1.
    Lachmann, G.N.V.: Boundary Layer and Flow Control. Its Principles and Application, Vol. I and II. Pergamon Press, Oxford (1961)Google Scholar
  2. 2.
    Gersten, K.; Gross, J.F.: Flow and heat transfer along a plane wall with periodic suction. ZAMP 25, 399–408 (1974)CrossRefMATHGoogle Scholar
  3. 3.
    Singh, K.D.: Three-dimensional Couette flow with transpiration cooling. Z. Angew. Math. Phys. 50(4), 661–668 (1999)CrossRefMATHGoogle Scholar
  4. 4.
    Chaudhary, R.C.; Goyal, M.C.; Gupta, U.: Three-dimensional Couette flow with transpiration cooling between two horizontal parallel porous plates. J. Mech. Cont. Math. Sci. 2(1), 46–58 (2007)Google Scholar
  5. 5.
    Guria, M.; Jana, R.N.: Three-dimensional fluctuating Couette flow through the porous plates with heat transfer. Int. J. Math. Math. Sci. 61023, 01–18 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Sharma, B.K.; Agarwal, M.; Chaudhary, R.C.: Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection. Appl. Math. Mech. (English Edition) 28(3), 309–316 (2007)CrossRefMATHGoogle Scholar
  7. 7.
    Chuahan, D.S.; Kumar, V.: Heat transfer effects in the Couette flow through a composite channel partially filled with porous medium with a transverse sinusoidal injection velocity and heat source. Thermal Sci. 15(Suppl 2), S175–S186 (2011)CrossRefGoogle Scholar
  8. 8.
    Schlichting, H.: Boundary Layer Theory. McGraw-Hill, New York (1968)MATHGoogle Scholar
  9. 9.
    Singh, P.; Sharma, R.N.; Misra, J.K.; Narayan, K.A.: Three-dimensional convective flow and heat transfer in a porous medium. Indian J. Pure Appl. Math. 19(11), 1130–1135 (1988)Google Scholar
  10. 10.
    Ahmad, N.; Sarma, D.: Three-dimensional free convective flow and heat transfer through a porous medium. Indian J. Pure Appl. Math. 28(10), 1345–1353 (1997)MATHGoogle Scholar
  11. 11.
    Kuznetsov, A.V.: Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid. Int. J. Heat Mass Transf. 41(16), 2556–2560 (1998)CrossRefMATHGoogle Scholar
  12. 12.
    Sharma, P.K.; Chaudhary, R.C.: Magnetohydrodynamics effect on three-dimensional viscous incompressible flow between two horizontal parallel porous plates and heat transfer with periodic injection/suction. IJMMS 62, 3357–3368 (2004)MathSciNetMATHGoogle Scholar
  13. 13.
    Guria, M.; Jana, R.N.: Hydrodynamics effect on the three-dimensional flow past a vertical porous plate. Int. J. Math. Sci. 20, 3359–3372 (2005)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sharma, P.K.; Saini, B.S.: The effect of injection/suction on flow past parallel plates with transpiration cooling. Turk. J. Eng. Environ. Sci. 32, 289–294 (2008)Google Scholar
  15. 15.
    Chuahan, D.S.; Kumar, V.: Three-dimensional Couette flow in a composite channel partially filled with a porous medium. Appl. Math. Sci. 4(54), 2683–2695 (2010)MathSciNetMATHGoogle Scholar
  16. 16.
    Gireesha, B.J.; Chamkha, A.J.; Vishalakshi, C.S.; Bagewadi, C.S.: Three-dimensional Couette flow of a dusty fluid with heat transfer. Appl. Math. Model. 36, 683–701 (2012)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Shoaib, M.; Rana, M.A.; Siddiqui, A.M.: Three-dimensional flow of upper convected Maxwell fluid along an infinite plane wall with periodic suction. J. Comput. Theor. Nanosci. 13(8), 5247–5253 (2016)Google Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan
  2. 2.COMSATS Institute of Information TechnologyAttockPakistan

Personalised recommendations