Skip to main content

A study on the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel: A numerical approach

Abstract.

The unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel is considered. In addition to the classical no-slip and hyper-stick conditions at the boundary, it is assumed that the fluid velocities and shear stresses are continuous across the fluid-fluid interface. Three cases for the applied pressure gradient are considered to study the problem: one with constant pressure gradient and the other two cases with time-dependent pressure gradients, viz. periodic and decaying pressure gradient. The Crank-Nicolson approach has been used to obtain numerical solutions for fluid velocity and microrotation for diverse sets of fluid parameters. The nature of fluid velocities and microrotation with various values of pressure gradient, Reynolds number, ratio of viscosities, micropolarity parameter and time is illustrated through graphs. It has been observed that micropolarity parameter and ratio of viscosities reduce the fluid velocities.

This is a preview of subscription content, access via your institution.

References

  1. 1

    A.C. Eringen, J. Math. Mech. 16, 1 (1966)

    MathSciNet  Google Scholar 

  2. 2

    A.C. Eringen, Microcontinnum Field Theories: II. Fluent Media (Springer, New York, 2001)

  3. 3

    J. Peddieson Jr., Int. J. Eng. Sci. 10, 23 (1972)

    Article  Google Scholar 

  4. 4

    G. Bayada, N. Benhaboucha, M. Chambat, Math. Mod. Methods Appl. Sci. 15, 343 (2005)

    Article  Google Scholar 

  5. 5

    A. Siddangouda, Lubr. Sci. 24, 339 (2012)

    Article  Google Scholar 

  6. 6

    J.R. Lin, T.C. Hung, T.L. Chou, L.J. Liang, Tribol. Int. 66, 150 (2013)

    Article  Google Scholar 

  7. 7

    N.B. Naduvinamani, S.S. Huggi, J. Eng. Tribol. 223, 1179 (2009)

    Google Scholar 

  8. 8

    C.K. Kang, A.C. Eringen, B. Math. Biol. 38, 135 (1976)

    Article  Google Scholar 

  9. 9

    M. Devakar, T.K.V. Iyenger, Eur. Phys. J. Plus 128, 41 (2013)

    Article  Google Scholar 

  10. 10

    Kh.S. Mekheimer, M.A.El. Kot, Acta Mech. Sin. 24, 637 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  11. 11

    D. Srinivasacharya, M. Shiferaw, Arab. J. Sci. Eng. 39, 5085 (2014)

    MathSciNet  Article  Google Scholar 

  12. 12

    L. Wang, Y. Jian, F. Li, Eur. Phys. J. Plus 131, 338 (2016)

    Article  Google Scholar 

  13. 13

    X. Si, L. Zheng, P. Lin, X. Zhang, Y. Zhang, Int. J. Heat Mass Transfer 67, 885 (2013)

    Article  Google Scholar 

  14. 14

    Z. Ziabakhsh, G. Domairry, H. Bararnia, J. Taiwan Inst. Chem. Eng. 40, 443 (2009)

    Article  Google Scholar 

  15. 15

    M.S. Abdel-wahed, Eur. Phys. J. Plus 132, 195 (2017)

    ADS  Article  Google Scholar 

  16. 16

    T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 11, 905 (1973)

    Article  Google Scholar 

  17. 17

    T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 12, 273 (1974)

    Article  Google Scholar 

  18. 18

    G. Lukaszewicz, Micropolar Fluids: Theory and Application (Birkhauser, Basel, 1999)

  19. 19

    C. Boodoo, B. Bhatt, D. Comissiong, Rheol. Acta 52, 579 (2013)

    Article  Google Scholar 

  20. 20

    R. Bird, W. Stewart, E.N. Lightfoot, Transport Phenomena, second edition (John Wiley & Sons, 2002)

  21. 21

    J.N. Kapur, J.B. Shukla, Appl. Sci. Res. 13, 55 (1964)

    Article  Google Scholar 

  22. 22

    V. Srinivasan, K. Vafai, J. Fluids Eng. 116, 135 (1994)

    Article  Google Scholar 

  23. 23

    J. Prathap Kumar, J.C. Umavathi, A.J. Chamkha, I. Pop, Appl. Math. Model. 34, 1175 (2010)

    MathSciNet  Article  Google Scholar 

  24. 24

    S.M. Zivojin, D.D. Nikodijevic, B.D. Blagojevic, S.R. Savic, Trans. Can. Soc. Mech. Eng. 34, 351 (2010)

    Article  Google Scholar 

  25. 25

    J. Srinivas, J.V. Ramana Murthy, J. Appl. Fluid Mech. 9, 501 (2016)

    Article  Google Scholar 

  26. 26

    J. Srinivas, J.V. Ramana Murthy, J. Eng. Thermophys. 25, 126 (2016)

    Article  Google Scholar 

  27. 27

    A. Borrelli, G. Giantesio, M.C. Patria, J. Fluids Eng. Trans. ASME 139, 101203 (2017)

    Article  Google Scholar 

  28. 28

    N. Kumar, S. Gupta, Meccanica 47, 277 (2012)

    MathSciNet  Article  Google Scholar 

  29. 29

    J.C. Umavathi, J. Prathap Kumar, A.J. Chamkha, Can. J. Phys. 86, 961 (2008)

    ADS  Article  Google Scholar 

  30. 30

    J.C. Umavathi, A.J. Chamkha, Can. J. Phys. 83, 705 (2005)

    ADS  Article  Google Scholar 

  31. 31

    A.K. Singh, Indian J. Pure Appl. Phys. 43, 415 (2005)

    Google Scholar 

  32. 32

    K.S. Sai, Defence Sci. J. 40, 183 (1990)

    Article  Google Scholar 

  33. 33

    K. Vajravelu, P.V. Arunachalam, S. Sreenadh, J. Math. Anal. Appl. 196, 1105 (1995)

    MathSciNet  Article  Google Scholar 

  34. 34

    J.C. Umavathi, A.J. Chamkha, A. Mateen, A. Al-Mudhaf, Heat Mass Transf. 42, 81 (2005)

    ADS  Article  Google Scholar 

  35. 35

    J.C. Umavathi, I.C. Liu, M. Shekar, Appl. Math. Mech. Engl. 33, 931 (2012)

    Article  Google Scholar 

  36. 36

    G. Ahmadi, Int. J. Eng. Sci. 14, 639 (1976)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. Devakar.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Devakar, M., Raje, A. A study on the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel: A numerical approach. Eur. Phys. J. Plus 133, 180 (2018). https://doi.org/10.1140/epjp/i2018-12011-5

Download citation