Skip to main content
SpringerLink
Log in

A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M.J. Stefan, Akad. Wissensch. Wien Math. Naturwiss. 69, 713 (1874)

    Google Scholar 

  2. R.L. Verma, Wear 72, 89 (1981)

    Article  Google Scholar 

  3. P. Singh, V. Radhakrishnan, K.A. Nayran, Ing. Arch. 60, 274 (1990)

    Article  Google Scholar 

  4. E.A. Hamza, J. Phys. D Appl. Phys. 32, 656 (1999)

    Article  ADS  Google Scholar 

  5. R.A. Rajagopal, A.S. Gupta, Int. J. Eng. Sci. 19, 1009 (1981)

    Article  Google Scholar 

  6. H.M. Duwairi, B. Tashtoush, R.A. Damseh, Heat Mass Transf. 41, 112 (2004)

    Article  ADS  Google Scholar 

  7. M. Mustafa, T. Hayat, S. Obaidat, Meccanica 47, 1581 (2012)

    Article  MathSciNet  Google Scholar 

  8. M.M. Rashidi, H. Shahmohamadi, S. Dinarvand, Math. Prob. Eng. 2008, 935095 (2008)

    Article  Google Scholar 

  9. S. Choi, ASME 66, 99 (1995)

    Google Scholar 

  10. U. Khan, N. Ahmed, S.T. Mohy-ud-Din, Neural Comput. Appl. (2016) DOI:10.1007/s00521-016-2596-x

  11. S. Kack, A. Pramuanjaronkij, Int. J. Heat Mass Transfer 52, 3187 (2009)

    Article  Google Scholar 

  12. K.V. Wong, O.D. Leon, Adv. Mech. Eng. 2, 519659 (2010)

    Article  Google Scholar 

  13. R. Saidur, K.Y. Leong, H.A. Mohammad, Renew. Sustain. Energy Rev. 15, 1646 (2011)

    Article  Google Scholar 

  14. D. Wen, G. Lin, S. Vafaei, K. Zhang, Particuology 7, 141 (2011)

    Article  Google Scholar 

  15. I. Buongiorno, J. Heat Transf. Trans. ASME 128, 240 (2006)

    Article  Google Scholar 

  16. Sheikholeslami, H.R. Ashorynejad, D.D. Gangi, A. Kolahdooz, Math. Probl. Eng. 2011, 258734 (2011)

    Article  Google Scholar 

  17. Sheikholeslami, H.R. Ashorynejad, G. Domairry, I. Hashim, J. Appl. Math. 2012, 421320 (2012)

    Article  Google Scholar 

  18. B.K. Dutta, P. Roy, A.S. Gupta, Int. Commun. Heat Mass Transf. 12, 89 (1985)

    Article  Google Scholar 

  19. H.I. Andersson, J.B. Aarseth, N. Braud, B.S. Dandapat, J. Non-Newtonian Fluid Mech. 62, 1 (1996)

    Article  Google Scholar 

  20. Sheikholeslami, D.D. Ganji, M.Y. Javed, R. Ellahi, J. Magn. & Magn. Mater. 374, 36 (2015)

    Article  ADS  Google Scholar 

  21. S. Aman, I. Khan, Z. Ismail, M.Z. Salleh, Neural Comput. Appl. (2016) DOI:10.1007/s00521-016-2688-7

  22. N. Athira, M. Zin, I. Khan, S. Shafie, J. Mol. Liq. 222, 138 (2016)

    Article  Google Scholar 

  23. A. Khalid, I. Khan, S. Shafie, J. Mol. Liq. 221, 1175 (2016)

    Article  Google Scholar 

  24. F. Ali, M. Gohar, I. Khan, J. Mol. Liq. 223, 412 (2016)

    Article  Google Scholar 

  25. I. Ullah, S. Shafie, I. Khan, J. King Saud Univ. (2016) DOI:10.1016/j.jksus.2016.05.003

  26. I. Ullah, I. Khan, S. Shafie, Nanoscale Res. Lett. 11, 527 (2016)

    Article  ADS  Google Scholar 

  27. I. Ullah, K. Bhattaacharyya, S. Shafie, I. Khan, PLoS One 11, e0165348 (2016)

    Article  Google Scholar 

  28. T.J. Pedley, N.A. Hill, J.O. Kessler, J. Fluid Mech. 195, 223 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  29. A.V. Kuznetsov, D.A. Nield, Int. J. Heat Mass Transf. 65, 682 (2013)

    Article  Google Scholar 

  30. P. Geng, A.V. Kuznetasov, Int. J. Transp. Phenom. 7, 321 (2005)

    Google Scholar 

  31. A.V. Kuznetsov, Int. Commun. Heat Mass Transf. 32, 574 (2005)

    Article  Google Scholar 

  32. H. Xu, I. Pop, Eur. J. Mech. B Fluids 46, 37 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  33. U. Khan, N. Ahmed, S.T. Mohy-ud-Din, J. Biol. Syst. 24, 409 (2016)

    Article  Google Scholar 

  34. A. Raees, H. XU, S.-J. Liao, Int. J. Heat Mass Transfer 86, 174 (2015)

    Article  Google Scholar 

  35. S.T. Mohy-ud-Din, U. Khan, N. Ahmed, S.M. Hassan, Appl. Sci. 5, 1639 (2015)

    Article  Google Scholar 

  36. Adnan, M. Asadullah, U. Khan, N. Ahmed, S.T. Mohyud-Din, J. Mol. Liq. 224, 768 (2016)

    Article  Google Scholar 

  37. Adnan, U. Khan, N. Ahmed, S.T. Mohyud-Din, J. Mol. Liq. 224, 1074 (2016)

    Article  Google Scholar 

  38. S.T. Mohyud-Din, U. Khan, N. Ahmed, S.M. Hassan, Appl. Sci. 5, 1639 (2015)

    Article  Google Scholar 

  39. Sheikholeslami, M. Azimi, D.D. Ganji, Int. J. Comput. Eng. Sci. Mech. 3, 1 (2015)

    Google Scholar 

  40. L.J. Crane, Z. Angew. Math. Phys. 21, 645 (1970)

    Article  Google Scholar 

  41. U. Khan, N. Ahmed, S.T. Mohy-ud-Din, Appl. Therm. Eng. 113, 1107 (2017)

    Article  Google Scholar 

  42. P.S. Gupta, A.S. Gupta, Can. J. Chem. Eng. 55, 744 (1977)

    Article  Google Scholar 

  43. A. Ishak, R. Nazar, I. Pop, Meccanica 44, 369 (2009)

    Article  MathSciNet  Google Scholar 

  44. A.K. Borkakoti, A. Bharali, Quart. Appl. Math. 40, 461 (1982)

    Article  MathSciNet  Google Scholar 

  45. K. Vjravelu, B.V. Kumar, Int. J. Non-Linear Mech. 39, 13 (2004)

    Article  Google Scholar 

  46. P. Vadasz (Editor), Emerging Topics in Heat and Mass Transfer in Porous Media (Springer, New York, NY, 2008)

  47. K. Vafai (Editor), Handbook of Porous Media, 2nd edition (Taylor and Francis, New York, NY, 2005)

  48. Sheikholeslami, D.D. Gangi, H.R. Ashorynejad, Powder Technol. 239, 259 (2013)

    Article  Google Scholar 

  49. Sheikholeslami, T. Hayat, A. A, Int. J. Heat Mass Transfer 96, 513 (2016)

    Article  Google Scholar 

  50. Sheikholeslami, R. MM, J. Braz. Soc. Mech. 38, 1171 (2016)

    Article  Google Scholar 

  51. R.U. Haq, N.F.M. Noor, Z.H. Khan, Adv. Powder Technol. 27, 1568 (2016)

    Article  Google Scholar 

  52. A.V. Kuznetsov, D.A. Nield, Int. J. Heat Mass Transfer 65, 682 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, PO. Box 2455, 11451, Riyadh, Saudi Arabia

    Bandar Bin-Mohsin

  2. Department of Mathematics, Faculty of Sciences, HITEC University Taxila Cantt, Taxila, Pakistan

    Naveed Ahmed & Syed Tauseef Mohyud-Din

  3. Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu and Kashmir, Pakistan

    Adnan

  4. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

    Umar Khan

Authors
  1. Bandar Bin-Mohsin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naveed Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Umar Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Syed Tauseef Mohyud-Din
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Umar Khan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bin-Mohsin, B., Ahmed, N., Adnan et al. A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms. Eur. Phys. J. Plus 132, 187 (2017). https://doi.org/10.1140/epjp/i2017-11454-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11454-4

Search

Navigation