Advertisement

Brazilian Journal of Physics

, Volume 48, Issue 3, pp 227–241 | Cite as

Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

  • Noor Saeed Khan
General and Applied Physics

Abstract

The bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. A real-life system evolves under the flow and various taxis. The study is initially proposed in the context of gyrotactic system, which is used as a key element for the description of complex bioconvection patterns and dynamics in such systems. The governing partial differential equations are transformed into a system of ordinary ones through the similarity variables and solved analytically via homotopy analysis method (HAM). The solution is expressed through graphs and illustrated which show the influences of all the parameters.

Keywords

Gravity-driven Thin film Second grade nanofluid Bioconvection Passively controlled nanofluid model Gyrotactic microorganisms Convective boundary conditions Homotopy analysis method 

Notes

Acknowledgments

The author is extremely grateful to the honorable reviewer for his excellent and informative comments which have certainly served to clarify and improve the present work.

Author Contributions

NSK modeled the problem and solved. NSK also wrote the paper. The author read and approved the final manuscript.

Funding Information

The author is thankful to the Higher Education Commission (HEC) Pakistan for providing the technical and financial support.

Compliance with Ethical Standards

Competing interests

The author declares that he has no competing interests.

Author Statement

The author agrees with the submission of the manuscript, and the material presented in the manuscript has not been previously published, nor it is simultaneously under consideration by any other journal.

References

  1. 1.
    M. Turkyilmazoglu, Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: exact solutions. Int. J. Heat Mass Transf. 106, 127–134 (2017).  https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.056 CrossRefGoogle Scholar
  2. 2.
    F. Mabood, W.A. Khan, A. Izani, M. Ismail, in Analytical modelling of free convection of non-Newtonian nanofluids flow in porous media with gyrotactic microorganisms using OHAM. AIP Conference Proceedings ICOQSIA, 2014, Langkawi, Malaysia, (2014)Google Scholar
  3. 3.
    K. Das, P.R. Durai, P.K. Kundu, Nanofluid bioconvection in presence of gyrotactic microorganisms and chemical reaction in porous medium. J. Mech. Sci. Technol. 29(11), 4841–4849 (2015)CrossRefGoogle Scholar
  4. 4.
    S.E. Ahmed, A. Mahdy, Laminar MHD Natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media. Appl. Math. Mech. Engl. Ed. 37(4), 471–484 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    M.T. Sk, K. Das, P.K. Kundu, Multiple slip effects on bioconvection of nanofluid flow containing microorganisms and nanoparticles. J. Mol. Liq. 220(2016), 518–526 (2016)CrossRefGoogle Scholar
  6. 6.
    H. Xu, I. Pop, Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. Int. J. Heat Mass Tranf. 75, 610–623 (2014)CrossRefGoogle Scholar
  7. 7.
    N.S. Khan, T. Gul, M.A. Khan, E. Bonyah, S. Islam, Mixed convection in gravity-driven thin film non-Newtonian nanofluids flow with gyrotactic microorganisms. Results Phys. 7, 4033–4049 (2017).  https://doi.org/10.1016/j.rinp.2017.10.017 ADSCrossRefGoogle Scholar
  8. 8.
    A. Raees, H. Xu, Q. Sun, I. Pop, mixed convection in gravity-driven nanoliquid film containing both nanoparticles and gyrotactic microorganisms. Appl. Math. Mech. Engl. Ed. 36(2), 163–178 (2015).  https://doi.org/10.1007/s10483-015-1901-7 CrossRefzbMATHGoogle Scholar
  9. 9.
    S.U.S. Choi, in Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of NonNewtonian Flows, FED-Vol. 231/MD-Vol. 66, ed. by D.A. Siginer, H.P. Wang (ASME, New York, 1995), pp. 99–105Google Scholar
  10. 10.
    J. Buongiorno, L.W. Hu, in Nanofluid heat transfer enhancement for nuclear reactor application. Proceedings of the ASME (2009) 2nd Micro/Nanoscale Heat & Mass Transfer International Conference MNHMT.  https://doi.org/10.1115/MNHMT2009-18062-18062, (2009)
  11. 11.
    G. Huminic, A. Huminic, Applications of nanofluids in heat exchangers, a review. Renew. Sust. Energ. Rev. 16, 5625–5638 (2012)CrossRefzbMATHGoogle Scholar
  12. 12.
    M. Turkyilmazoglu, Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces. Phys. Fluids. 29, 013302 (2017).  https://doi.org/10.1063/1.4965926 ADSCrossRefGoogle Scholar
  13. 13.
    N.S. Khan, T. Gul, S. Islam, W. Khan, Thermophoresis and thermal radiation with heat and mass transfer in a magnetohydrodynamic thin film second-grade fluid of variable properties past a stretching sheet. Eur. Phys. J. Plus. 132, 11 (2017).  https://doi.org/10.1140/epjp/i2017-11277-3 CrossRefGoogle Scholar
  14. 14.
    M.S. Abel, M.M. Nandeppanavar, S.B. Malipatail, Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink. Int. J. Heat Mass Transf. 53, 1788–1795 (2010)CrossRefzbMATHGoogle Scholar
  15. 15.
    N.S. Khan, T. Gul, S. Islam, W. Khan, I. Khan, L. Ali, Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer. Alex. Eng. J. (2017).  https://doi.org/10.1016/j.aej.2017.01.036
  16. 16.
    I. Ahmad, M. Sajjad, T. Hayat, Heat transfer in unsteady axisymmetric second grade fluid. Appl. Math. Comput. 215, 1685–1695 (2009)MathSciNetzbMATHGoogle Scholar
  17. 17.
    N.S. Khan, T. Gul, S. Islam, I. Khan, A.M. Alqahtani, A.S. Alshomrani, Magnetohydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer. J. Appl. Sci. 7, 271 (2017)CrossRefGoogle Scholar
  18. 18.
    B. Sahoo, Hiemenz flow and heat transfer of a third grade fluid. Commun. Nonlinear Sci. Numer. Simul. 14, 811–826 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    N.S. Khan, T. Gul, S. Islam, A. Khan, Z. Shah, Brownian motion and thermophoresis effects on MHD mixed convective thin film second-grade nanofluid flow with Hall effect and heat transfer past a stretching sheet. J. Nanofluids. 6(5), 812–829 (2017).  https://doi.org/10.1166/jon.2017.1383 CrossRefGoogle Scholar
  20. 20.
    S.J. Liao, Homotopy analysis method in non-linear differential equations (Higher Education Press, Beijing and Springer, Berlin Heidelberg, 2012)Google Scholar
  21. 21.
    M. Turkyilmazoglu, The Airy equation and its alternative analytic solution. Phys. Scr. 86, 055004 (2012).  https://doi.org/10.1088/0031-8949/86/05/055004  https://doi.org/10.1088/0031-8949/86/05/055004. IOP PublishingCrossRefzbMATHGoogle Scholar
  22. 22.
    M. Turkyilmazoglu, An effective approach for approximate analytical solutions of the damped Duffing equations. Phys. Scr. 86, 015301 (2012).  https://doi.org/10.1088/0031-8949/86/01/015301 ADSCrossRefzbMATHGoogle Scholar
  23. 23.
    M. Turkyilmazoglu, Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian decomposition method. Mediterr. J. Math. (2016).  https://doi.org/10.1007/s00009-016-0730-8
  24. 24.
    M. Turkyilmazoglu, Is homotopy perturbation method the traditional Taylor series expansion. Hacettepe J. Math. Stat. 44(3), 651–657 (2015)MathSciNetzbMATHGoogle Scholar

Copyright information

© Sociedade Brasileira de Física 2018

Authors and Affiliations

  1. 1.Department of MathematicsAbdul Wali Khan UniversityMardanPakistan

Personalised recommendations