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Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

  • General and Applied Physics
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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.

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References

  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

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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. 99–105

  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. G. Huminic, A. Huminic, Applications of nanofluids in heat exchangers, a review. Renew. Sust. Energ. Rev. 16, 5625–5638 (2012)

    Article  MATH  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. I. Ahmad, M. Sajjad, T. Hayat, Heat transfer in unsteady axisymmetric second grade fluid. Appl. Math. Comput. 215, 1685–1695 (2009)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  18. B. Sahoo, Hiemenz flow and heat transfer of a third grade fluid. Commun. Nonlinear Sci. Numer. Simul. 14, 811–826 (2009)

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  20. S.J. Liao, Homotopy analysis method in non-linear differential equations (Higher Education Press, Beijing and Springer, Berlin Heidelberg, 2012)

  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 Publishing

    Article  MATH  Google Scholar 

  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

    Article  ADS  MATH  Google Scholar 

  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. M. Turkyilmazoglu, Is homotopy perturbation method the traditional Taylor series expansion. Hacettepe J. Math. Stat. 44(3), 651–657 (2015)

    MathSciNet  MATH  Google Scholar 

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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.

Funding

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

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan

    Noor Saeed Khan

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

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Correspondence to Noor Saeed Khan.

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The author declares that he has no competing interests.

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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.

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Khan, N.S. Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms. Braz J Phys 48, 227–241 (2018). https://doi.org/10.1007/s13538-018-0567-7

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  • DOI: https://doi.org/10.1007/s13538-018-0567-7

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