Advertisement

Applied Nanoscience

, Volume 8, Issue 6, pp 1523–1544 | Cite as

Non-Newtonian nanoliquids thin-film flow through a porous medium with magnetotactic microorganisms

  • Zaman Palwasha
  • Saeed Islam
  • Noor Saeed Khan
  • Hamza Ayaz
Original Article
  • 12 Downloads

Abstract

Gravity-driven non-Newtonian nanoliquids (Casson and Williamson) thin-film flow through a porous medium containing both nanoparticles and magnetotactic microorganisms is analyzed using passively controlled nanofluid model boundary conditions. Buongiorn’s nanofluid model is used. The thin bio-nanoliquid films contain the copper nanoparticles and magnetotactic microorganisms simulating the forced/free bioconvection in buoyancy-driven flow. The comparison between the role of both the thin nanoliquid films has carefully noticed and discussed the differences in behaviors in detail. The governing equations accompanying the boundary conditions of the problem are reduced to non-linear differential equations by applying particular transformations. These equations along with the boundary conditions are solved analytically by employing homotopy analysis method. The solution consists of the expressions of four different profiles, and with the help of different curves, these profiles are shown graphically and discussed for the impacts of each parameter.

Keywords

Gravity-driven Thin film Casson and Williamson nanofluids Bioconvection Passively controlled nanofluid model Porous medium Magnetotactic microorganisms Convective boundary conditions Homotopy analysis method 

Notes

Acknowledgements

All the comments and valuable suggestions of the reviewers are highly appreciated. The reviewers diplomatic and professional transformation of crude to refine mind in the realm of research and academics is noticed and highly appreciated.

Compliance with ethical standards

Author statement

The authors are agree 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.

Conflict of interests

The authors declare that they have no actual or potential conflict of interest including any financial, personal, or other relationships with other people or organizations.

References

  1. Abegunrin OA, Okhuevbie SO, Animasaun IL (2016) Comparison between the flow of two non-Newtonian fluids over an upper horizontal surface of paraboloid revolution: Boundary layer analysis. Alex Eng J 55:1915–1929.  https://doi.org/10.1016/j.aej.2016.08.002 CrossRefGoogle Scholar
  2. Adesanya SO (2014) Free convective flow of heat generating fluid through a porous vertical channel with slip and temperature jump. Ain Shams Eng J 6(3):1045–1052CrossRefGoogle Scholar
  3. Ali N, Asghar Z, Beg OA (2016) Bacterial gliding fluid dynamics on a layer of non-Newtonian slim: Perturbation and numerical study. J Theor Bio 397:22–32.  https://doi.org/10.1016/j.jtbi.2016.02.011 CrossRefGoogle Scholar
  4. Andersson HI, Santra B, Dandapat BS (2006) Gravity-driven film flow with variable physical properties. Phys Fluids 18:083602.  https://doi.org/10.1063/1.2241950 CrossRefGoogle Scholar
  5. Animasaun IL, Adebile EA, Fagbade AI (2015) Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. J Nigerian Math Soc.  https://doi.org/10.1016/j.jnnms.2015.02.001 Google Scholar
  6. Beg OA, Basir MdFMd, Uddin MJ, Ismail AIMd (2017) Numerical study of slip effects on unsteady asymmetric bioconvective nanofluid flow in a porous microchannel with an expanding/contracting upper wall using Buongiorno’s model. J Mech Med Bio 17(5):1750059.  https://doi.org/10.1142/S0219519417500592 ((28 pages) World Scientific Publishing Company)CrossRefGoogle Scholar
  7. Bujurke NM, Madalli VS, Mulimani BG (1998) Long series analysis of laminar flow through parallel and uniformly porous walls of different permeability. Comput Methods Appl Mech Eng 160:39–56CrossRefGoogle Scholar
  8. Casson N (1959) Rheology of disperse systems in flow equations for pigment oil-suspensions of the printing ink type. In: Mill CC (ed) Rheology of disperse systems. Pergamon Press, UK, pp 84–102Google Scholar
  9. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. In: International mechanical engineering congress and exposition, San Francisco, USA, ASME, FED 231/MD, vol 66, pp 99–105Google Scholar
  10. Du Y, Huang Z, Wu S, Xiong K, Zhang X, Zheng B, Nadimicherla R, Fu R, Wu D (2018) Preparation of versatile yolk-shell nanoparticles with a precious metal yolk and a microporous polymer shell for high-performance catalysts and antibacterial agents. Polymer 137:195–200.  https://doi.org/10.1016/j.polymer.2017.12.069 CrossRefGoogle Scholar
  11. Ghorai S, Hill NA (2007) Gyrotactic bioconvection in three dimensions. Phys Fluids 19(5):054107CrossRefGoogle Scholar
  12. Gong Z, Karandikar S, Zhang X, Kotipalli V, Lvov Y, Que L (2010) Composite nanomaterial thin film-based biosensors. IEEE sensors conference. IEEE, pp 29–32Google Scholar
  13. Kessler JO (1984) Gyrotactic buoyant convection and spontaneous pattern formation in algal cell cultures. In: Velarde MG (ed) Non-equilibrium cooperative phenomena in physics and related fields. Plenum, New York, pp 241–248CrossRefGoogle Scholar
  14. Khan NS (2018) Bioconvection in second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms. Braz J Phys 43(4):227–241.  https://doi.org/10.1007/s13538-018-0567-7 CrossRefGoogle Scholar
  15. Khan NS, Gul T, Islam S, Khan W (2017) 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.  https://doi.org/10.1140/epjp/i2017-11277-3 CrossRefGoogle Scholar
  16. Khan NS, Gul T, Islam S, Khan I, Alqahtani AM, Alshomrani AS (2017) Magnetohydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer. J Appl Sci 7:271CrossRefGoogle Scholar
  17. Khan NS, Gul T, Islam S, Khan W, Khan I, Ali L (2017) Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer. Alex Eng J.  https://doi.org/10.1016/j.aej.2017.01.036 Google Scholar
  18. Khan NS, Gul T, Islam S, Khan A, Shah Z (2017) 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.  https://doi.org/10.1166/jon.2017.1383 CrossRefGoogle Scholar
  19. Khan NS, Gul T, Khan MA, Bonyah E, Islam S (2017) Mixed convection in gravity-driven thin film non-Newtonian nanofluids flow with gyrotactic microorganisms. Results Phys 7:4033–4049.  https://doi.org/10.1016/j.rinp.2017.10.017 CrossRefGoogle Scholar
  20. Khan WA, Makinde OD, Khan ZH (2014) MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. Int J Heat Mass Transf 74:285–291CrossRefGoogle Scholar
  21. Liao SJ (2012) Homotopy analysis method in non-linear differential equations. Higher Education Press, Springer-Verlag, Beijing, Berlin HeidelbergCrossRefGoogle Scholar
  22. Lin X, Liang Y, Lu Z, Lou H, Hang X, Liu S, Zheng B, Liu R, Fu R, We D (2017) Mechanochemistry: a green, activation-free and topdown strategy to high-surface-area carbon materials. ACS Sustain Chem Eng.  https://doi.org/10.1021/acssuschemeng.7b02462
  23. Loefer JB, Meffered RB (1952) Concerning pattern formatting by free-swimming microorganism. Am Nat 86(830):325–329CrossRefGoogle Scholar
  24. Lvov YM, Pattekari P, Zhang X, Torchilin V (2011) Converting poorly soluble materials into stable aqueous nanocolloids. Langmuir 27(3):1212–1217.  https://doi.org/10.1021/la1041635 CrossRefGoogle Scholar
  25. Mai W, Zuo Y, Li C, Wu J, Leng K, Zhang X, Liu R, Fu R, Wu D (2017) Functional nanonetwork-structured polymers with inbuilt poly(acrylic acid) linings for enhanced adsorption. Polym Chem 8(33):4771–4775.  https://doi.org/10.1039/c7py01032 CrossRefGoogle Scholar
  26. Pattekari P, Zheng Z, Zhang X, Levchenko T, Torchilin V, Lvov Y (2011) Top-down and bottom-up approaches in production of aqueous nanocolloids of low solubility drug paclitaxel. Phys Chem Chem Phys 13:9014–9019.  https://doi.org/10.1039/c0cp02549f CrossRefGoogle Scholar
  27. Raees A, Xu H, Sun Q, Pop I (2015) Mixed convection in gravity-driven nanoliquid film containing both nanoparticles and gyrotactic microorganisms. Appl Math Mech 36:163–178CrossRefGoogle Scholar
  28. Tian Y, Zhang X, Geng HZ, Yang HJ, Li C, Da SX, Lu X, Wang J, Jia SL (2017) Carbon nanotube/polyurethane films with high transparency, low sheet resistance and strong adhesion for antistatic application. RSC Adv 7:53018–53024.  https://doi.org/10.1039/c7ra10092b CrossRefGoogle Scholar
  29. Uchida S, Aoki H (1977) Unsteady flows in a semi-infinite contracting or expanding pipe. J Fluid Mech 82:371–387CrossRefGoogle Scholar
  30. Vergara D, Bellomo C, Zhang X, Vergaro V, Tinelli A, Lorusso V, Rinaldi R, Lvov YM, Leporatti S, Maffia M (2012) Lapatinib/paclitaxel polyelectrolyte nanocapsules for overcoming multidrug resistance in ovarian cancer. Nanomed NBM 8:891–899.  https://doi.org/10.1016/j.nano.2011.10.014 CrossRefGoogle Scholar
  31. Vergara V, Scarlino F, Bellomo C, Rinaldi R, Vergara D, Maffia M, Baldassarre F, Giannelli G, Zhang X, Lvov YM, Leporatti S (2011) Drug-loaded polyelectrolyte microcapsules for sustained targeting of cancer cells. Adv Drug Deliv Rev 63:847–864.  https://doi.org/10.1016/j.addr.2011.05.007 CrossRefGoogle Scholar
  32. Waisbord N, Lefevre C, Bocquet L, Ybert C, Cottin-Bizonne C (2016) Destabilization of a flow focused suspension of magnetotactic bacteria. arXiv:1602.02966v1
  33. Williamson RV (1929) The flow of pseudoplastic materials. Ind Eng Chem 21(11):1108–1111CrossRefGoogle Scholar
  34. Xu H, Pop I (2014) Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticle and gyrotactic microorganisms. Int J Heat Mass Transf 75:610–623CrossRefGoogle Scholar
  35. Zhang X (2015) Tea and cancer prevention. J Can Res Updates 4(2):65–73CrossRefGoogle Scholar
  36. Zheng Z, Zhang X, Carbo D, Clark C, Nathan CA, Lvov Y (2010) Sonication-assisted synthesis of polyelectrolyte-coated curcumin nanoparticles. Langmuir 26(11):7679–7681.  https://doi.org/10.1021/la101246a CrossRefGoogle Scholar
  37. Zohra FTTUZ, Uddin MJ, Ismail AIMD, Beg OA (2018) Bioconvective electromagnetic nanofluid transport from a wedge geometry: simulation of smart electro-conductive bio-nanopolymer processing. Heat Transf Asian Res 47:231–250.  https://doi.org/10.1002/htj.21300 CrossRefGoogle Scholar
  38. Zuhra S, Khan NS, Khan MA, Islam S, Khan W, Bonyah E (2018) Flow and heat transfer in water based liquid film fluids dispensed with graphene nanoparticles. Result Phys 8:1143–1157.  https://doi.org/10.1016/j.rinp.2018.01.032 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zaman Palwasha
    • 1
  • Saeed Islam
    • 1
  • Noor Saeed Khan
    • 1
  • Hamza Ayaz
    • 2
  1. 1.Department of MathematicsAbdul Wali Khan UniversityMardanPakistan
  2. 2.Department of Mechanical EngineeringIslamic University of TechnologyDhakaBangladesh

Personalised recommendations