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


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.


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



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.


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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

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