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

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.