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This article describes the unsteady flow of liquid containing nanoparticles and motile gyrotactic microorganisms between two parallel plates while keeping one moving and other fixed. The passively controlled nanofluid model is used to describe the nanoparticles concentration. Some instances of direct application of this nanofluid bioconvection study can be found in pharmaceutical industry, microfluidic devices, microbial enhanced oil recovery, modeling oil and gas-bearing sedimentary basins and many more. The governing partial differential equations are transformed to ordinary differential equations using the similarity transformations. The mathematica package based on homotopy analysis method is used to solve this problem. The physical phenomenon is explained by drawing the graphs for the temperature, nanoparticles concentration and density of motile microorganisms profiles. Also the tables are given which completely depicts the convergence of gained results.
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