Fully developed mixed convection flow in a horizontal channel filled by a nanofluid containing both nanoparticles and gyrotactic microorganisms

•The passively controlled mathematical model for nanofluids is introduced, which could be physically more realistic than the previous models.•The influence of nanoparticles on the bioconvection is investigated.•An improved HAM technique for nonlinear problems with complicated boundary conditions is developed.

In this paper, an analysis is made for the fully developed mixed bioconvection flow in a horizontal channel filled with a nanofluid that contains both nanoparticles and gyrotactic microorganisms. The passively controlled nanofluid model proposed by Kuznetsov and Nield (2013) is then introduced for modeling this flow problem, which is found to be more physically realistic than previous nanofluid models. Analytical approximations with high precision are obtained by the improved homotopy analysis technique for complicated boundary conditions. Besides, the influences of various physical parameters on the distributions of temperature, the nanoparticle volume fraction, as well as the density of motile microorganisms are investigated in detail.