Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms

In this paper, a detailed analysis is given for the mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. By means of a novel nanofluid model proposed by Kuznetsov and Nield (2013) [24], we reduce the original governing equations embodying the conservation of mass, momentum, thermal energy, nanoparticle volume fraction and conservation equation for microorganisms to a set of five ordinary differential equations with coupled linear boundary conditions. The recursively analytical solutions with high precision are then obtained by the improved homotopy analysis method (HAM). Besides, the influences of important physical parameters such as the Brownian motion parameter Nb, the thermophoresis parameter Nt, the bioconvection Rayleigh number Rb, the bioconvection Péclet number Pe on the local wall friction, the local Nusselt number, the local wall mass flux, the local wall motile microorganisms flux, as well as the profiles of velocity, temperature, nanoparticles concentration and density of motile microorganisms are examined and discussed in detail.