Three-dimensional magnetohydrodynamic (MHD) flow of Maxwell nanofluid containing gyrotactic micro-organisms with heat source/sink

This paper discusses the three-dimensional flow of Maxwell nanofluid containing gyrotactic micro-organisms over a stretching surface. The effects of magnetic field and heat source/sink are also considered. Theory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the effects of buoyancy forces. HAM (homotopy analysis method) is used to acquire analytic solution for the governing nonlinear equations. The effects of Deborah number, Hartmann number, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayeigh number, stretching ratio parameter, brownian diffusion and thermophoresis diffusion parameters, Prandtl number, Lewis number, micro-organisms concentration difference parameter, bioconvection Peclet number and the bioconvection Lewis number on velocity, temperature, density of motile microorganisms and nanoparticle concentration are discussed graphically. The local Nusselt, Sherwood and motile micro-organisms numbers are also analyzed graphically. The reduction of the boundary layer thickness and velocity due to magnetic field is noted. The heat source/sink parameter have opposite effects on the temperature profile. We found that In comparison to the case of heat sink the thermal boundary layer thickness and temperature increases in the case of heat source.