In this article, the effects of thermal diffusion and diffusion thermo on the motion of a non-Newtonian Eyring Powell nanofluid with gyrotactic microorganisms in the boundary layer are investigated. The system is stressed with a uniform external magnetic field. The problem is modulated mathematically by a system of a nonlinear partial differential equation, which governs the equations of motion, temperature, the concentration of solute, nanoparticles, and microorganisms. This system is converted to nonlinear ordinary differential equations by using suitable similarity transformations with the appropriate boundary conditions. These equations are solved numerically by using the Rung-Kutta-Merson method with a shooting technique.The velocity, temperature, concentration of solute, nanoparticles, and microorganisms are obtained as functions of the physical parameters of the problem.The effects of these parameters on these solutions are discussed numerically and illustrated graphically through figures. It is found that the velocity decreases with the increase in the non-Newtonian parameter and the magnetic field, whereas, the velocity increases with a rise in thermophoresis and Brownian motion. Also, the temperature increases with an increase in the non-Newtonian parameter, magnetic field, thermophoresis, and Brownian motion. These parameters play an important role and help in understanding the mechanics of complicated physiological flows. K E Y W O R D SEyring-Powell model, microorganisms, nanofluid, Soret and Dufour effects

The effect of the induced magnetic field on the motion of Eyring-Powell nanofluid Al2O3, containing gyrotactic microorganisms through the boundary layer is investigated. The viscoelastic dissipation is taken into consideration. The system is stressed by an external magnetic field. The continuity, momentum, induced magnetic field, temperature, concentration and microorganisms equations that describe our problem are written in the form of two-dimensional nonlinear differential equations. The system of nonlinear partial differential equations is transformed into ordinary differential equations using appropriate similarity transformations with suitable boundary conditions and solved numerically by applying the ND Solve command in the Mathematica program. The obtained numerical results for velocity, induced magnetic field, temperature, the nanoparticles concentration and microorganisms are discussed and presented graphically through some figures. The physical parameters of the problem play an important rule in the control of the obtained solutions. Moreover, it is obvious that as Grashof number Gr increases, both the velocity f' and the induced magnetic field h' increase, while, the reciprocal magnetic Prandtl number A works on decreasing both f' and h'. As Eckert number Ec increases the temperature increases, while it decreases as the velocity ratio B increases.

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