In this study, Galerkin weighted residual Finite Element Method is used to find the thermopho- resis and Brownian diffusion motion of two phase nanofluid flow around a vertical cone in porous media. Gravity, Drag, Thermophoresis and Brownian forces are confided on the nanoparticles to find their motion during the time. The problem is solved in both transient and steady conditions. The effect of Nc and Nv parameters on the temperature and velocity profiles are investigated. Also, the effect of boundary conditions on the temperature and nanoparticles concentrations are investigated through the graphical contours. As a main result, variable thermal conductivity parameter (Nc) increament from zero to unity increased the velocity and temperature profile values, while had not significant effect on the nanoparticles concentration. Also, results revealed that increasing the Nv (from 2 to 200) and Nc (from 0 to 1), increased the ( θ ′ ( 0 ) ) and ( f ′ ( 0 ) ) to 1.36% and 0.15%, respectively.

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