In this study, concentration distribution was obtained for nanofluid laminar flow in circular pipe. The effects of viscosity gradient, shear rate and Brownian diffusion on particle migration were considered. One needs to determine the phenomenological constants in order to find the diffusion fluxes. The two-phase Euler–Lagrange method was used to find these constants, where gravity, drag, Saffman’s lift, Brownian and thermophoretic forces were considered. The constants are not much dependent on the concentration, but they change significantly by varying Peclet number. They increase with increasing Peclet number, which shows that at higher Peclet numbers, the effects of shear rate and viscosity gradient are intensified on particle migration. Meanwhile, by raising Peclet number, the role of shear rate becomes more pronounced in comparison with the viscosity gradient. At lower Peclet numbers with intensified effect of the Brownian diffusion, a more uniform concentration distribution was achieved. Moreover, the particles enlargement considerably intensifies the non-uniformity in concentration distribution. Furthermore, particle migration causes non-uniformity in the properties distribution and consequently reduces the thermal conductivity and viscosity adjacent to the wall due to lower concentration there. Thus, smaller pressure drop and heat transfer coefficient were obtained in comparison with the case of applying uniform properties.
