We present a numerical study of the movement of nanoparticles (Cu) and heat transfer of nanofluids with Newtonian and non-Newtonian base fluids in this paper. The computing domain is a circular groove with a fixed slow speed of revolution. Two kinds of models with different definitions of thermal conductivity and concentrations of nanoparticles are considered in the numerical calculation process, as are the influences of thermophoresis and Brownian motion. A continuous finite element scheme in space and a modified midpoint scheme in time are used, and numerical solutions are obtained by using the finite element method. Compared with base fluids only, the heat transfer enhancement of nanofluids can be found easily and is more intuitive. The correlation of the heat transfer enhancement and power law index of base fluids used to distinguish different power law fluids is investigated. This contributes to determining the reasons for heat transfer enhancement in nanofluids. It is found that the Maxwell Model has a higher enhancement of heat transfer than the Traditional Model and the thermophoresis effect breaks the dynamic equilibrium of nanoparticles in the rotating circular groove. (C) 2018 Elsevier Ltd. All rights reserved.