The figure of merit for nanofluids represents the heat transfer performance of nanofluids against basic fluid. In previous studies, only the material properties of nanofluids have been considered for the figure of merit. In this study, the computational thermal flow analyses are performed including not only the material properties but also the geometric shapes and the external effects. The figures of merit are obtained with the four parameters, which are the inlet pressure, the number of return bends, the radius of curvature, and the volume fraction of nanoparticles in the pipes with the return bends. The results show that the three remaining parameters other than the number of return bends act on the figures of merit in a complicated manner. Therefore, a correlation equation with Euler number, Dean number, and Prandtl number associated with the three parameters is derived through the nonlinear regression. These results are expected to be helpful in designing and manufacturing heat exchangers using nanofluids.