In the present work, a numerical study is made on the fully-developed forced convective heat transfer of nanofluids in a curved square duct using Eulerian-Lagrangian two-phase approach. The curvature ratio of the duct is 0.02 and its hydraulic diameter is 8 mm. The Al2O3-water nanofluids contain spherical nanoparticles with particle diameter of 30 nm and volume fraction of 0.5%. Three different flow structures of nanofluids are obtained through the small perturbations generated by three different computers at the same conditions. The flow has a structural 2-cell, 3-cell or 4-cell at different Dean numbers and on different solutions, which leads to multiple non-uniform nanoparticle concentration distributions and multiple temperature fields. Multiple flow fields are symmetric in a low Dean number region and asymmetric in a high Dean number region, which leads to multiple symmetric (asymmetric) nanoparticle concentration distribution and temperature distribution fields, multiple symmetric (asymmetric) local Nusselt number and local friction factor along the outer wall at low De values (high De values), and finally lead to multiple mean friction factor and multiple mean Nusselt number. A significant enhancement of heat transfer (e.g. 23.79% at De of 335.2) can be achieved at the expense of a slight increase of flow friction (e.g. 6.84% at De of 335.2) in curved square duct through switching the solutions. This study could provide an explanation, from a new respect, for the inconsistent results of convective heat transfer of nanofluid in the literature. (C) 2018 Elsevier Ltd. All rights reserved.