Nanofluid is a kind of new engineering medium which is created by dispersing small quantity of nano-sized particles in the base fluid. The dispersion of solid nanoparticles in conventional fluids changes their transport properties remarkably. Molecular dynamics simulation (MDS) is an important approach to study the transport properties of nanofluids. However, the computation amount is huge, and it is very difficult to use the normal MDS to capture the transient flow and heat processes in Cu-H2O nanofluids if the regions in the simulation reach 149.6443 nm3 or 299.2883 nm3, and the number of Cu nano-particles reaches 6-64. Further study by means of simulation on the effects on effective transport properties of nanofluids is also difficult. In this paper, the water-based fluid region of 149.6443 nm3 or 299.2883 nm3 is assumed as continuum phase because of the very low Knudsen number of fluid, and the effects of water on nano-particles are fitted into the Cu-Cu potential parameters. Using the proposed method, the computation amount is significantly reduced. The effective thermal conductivity and dynamic viscosity coefficient of Cu-H2O nanofluids under the stationary condition are simulated and the results are verified with existing experimental data. The motion and aggregation processes of nano-particles in the water-based fluids at different velocity shear rate are simulated. Effects of velocity shear rate, fluid velocity, temperature gradient, and average temperature on the effective thermal conductivity and the dynamic viscosity of Cu-H2O nanofluids in the processes of flow and heat transfer are studied. Three conclusions can be drawn from the obtained results. Firstly, the proposed method is feasible to capture the transient flow and heat processes in Cu-H2O nanofluids, and is also capable to further study the transport properties of Cu-H2O nanofluids. Secondly, the velocity shear rate acting on a nanofluid can effectively prevent the aggregating process of nano-particles, and therefore reduce the diameter of particle-aggregations. Finally, the velocity shear rate and the average temperature of Cu-H2O nanofluids have much more effects on the transport properties, while the fluid velocity and temperature gradient have less effects; the velocity shear rate increases the effective thermal conductivity of a nanofluid but decreases its dynamic viscosity. A rise of average temperature increases the effective thermal conductivity but decreases the dynamic viscosity.