A nonhomogeneous model is used to simulate convective transport in nanofluids. The model is a thermodynamically consistent version of the celebrated Buongiorno model. We study two situations in detail: flow through a pipe that is heated periodically in time at one lateral wall and a lid-driven cavity with a triangular heat source placed within. Both studies reveal the mechanisms of enhanced heat transfer by nanofluids through thermophoresis: the temperature gradient at the wall leads to a reduced concentration of nanoparticles. This reduces the concentration-dependent viscosity of the suspension close to the boundary, which in turn leads to a stronger convective transport.