This paper is devoted to the modeling of the dynamics of nano-aerosols under Brownian motion and turbulence effects. An Eulerian point of view is considered through a population balance equation which is solved in a differential–algebraic framework (DAE-QMOM). This choice is supported by making a brief comparison with reference numerical methods. In order to evaluate the physical insights of the model, a comparison with five available experiments is carried out. The present results reveal the necessity to take into consideration the Brownian and turbulence effects together in the coagulation kernel and also highlight the need to introduce the fractal dimension of aggregates.