During the fabrication process of advanced composites using nanoparticle-filled matrices, many problems potentially could arise. One such problem is the clogging of the channels of the microfiber matrix used due to strong interactions between the nanoparticle additives and the matrix walls. In the present paper, a two-dimensional simulation model based on an Eulerian multiphase flow approach is introduced to investigate and predict the flow characteristics of carbon nanoparticle-filled fluid around carbon microfiber matrix. The interactions between the microfiber matrix walls and the nanoparticle additives have been studied, and an energy “imbalance” technique has been applied between the fluid and the microfiber walls to prevent any potential sticking of the nanoparticle additives on the microfiber matrix walls during the flow process. The concept of phasic volume fractions is utilized, and the effects of external body forces, lift forces, and virtual mass forces are introduced into the momentum equations. The phase coupled SIMPLE algorithm is employed to solve the model.