In a steel making process, the fine molten steel slab is required to make high quality sheet. From this point of view, it is very important to remove inclusions in molten steel. So a mathematical model, to predict the behavior of various sizes of aluminum inclusions in a molten steel flow, has been developed. In this model, three kinds of collision terms are considered: the first one is due to the flow field acceleration, the second one is due to the gravity acceleration, and the third one is due to the effect of the turbulent eddies. In the process of the collision, total 1 025 particle sizes are taken into consideration. In each particle size, number density should be calculated. But only 13 particles among 1 025 are selected to solve the number density conservation equation. For the rest of the particle sizes, the number density is evaluated by linear interpolation based on selected 13 particles in order to save the computational time. Using this model, the behavior of aluminum inclusions in molten steel, which is dominated by the natural convection, has been simulated. The mechanism of the aluminum collision and coagulation has been studied.