There have been several reports that suspending nano-particles in a fluid, or nanofluids, can enhance heat transfer properties such as conductivity. However, the extend of the reported enhancement is inconsistent in the literature and the exact mechanisms that govern these observations (or phenomena) are not fully understood. Although the interaction between the fluid and suspended particles is suspected to be the main contributor to this phenomenon, literature shows contradicting conclusions in the underlying mechanism responsible for these effects. This highlights the need for development of computational tools in this area. In this study, a computational approach is developed for simulating the induced flow field by randomly moving particles suspended in a quiescent fluid. Brownian displacement is used to describe the random walk of the particles in the fluid. The steady state movement is described with simplified Navier-Stokes equation to solve for the induced fluid flow around the moving particles with constant velocity at small time steps. The unsteady behavior of the induced flow field is approximated using the velocity profiles obtained from FLUENT. Initial results show that random movements of Brownian particles suspended in the fluid induce a random flow disturbance in the flow field. It is observed that the flow statistics converge asymptotically as time-step reduces. Moreover, inclusion of the transitional movement of the particles significantly affects the results.