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Dielectric Barrier Discharge (DBD) is a discharge phenomenon where a high voltage is applied on at least two electrodes separated by an insulating dielectric material. Dielectric Barrier Discharge plasma actuator has been studied widely in this last decade but mostly the study is focusing on experimental research rather than mathematical modeling. The limitation with studying DBD plasma actuator experimentally is that it does not obtain direct information on the physics of the plasma flow, which is important in determining its efficiency. In this paper, we model the steady fluid model DBD plasma actuator mathematically. The preliminary result of the model are presented and discussed. To initiate the modeling process, the stream-function and vorticity are defined so that the Navier-Stokes momentum equation could be transformed into vorticity equation. The resulting two governing equations, which are vorticity and stream-function equations are solved numerically to obtain the vorticity of the flow in x and y directions. Finite difference method was adopted to discretize both equations and the system of equations is solved by the Gauss-Seidel method. Our numerical solutions show that the applied voltage plays an important role in the model. We found that as the applied voltage increases, the vorticity of the plasma flow also increases.