: Electrohydrodynamics (EHD), as a phenomenon which covers the wide range of electric and hydrodynamic couples, has variety applications. Hence, the field has been concentrated on by various scholars. In this thesis, numerical analysis of the effect of surface-charge convection or the effect of a neglected non-dimensional electric number, electric Reynolds number, has been studied. The electric field is created by imposing an electric potential difference across the channel walls while the computational domains are considered a square and a cube for two- and three-dimensional analysis respectively. The leaky dielectric model developed by Taylor is used to compute the electric force with inclusion of the effects of charge displacement due to fluid convection. This force is directly added to the Navier-Stokes equations as a body force. This force can deform the drop in the direction of the electric field (prolate) or perpendicular to the direction of the electric field (oblate). Also, if a drop is not introduced in the middle of the computational domain, an interaction with surrounding walls is expected. Both previous incidents have been covered in this work. Regarding the achievements of this research and their sensitivity, whole results of this research have been compared with other results from the literature and after a thorough investigation, no deviation is found; therefore, whole results are considered as the validation for the conclusions made in this thesis. It has been concluded that if the effects of charge convection are included in simulations, electric Reynolds number plays a significant role in determining the behaviour and terminal deformation of a drop. Thereafter, it has been proved that the famous deformation equation introduced by Taylor derived from his discrimination function which calculates the terminal mode and deformation of a drop is only valid when convection of charges is not included in mathematical model. It must be noted that although it has been stated that the results obtained during this research all act as the validation process, the results themselves are totally unique and consequently, they have thoroughly been analysed. Keywords: Electrohydrodynamics, multiphase flow, Finite difference/front-tracking method, Oblate/prolate drops, drop behaviour, wall interaction