## 1 Introduction  
Unlike free or forced convection, Electrohydrodynamic convection has not yet been well described. In the previous works, an experimental method is applied to investigate electric field effect. Also, there are few papers in which authors considered the combined effect of nanofluid and electric field for enhancement in heat transfer. Furthermore, there is no paper in which Control Volume based FiniteElement Method applied for Electrohydrodynamic nanofluid flow and heat transfer. Replacing a smooth wall with a wavy-wall is another commonly used passive method for enhancing the heat transfer in applications where space restrictions are stringent. A wavy-walled geometry is easy to generate and can provide significant heat transfer augmentation if operated in an appropriate Reynolds number range. The corrugations in the wavy-wall act as turbulence generators with the sole purpose of improving the heat transfer. The wavy surface structure adds a degree of complexity to the flow by inducing streamline curvature, flow separation and flow reattachment, thus leading to complex flow situations. The wavy wall provides considerable enhancement of heat transfer with a low pressure drop penalties, thus posing a potential to be considered in several applications such as turbine blade cooling. The target of the current article is to investigate Electrohydrodynamic nanofluid flow and force convective heat transfer via CVFEM. One of the important active methods for improving rate of heat transfer is utilizing an electric field. The influence of electric field on buoyancy-induced flow was studied by [PERSON] and [PERSON] [1]. In their study, electrodynamics equations are separated from fluid dynamics equations. The influence of electrode arrangements on rate of heat transfer was studied by [PERSON] _et al._[2]. The influence of electric field on fluid flow over a plate has been investigated by [PERSON] and [PERSON] [3]. [PERSON] _et al._[4] changed the fluid flow style in a channel by adding electric field. [PERSON] [5] studied the heat and mass transfer of a steady laminar boundary-layer flow of an electrically magnetic conducting fluid of second-grade subject to suction and to a transverse uniform magnetic and electric field past a semi-infinite stretching sheet. In order to improve the thermo physical characteristics of base fluid, nano scale metal can be added in the base fluid. In which way, thermal conductivity of fluid rises and in turn heat transfer can be enhanced. [PERSON] _et al._[6] used Finite Volume Method to simulate nanofluid hydrothermal improvement. They indicated that adding nanoparticles leads to rise in Nusselt number. [PERSON] _et al._[7] investigated nanofluid hydrothermal treatment in a tilted enclosure with moving wall. They proved that temperature enhances with rise of nanofluid volume fraction. Combined nanofluid free and force convection heat transfer in an enclosure with moving wall has been studied by [PERSON] _et al._[8]. They verified that rate of improvement is more pronounced at higher tilt angle. [PERSON] and [PERSON] [9] studied three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. They found that thermal boundary layer thickness increases with increase of Lorentz forces. Energy conversion for conjugate conduction, convection and radiation analysis has been performed by [PERSON] [10] for free convection heat transfer. Their results were shown that the free convection effect will be produced a larger heat transfer effect better than the forced convection. [PERSON] _et al._[11] studied the effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer. They found that found that concentration boundary layer thickness decreases with the increase of radiation parameter. [PERSON] and [PERSON] [12] presented the laminar mixed convection air-cooling of two identical heat sources, simulating electronic components, mounted in an inclined channel.