In this research, electrically driven flows are investigated numerically in the OpenFoam open source code with the final volume scheme. Poisson Nernst Planck model I used to simulate the traort of charged species and it is solved coupled with the Navier stokes equations. Also, the Poisson Boltzmann and Debye Huckel models are used and the results are compared with the Nernst Planck equation. Constant heat flux and no-slip boundary conditions are considered on the walls in the governing equations. Results indicate that Debye Huckel and Poisson Boltzmann models are the simple forms of the Nernst Planck equation and can be used instead of the Nernst Planck model because of decreasing the computational cost. In some cases, these simple models haven’t enough accuracy. For a very thin EDL Poisson Boltzmann model is an accurate model in comparison with the Nernst Planck model and for thick EDL, the Debye Huckel model is the accurate one. So it is concluded that the Poisson Boltzmann model is based on the equilibrium distribution of ions in the EDL, and the Debye Huckel model can’t be used in higher Zetta potentials. In these conditions, the Poisson Nernst Planck model should be used for improving accuracy. Because of the matching of Poisson Boltzmann and Debye Huckel models with the Nernst Planck model in most of the cases, flow and heat transfer of the flows are investigated with the Nernst Planck model and similar results with Poisson Boltzmann and Debye Huckel model has been reached. So parameters like side electric and magnetic fields and aspect ratio have a great effect in controlling the flow with critical Hartmann number. Also energy equation is simulated and the effect of side electric and magnetic fields with the ciritical Hartmann number on dimensionless temperature and nusselt number is investigated. Keywords: Aspect ratio, Critical Hartmann number, Debye Hückel, Electric double layer, Electroosmotic flow, Magnetohydrodynamics, Microchannel, Poisson Boltzmann, Poisson Nernst Planck, OpenFoam
