The solution of the coupled set of the governing equations, in which the Navier Stokes equations couple the velocity and pressure via Eq. 31 and ionic and electronic conductivities are coupled via Eqs. 28, 29 and 30, was facilitated by taking advantage of a mixed finite element formulation. In this approach, the weak formulation results in a set of coupled integral equations, each reflecting the physics of a different field. The simultaneous solution to the weak form of the coupled PDEs then requires the construction of a composite system matrix, which reflects the interactions between the codependent fields. In the current study, two mixed formulation problems were implemented for the fluid flow and charge transport separately.