A complete system of partial differential equations governing three-dimensional laminar flow of an incompressible viscous neutrally charged carrier fluid injected with an electrically charged fluid has been elaborated. The model accounts for temperature dependent physical properties via an extended Boussinesq approximation while including a Joule heating effect. The system of coupled partial differential equations was solved using an artificial compressibility formulation and explicit finite differencing with a four step Runge-Kutta time integration. tow-dimensional numerical results demonstrate cases of electrohydrodynamic instability in horizontal and vertical closed containers. Simulations of the plane Couette flow under the influence of a steady electric fields is also demonstrated including the results were viscosity was treated as a function of local electric charge concentrations.
