A mathematical model for laminar steady flow of an incompressible, viscous, neutrally-charged carrier fluid mixed with a fluid having electrically charged particles is presented. Thermally induced buoyancy was incorporated via an extended Boussinesq approximation allowing for temperature-dependent density, viscosity, heat conductivity and heat capacity while including Joule heating and troconvective motions due to Lorentz forces. Induced magnetic fields and viscous dissipation in energy conservation equation have been neglected. Viscosity was modeled as a function of local electrical charge concentration thus simulating particle chaining phenomena in electrorheological fluids. Numerical results clearly demonstrate the influence that an applied electrostatic field and the consequent electric charge gradients can have on the flow pattern, temperature field and surface convective heat fluxes.
