Thermally Developing Flow Induced by Electro-Osmosis in a Circular Micro-Channel

The steady-state electro-kinetic-driven flow and heat transfer in circular micro-channels are studied under hydrodynamic fully developed and thermally developing conditions. Based on the linearized Poisson-Boltzmann equation, an exact solution of the electrical potential distribution is obtained. The analytic solutions of the velocity and temperature profiles are then obtained, and the effects of some hydrodynamic and thermal parameters on flow and heat transfer are investigated. The interesting plug-like velocity profile produced by external electrical field is not usually observed in the pressure-driven flows. In this case, the very large velocity gradient near the wall of the micro-channel may result in the enhanced temperature close to the wall (depending on the relative importance of viscous dissipation compared with the other terms); the temperature values of other portions of the flow field are increased slightly. Decreasing both Reynolds and Prandtl numbers leads to increasing the bulk fluid temperature. Nusselt number decreases in the thermally developing region.