Heat Transfer Characteristics of Mixed Electroosmotic and Pressure Driven Micro-Flows∗

We analyze heat transfer characteristics of steady electroosmotic flows with an arbitrary pressure gradient in two-dimensional straight microchannels considering the effects of Joule heating in electroosmotic pumping. Both the temperature distribution and local Nusselt number are mathematically derived in this study. The thermal analysis takes into consideration of the interaction among advective, diffusive, and Joule heating terms to obtain the thermally developing behavior. Unlike macro-scale pipes, axial conduction in micro-scale cannot be negligible, and the governing energy equation is not separable. Thus, a method that considers an extended Graetz problem is introduced. Analytical results show that the Nusselt number of pure electrooosmotic flow is higher than that of plane Poiseulle flow. Moreover, when the electroosmotic flow and pressure driven flow coexist, it is found that adverse pressure gradient to the electroosmotic flow makes the thermal entrance length smaller and the heat transfer ability stronger than pure electroosmotic flow case.