Thermal Characteristics of Mixed Electroosmotic and Pressure-Driven Microflows

Abstract

Analytical solutions for the temperature distribution, heat transfer coefficient, and Nusselt number of steady electroosmotic flows with an arbitrary pressure gradient are obtained for two-dimensional straight microchannels. The thermal analysis considers interaction among advective, diffusive, and Joule heating terms in order to obtain the thermally developing behavior of mixed electroosmotic and pressure-driven flows with isothermal boundary conditions. Heat transfer characteristics are obtained for low Reynolds number microflows where the viscous and electric field terms are very dominant. The electroosmotic component of the flow velocity is modelled with Helmholtz-Smoluchowski slip velocity, and the mixed flow velocity is presented as linear superposition of pure electroosmotic velocity and plane Poiseuille velocity. In mixed flow cases, the governing equation for energy is not separable in general. Therefore, we introduced a method that considers the extended Graetz problem. Analytical results show that the heat transfer coefficient of mixed electroosmotic and pressure-driven flow is smaller than that of pure electroosmotic flow. For the parameter range studied here (Re < 0.7), the fully developed Nusselt number is independent of the thermal Peclet number for both pure electroosmotic and mixed electroosmotic-pressure driven microflows. In mixed electroosmotic and pressure-driven flows, the thermal entrance length increases with the imposed pressure gradient.