Analytical solutions for the temperature distributions, heat transfer coefficients and Nusselt numbers of steady electroosmotic flows are obtained for two-dimensional straight micro-channels. This analysis is based on infinitesimal electric double layer (EDL) in which flow velocity becomes “plug-like” uniform except very close to the wall. Both constant surface temperature and constant surface heat flux conditions are considered in this study. Separation of variables techniques are applied to obtain analytical solutions of temperature distributions from the energy equation in which Joule heating is a significant contributor due to the applied electric field. The thermal analysis considers interaction among inertial, diffusive and joule heating terms in order to obtain the thermally developing behavior of electroosmotic flows. Heat transfer characteristics are presented for low Reynolds number microflows where the viscous and electric field terms are very dominant. For the parameter range studied here (Re ≤ 0.7), the Nusselt number is independent of the thermal Peclet number, except in the thermally developing region. In both isothermal and constant surface heat flux boundary conditions, the Nusselt number becomes constant in the fully developed region for a uniform volumetric heat generation. Analytical results for no Joule heating cases are also compared with the classical heat transfer results, and in the thermally fully developed region an excellent agreement is obtained between them.
Heat Transfer Characteristics of Steady Electroosmotic Flows in Two-Dimensional Straight Microchannels
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Horiuchi, K, & Dutta, P. "Heat Transfer Characteristics of Steady Electroosmotic Flows in Two-Dimensional Straight Microchannels." Proceedings of the ASME 2003 Heat Transfer Summer Conference. Heat Transfer: Volume 1. Las Vegas, Nevada, USA. July 21–23, 2003. pp. 221-228. ASME. https://doi.org/10.1115/HT2003-47097
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