In this paper, a three-dimensional numerical model is developed to analyze the influence of the Joule heating on flow characteristics of an electroosmotic flow through square cross section micro-channels. The governing system of equations consists of three sets of equations: electric potential distribution, flow-field and energy equations. The solution procedure involves three steps. The net charge distribution on the cross section of the micro-channel is computed by solving two-dimensional Poisson-Boltzmann equation using the finite element method. Then, using the computed fluid's charge distribution, the magnitude of the resulting body force due to interaction of an external electric field with the charged fluid elements is calculated along the micro-channel. Finally, three dimensional coupled Navier-Stokes and energy equations are solved by considering the presence of the electro-kinetic body forces and the volumetric heat generation due to Joule heating for three different external electric field strengths. The results reveal that flow patterns are significantly affected by temperature field distribution caused by Joule heating effect especially for high electric field strength cases.
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