Electro-osmotic heat transfer in elliptical microchannels under H1 boundary condition

This work presents a detailed numerical analysis of electro-osmotic flows inside silicon microchannels characterized by an elliptical cross-section. A finite element method is used to solve the governing equations and perform an extensive parametric study. Particular attention is given to the effect of the aspect ratio of the elliptical cross-section, the electro-kinetic diameter, the ratio of the Joule heating to the imposed wall heat flux on the dynamic and thermal behavior of electro-osmotic flows in the case of H1 boundary conditions. The analysis presented in this paper can be useful to optimize design and thermal performances of silicon micro heat sinks based on electro-osmotic flows. Results point out that as the electro-kinetic diameter increases, the influence of the Joule heating on the temperature distribution becomes less relevant. This trend becomes more pronounced as the aspect ratio increases. Numerical results also show that an increment of the electro-kinetic diameter leads to an enhancement of the convective heat transfer. A comparison between numerical results obtained for electro-osmotic flows through elliptical and rectangular geometries is finally shown and discussed. Such comparison highlights that rectangular microchannels have better performances at small values of the aspect ratio, while elliptical microchannels are more effective for greater values of aspect ratio.