A heat sink consisting of microchannels of rectangular or trapezoidal cross-section through which a polar fluid is circulated by means of an electro-osmotic pump was studied numerically. The equivalent pressure head—volume flow rate curve was determined for both geometries and the influence of the aspect ratio was investigated. The dimensionless temperature profile was calculated taking also the effect of Joule heating into account. The cross-sectional Nusselt number was determined for the above conditions and was found to be strongly influenced by the ratio of Joule heating to convective heat flux, Mz. The dependence of the Nusselt number on the dimensionless electro-osmotic diameter (kDh) was also investigated for the two geometries and for increasing values of Mz, and a comparison with the values obtained analytically for slug flow under the same conditions was made. The value of the Nusselt number, as a function of the aspect ratio, was also calculated for increasing values of Mz. The numerical data presented in this paper can be useful to optimize silicon micro heat-sinks in terms of thermal performance.
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