Electro-osmotic non-isothermal flow in rectangular channels with smoothed corners

Microchannel heat sinks are able to provide high cooling capabilities in terms of heat flux rates. This makes them particularly interesting for the thermal management of electronic components such as CPUs, which have high power density and small dimensions. Pressure drop of the coolant across the microchannels may, however, be significant and give rise to viscous heating, thereby preventing the practical use of these devices. When the coolant is a polar fluid and the channel walls possess a net electric charge, an alternative means of moving the fluid is through an applied external electric field. The flow which originates is called electro-osmotic (EOF). EOF does not require moving parts, is free of vibrations and does not need lubrication, but is subject to Joule heating of the fluid and has flow and heat transfer characteristics which differ from those of pressure-drive flows. In spite of several previous investigation on EOF, no attention has been paid to the changes in velocity and temperature distributions caused by modifying the base cross-section of the channels which may be circular, rectangular or polygonal, thanks to the current capabilities of microfabrication. This work investigates numerically the influence of smoothing the corners of the cross-section at fixed hydraulic diameter on the values of the Poiseuille and Nusselt numbers for the laminar, steady and fully developed, electro-osmotic flow in a rectangular channel subject to uniform heat flux and Joule heating. Several aspect ratios are considered, as are different values of the ratio of Joule heating to heat flux through the walls. The results highlight a very slight increase of the Poiseuille number with the radius of curvature, whereas the Nusselt number experiences a significant improvement. Correlations are obtained for both the Poiseuille and Nusselt number as a function of the radius of curvature, aspect ratio and Joule heating-to-heat flux ratio.