Performance assessment of electro-osmotic flow of rectangular microchannels with smoothed corners

Microchannel heat sinks are a viable alternative to traditional thermal management systems when high fluxes over small surfaces are involved. To avoid high pressure drops especially when liquids are concerned, electro-osmotic flow, a phenomenon which is relevant at the microscales only, can be employed profitably. Joule heating, which occurs every time an electrical current is circulated through a conductor with finite electrical resistance, may hamper the application of electro-osmotic flows significantly; its effects must therefore be investigated, as should the influence of the entry length on the overall transport phenomena which occur in the microchannel, especially so since channels with uniform temperature at the walls tend to be somewhat short, to mitigate heat generation due to Joule heating. In this paper the transport phenomena occurring within a microchannel of rectangular cross-section with uniform wall temperature through which an electro-osmotic flow occurs is studied, while considering the flow fully developed hydrodynamically but thermally developing (Graetz problem). The corners are then smoothed progressively and the effect of this change in the shape of the cross-section over the non-dimensional dissipated power or temperature difference between wall and fluid is investigated using the performance evaluation criteria introduced by Webb. Correlations are suggested for the Poiseuille and Nusselt numbers for all configurations as are criteria to obtain the maximum allowable channel length, i.e. the length of the channel over which the walls start to cool the fluid, owing to Joule heating, in terms of the hydraulic diameter.