Numerical investigation of thermally developing and fully developed electro-osmotic flow in channels with rounded corners

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating.