The influence of viscous dissipation on thermal performance of microchannels with rounded corners

Laminar regime is a recurring feature in microchannel liquid flows, mainly owing to the small dimensions of the ducts. For cooling purposes, the advantages of miniaturization may be completely offset by the influence of viscous dissipation due to high velocity gradients at the walls: the problem was studied for rectangular geometries, which are among the most common for microchannels, due to the manufacturing process. As to fabrication, rounding the corners of traditional crossâ€' sections results in higher pressure drops but higher heat transfer coefficients too. In this paper it is demonstrated that the increase in the latter feature more than compensates for the effects of viscous dissipation through a numerical investigation of the heat transfer characteristics in rectangular geometries with rounded corners for fully developed, laminar flow of an incompressible fluid, with channel walls subject to H1 boundary conditions (uniform heat flux over the duct and uniform temperature over the perimeter), in the presence of viscous dissipation, for increasing values of the radius of curvature of the crossâ€' section corners. The results are presented in terms of Poiseuille number for the friction factor and of Nusselt number for the heat transfer coefficient as a function of the radius of curvature for different aspect ratios of the crossâ€' sections and intensities of the viscous dissipation, as embodied by the Brinkman number. The limit of significance for convective cooling (as given by Nu=1) is identified for each geometrical configuration, giving the corresponding value of the Brinkman number. As practical tool for the design of microchannel heat sinks, polynomial relations are presented for the different geometries investigated and Brinkman numbers involved. © Société Hydrotechnique de France, 2013.