Optimal geometrical duct configurations for microchannel heat sinks under constraints

This work aims at studying the influence of smoothing the corners of microchannels of rectangular cross-section on their thermal performance. A laminar, steady incompressible flow is assumed with thermal boundary conditions of type H1 (uniform axial heat flux and uniform temperature on the heated perimeter of each cross-section), and several aspect ratios are considered, from unity (square channel) to 0.03 (thin slot). The analysis is carried out in terms of performance evaluation criteria, namely the case FG1a (maximize heat duty) and entropy generation minimization. Four geometrical constraints are applied to the geometry (fixed reference length, fixed heated perimeter, fixed cross-sectional area and fixed hydraulic diameter) and the results are commented both separately and through a combination of the outcomes of first- and second-law analysis. It turns out that smoothing of the corners is beneficial in terms of entropy generation when the cross-sectional area or the heated perimeter are constrained, whereas it worsens -although only slightly - the heat duty. The best results are obtained for high aspect ratios and high reference irreversibility ratios.