Poiseuille and Nusselt numbers for laminar flow in microchannels with rounded corners

Abstract

This work investigates the frictional and heat transfer behaviour of laminar, fully-developed flow in microchannels with trapezoidal and rectangular cross-section and rounded corners under H1 boundary conditions. The equations of momentum and energy are solved numerically, and the results validated with analytical data, when available. The runs have been carried out for different aspect ratios and nondimensional radii of curvature Rc, with either all sides or three sides heated, one short side adiabatic for rectangular geometries and three sides heated, the longest one adiabatic for trapezoidal geometries. The Poiseuille and Nusselt numbers are reported and show, for the rectangular cross-section heated on all sides, a maximum increase for the highest value of the aspect ratio (β=1) with increments in the Poiseuille and Nusselt numbers of about 11% and 16% respectively for values of Rc * of 0.5, increasing as the geometry approaches the circular duct (12.5% and 21%). The increase is less pronounced as β decreases and also when only three sides are heated (maximum increase of Nu around 10%); in the case of the trapezoidal geometry the effects of rounding the corners are almost negligible (a maximum increase in Nu of around 2%).