Single-Phase Laminar Forced Convection in Microchannels With Rounded Corners

Abstract

This work investigates the frictional and heat transfer behavior of laminar, fully developed flow in microchannels with trapezoidal and rectangular cross-section and rounded corners under boundary conditions of uniform heat flux along the channel length and perimeter and uniform temperature on the heated perimeter of each cross section. The equations of momentum and energy are solved numerically using the least square method, and the results are validated with analytical data, when available. The runs have been carried out for different aspect ratios and nondimensional radii of curvature, 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 with increments in the Poiseuille and Nusselt numbers of about 11% and 16%, respectively, for values of the nondimensional radius of curvature of 0.5, increasing as the geometry approaches the circular duct (12.5% and 21%). The increase is less pronounced as the aspect ratio decreases and also when only three sides are heated (maximum increase of the Nusselt number around 10% for the latter); in the case of trapezoidal geometry the effects of rounding the corners are almost negligible (a maximum increase in the Nusselt number of around 2%).

Acknowledgments

The research leading to these results has received funding from the Seventh Framework Program under grant agreement PITN-GA-2008-215504, “Gas Flows in Micro Electro Mechanical Systems.”

Marco Lorenzini graduated in mechanical engineering from Bologna University in 1995. In 2001 he received a Ph.D. from the University of Pisa. He joined the Faculty of the School of Engineering in Bologna in 2002 and since 2006 has been an assistant professor at the same university. He is a member of the Italian Society of Thermo-Fluid Dynamics. He is co-author of some 50 scientific papers. His interests include heat and fluid flow in microchannels under single-phase conditions and industrial applications of thermal management.

Gian Luca Morini started as an assistant professor at the University of Ferrara in 1996. Since 2002, he has been an associate professor at the University of Bologna. He is a member of the EUROTHERM and of the Assembly of the World Conference. He is a member of the Italian Society of Thermo-Fluid Dynamics, the Italian Society of Air Conditioning, and of the Scientific Committee of the Hydrotechnic Society of France. His research interests lie in microfluidics and heat transfer in micro-devices.