Numerical investigation of viscous dissipation in elliptic microducts

In this work a numerical analysis of heat transfer in elliptical microchannels heated at constant and uniform heat flux is presented. A gaseous flow has been considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effects. The velocity and temperature distributions have been determined in the elliptic cross section, for different values of aspect ratio, Knudsen number and Brinkman number, solving the Navier-Stokes and energy equations within the Comsol Multiphysics® environment. The numerical procedure has been validated resorting to data available in literature for slip flow in elliptic cross sections with Br =0 and for slip flow in circular ducts with Br > 0. The comparison between numerical results and data available in literature shows a perfect agreement. The velocity and temperature distributions thus found have been used to calculate the average Nusselt number in the cross section. The numerical results for Nusselt number are presented in terms of rarefaction degree (Knudsen number), of viscous dissipation (Brinkman number), and of the aspect ratio. The results point out that the thermal fluid behavior is significantly affected by the viscous dissipation for low rarefaction degrees and for aspect ratios of the elliptic cross-section higher than 0.2.