Nonlinear Study of Convective Heat Transfer in Tightly Curved Rectangular Microchannels

Abstract

To address the effects of curvature, initial conditions and disturbances, a numerical study is made on the fully-developed bifurcation structure and stability of the forced convection in tightly curved rectangular microchannels of aspect ratio 10 and curvature ratio 0.5 at Prandtl number 7.0. Eleven solution branches (seven symmetric and four asymmetric) are found with 10 bifurcation points and 27 limit points. The flows on these branches are with 2, 4, 6, 7, 8, 9 or 10-cell structures. The flow structures change along the branch because of the flow instability. The average friction factor and Nusselt Number are different on different solution branches. It is found that more than 22.33% increase in Nu can be achieved with less than 9.34% increase in fRe at Dk of 2000. As Dean number increases, finite random disturbances lead the flows from a stable steady state to another stable steady state, a periodic oscillation, an intermittent oscillation, another periodic oscillation and a chaotic oscillation. The mean friction factor and mean Nusselt Number are obtained for all physically realizable flows. A significant enhancement of heat transfer can be obtained at the expense of a slightly increase of flow friction in tightly coiled rectangular ducts.