Forced convection in slightly curved microchannels

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 curved microchannels of square cross-section and curvature ratio 5 × 10⁻⁶. No matter how small it is, the channel curvature always generates the secondary flow in the channel cross-plane which increases the mean friction factor moderately and the Nusselt number significantly. Unknown initial conditions of convection lead to the co-existence of multiple steady fully-developed flows of various structures. Ten solution branches (either symmetric or asymmetric) are found with eight symmetry-breaking bifurcation points and thirty-one limit points. Thus a rich solution structure exists with the co-existence of various flow states over certain ranges of governing parameters. Dynamic responses of the multiple steady flows to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully-developed flows under the effect of unknown disturbances evolve, as the Dean number increases, from a stable steady 2-cell state at lower Dean number to a temporal periodic oscillation, another stable steady 2-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. There exist no stable steady fully-developed flows in some ranges of governing parameters. Both the mean friction factor and the mean Nusselt number are also obtained and analyzed with their correlating relations listed.