Multiplicity and Stability of Forced Convective Heat Transfer in Microchannels

A numerical study is made on the fully-developed bifurcation structure and stability of the forced convection in a curved microchannel of square cross-section. Two symmetric and four asymmetric solution branches are found. Thus a rich solution structure is found with up to eleven solutions over certain ranges of governing parameters. This multiplicity is at least partially responsible for the large differences in the reported friction factors and heat transfer coefficients in the literature. Dynamic responses of the multiple solutions to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully-developed flows evolve, as the Dean number (or Reynolds number) increases, from a stable steady 2-cell state at lower Dean number to a temporal periodic oscillation state, another stable steady 2-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation.