Heat transfer enhancement by regular and chaotic mixing in laminar channel flow

The work considered here presents a combined analytical and numerical study of the effects of laminar mixing on heat transfer in channel flows. Two specific geometries are considered: a corrugated channel with symmetric, sinusoidal corrugations on both walls and a channel with walls which are corrugated in two perpendicular directions. The corrugations induce recirculation and result in enhanced heat transfer. The Nusselt number in the corrugated channel can be significantly higher than that in a flat plate, but is limited by the presence of a bounding streamline which separates the recirculation region from the mid-channel flow. The addition of a second set of corrugations in the eggcarton channel causes chaotic particle behavior which destroys the bounding streamline and further increases the heat transfer.; A perturbation solution is obtained for the flow through channels with long wavelength corrugations. This analytical solution allows the Lagrangian behavior of both channels to be investigated. The breakup of the bounding streamline in the eggcarton channel can be clearly seen by the following particle paths, and the chaotic behavior this implies is confirmed by the existence of a positive Lyapunov exponent. Numerical solutions are obtained using a finite-volume formulation with boundary-fitted coordinates. It is found that the heat transfer enhancement in corrugated channels is due to a combination of local enhancement near a stagnation point and the asymmetry of the recirculation region in the downstream direction. A slight perturbation of the corrugated channel allows mixing between the recirculation region and the mid-channel flow, which enhances the heat transfer slightly. If the flow becomes strongly chaotic, the recirculation region is destroyed, removing the primary enhancement mechanism and causing a decrease in the overall heat transfer. There is some indication that chaotic mixing might produce more significant enhancement for channels with large corrugation amplitudes.