Flow instability and its effect on heat transfer in a sinusoidal wavy duct with rectangular cross section

Flow instability and its effect on heat transfer in rectangular-section sinusoidal wavy ducts are investigated using a numerical method. The intensity of secondary flow and the cross-sectional average temperature, both of which have local characteristics, can be used to indicate the position where instability begins. The instability starting points indicated by these two parameters are nearly identical. When the longitudinal vortices generated near two lateral walls meet downstream, the flow instability starts. The span-averaged flow resistance factor changes with very small pulsatile amplitudes even in every position of the duct and under a very low Reynolds number. The average flow resistance cannot be determined by the intensity of secondary flow alone. The average Nusselt number is closely related to the intensity of secondary flow, which means the average Nusselt number can be determined by the intensity of secondary flow alone. The occurrence of flow instability in the duct can greatly enhance heat transfer. From the onset of flow instability, the mean value of f(x) in the unsteady model is approximately 0.8 % lower than that observed in the steady-state model, whereas the mean value of Nu(x) in the unsteady model is elevated by approximately 14 %. A stable numerical model can be used to simulate the duct only when the volumetric intensity of the secondary flow is less than 200; otherwise, an unstable model must be employed. The flow transitions from a steady state to a quasi-periodic state, and then to a chaotic state.