Vortex-structure and unsteady solutions with convective heat transfer through a curved duct

The present paper investigates the onset of secondary vortices and unsteady solutions with convective heat transfer through a curved rectangular duct of large aspect ratio by using a spectral-based numerical scheme and covering a wide range of the Grashof number Gr. The outer wall of the duct is heated, whereas the inner wall is cooled, with the top and bottom walls being thermally insulated. Numerical calculations are carried out for two cases of the Dean numbers: Dn = 100 (case 1) and Dn = 500 (case 2). Time history analyses of the Nusselt numbers show that, at Dn = 100, the steady-state flow turns into multiperiodic flow via periodic flow, if the Grashof number is increased. For Dn = 500, however, the unsteady flow is always chaotic for any value of Grashof number investigated in this study. The present study well demonstrates the transitional behavior of the unsteady solutions with vortex structure of secondary flows, where single-, two-, and four-vortex solutions are obtained for the periodic solution and four-to 10-vortex for the chaotic solution. The study specifically describes the role of secondary vortices on convective heat transfer, which shows that convective heat transfer is significantly enhanced by the secondary flow; the chaotic flow, which occurs at large Dean numbers, enhances heat transfer more effectively than the periodic solutions. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.