Unsteady Solutions with Convective Heat Transfer through a Curved Duct Flow

Unsteady solutions with convective heat transfer through a curved duct flow has been studied numerically by using a spectral method, and covering a wide range of the temperature difference between the vertical sidewalls for the Grashof number, 100 ≥ Gr ≥ 2000, where the outer wall is heated and the inner wall cooled. In this paper, unsteady solutions are obtained by the time evolution calculations for two cases of the Dean numbers, Case I: Dn = 100 and Case II: Dn = 500 for the aspect ratio 1 ≤ l ≤ 3. It is found that, at Dn = 100 there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into periodic solution, if the aspect ratio is increased. For Dn = 500, on the other hand, it is found that the steady-state solution turns into chaotic solution for small and large Gr for any aspect ratio lying in the range. For moderate Gr, however, the steady-state solution turns into chaotic solution through periodic solutions in the scenario “steady→periodic→chaotic”, if the aspect ratio is increased. Effects of secondary flow on convective heat transfer are also investigated.