Effects of Curvature and Convective Heat Transfer in Curved Square Duct Flows

Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, $δ$⁠, $0<δ≤0.5$ and the Dean number, Dn, $0≤Dn≤6000$⁠. A temperature difference is applied across the vertical sidewalls for the Grashof number $Gr=100$⁠, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from $δ$ = 0.23 to 0.24. When there is no stable steady solution, time evolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what $δ$ is. The transition to a periodic or chaotic state is retarded with an increase of $δ$⁠. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.