Dean-Taylor flow with convective heat transfer through a coiled duct

Due to engineering application and its intricacy, flow in a rotating coiled duct has become one of the most challenging research fields of fluid mechanics. In this paper, a spectral-based numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating coiled rectangular duct. The emerging parameters controlling the flow characteristics are the rotational parameter i.e. the Taylor number, Tr; the Grashof number, Gr; the Prandtl number, Pr and the pressure-driven parameter i.e. the Dean number, Dn. The rotation of the duct about the center of curvature is imposed in both the positive and negative direction and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated, in detail, for two cases of the Dean Numbers, Case I: Dn = 1000 and Case II: Dn = 1500. For positive rotation, we investigated unsteady solutions for 0 ≤ Tr ≤ 500, and it is found that the chaotic flow turns into steady-state flow through periodic or multi-periodic flows, if Tr is increased in the positive direction. For negative rotation, however, unsteady solutions are investigated for −700≤Tr≤−50, and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature distributions are obtained at several values of Tr, and it is found that the unsteady flow consists of asymmetric two- to eight-vortex solutions. The present study demonstrates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at large Dn's, enhances heat transfer more effectively than the steady-state or periodic solutions. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.