Pressure-driven flow instability with convective heat transfer through a rotating curved rectangular duct with differentially heated top and bottom walls

In this paper, a spectral-based numerical result is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the duct about the centre of curvature is imposed in the positive direction for the constant Dean number Dn = 1000 over a wide range of the Taylor number 0≤Tr≤2000. First, solution structure of the steady solutions is obtained by the Newton-Raphson iteration method. Then, we investigated unsteady solutions by time evolution calculations justified by power spectrum of the solutions, and it is found that when there is no rotation, the flow is chaotic but as the rotational speed increases, the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. This study shows that combined effects of the centrifugal and Coriolis forces counteract each other in a nonlinear manner which results in to turn the chaotic flow into steady-state flow. The present study demonstrates the role of secondary vortices on convective heat transfer which shows that secondary flow enhances heat transfer in the flow. Typical contours of secondary flow patterns and temperature distribution are also obtained at several values of Tr, and it is found that the unsteady flow consists of two- to eight-vortex solutions if the duct rotation is involved in the present case.In this paper, a spectral-based numerical result is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the duct about the centre of curvature is imposed in the positive direction for the constant Dean number Dn = 1000 over a wide range of the Taylor number 0≤Tr≤2000. First, solution structure of the steady solutions is obtained by the Newton-Raphson iteration method. Then, we investigated unsteady solutions by time evolution calculations justified by power spectrum of the solutions, and it is found that when there is no rotation, the flow is chaotic but as the rotational speed increases, the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. This study shows that combined effects of the centrifugal and Coriolis forces counteract each other in a nonlinear manner which results in to turn the chaotic flow into stea...