On the Onset of Hydrodynamic Instability with Convective Heat Transfer Through a Rotating Curved Rectangular Duct.

The present paper addresses numerical prediction of hydrodynamic instability with convective heat transfer through a rotating curved rectangular duct of curvature 0.1. The bottom wall of the duct is heated while cooling from the ceiling. Numerical calculations are carried out by using a spectral method and covering a wide range of the Taylor number 0 2000 ≤ Tr ≤ for the constant pressure gradient force, the Dean number, 1000 Dn = . First, solution structure of the steady solutions is investigated. As a result, three branches of asymmetric steady solutions with two- to ten-vortex solutions are obtained by using Newton-Raphson iteration method. Then unsteady solutions are obtained by time evolution calculations and flow transitions are well justified by obtaining the phase space and power spectrum of the solutions. It is found that chaotic flow turns into steady-state flow through periodic oscillating flow, if Tr is increased. Streamlines and isotherms are also obtained at several values of Tr, and it is found that the unsteady flow consists of two- to ten-vortex solutions. The present study shows that combined action of the centrifugal-Coriolis-buoyancy forces contribute to generate the vorticity. The present study exposes the role of secondary vortices on convective heat transfer, which shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at small Tr but at large Dn, enhances heat transfer more effectively than the steady-state or periodic solutions. [ABSTRACT FROM AUTHOR]