Numerical Prediction of Unsteady Heat and Fluid Flow through a Curved Rectangular Duct of Large Aspect Ratio

In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct of aspect ratio 3. Unsteady solutions are obtained by using a spectral method and covering a wide range of Dean number 100 Dn 1000 and the Grashof number100 Gr 2000. The outer wall of the duct is heated while the inner wall is cooled. The main concern of this study is to find out the unsteady flow behavior i.e whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if the Dean number or the Grashof number is increased. It is found that the unsteady flow is a steady-state solution for Dn = 100 at Gr 100 and Gr 2000 but periodic at Gr 500, 1000, 1500. If the Dean number is increased, the unsteady flow becomes chaotic for any value of Gr in the range. Contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of a two-, four-, six- and eight-vortex solutions. It is also found that the chaotic flow enhances heat transfer more significantly than the steady-state or periodic solutions, if the Dean number is increased.