Numerical Study of Unsteady Heat and Fluid Flow through a Curved Rectangular Duct of Small Aspect Ratio

Abstract

In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct of aspect ratio 0.5 and curvature 0.1. The outer wall of the duct is heated while the inner wall cooled, the top and bottom walls being adiabatic. Numerical calculations are carried out by using the spectral method, and covering a wide range of the Dean number and the Grashof number . The main concern of the present study is to investigate the nonlinear behavior of the unsteady solutions i.e. whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn or Gr is increased. Time evolution calculations as well as their phase spaces show that the unsteady flow is steady-state for and this region increases as Gr becomes large. It is found that the steady-state flow turns into chaotic flow through periodic and multi-periodic flows, if Dn is increased. Typical contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of asymmetric single-, two-, three- and four-vortex solutions. The present study shows that chaotic flow enhances heat transfer more significantly than the steady-state or periodic solutions due to many secondary vortices at the outer concave wall.

Keywords: Curved rectangular duct; secondary flow; time-evolution; periodic solution; chaos