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In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved duct with square cross section. Numerical calculations are carried out over a wide range of the Dean number 100 Dn 6500 for the curvature 0.5 . A temperature difference is applied across the vertical sidewalls for the Grashof numberGr 100 , where the outer wall is heated and the inner one cooled. Spectral method is used as a basic tool to solve the system of non-linear differential equations. After a compressive survey over the parametric ranges, two branches of asymmetric steady solutions with two- and four-vortex solutions are obtained by the Newton- Raphson iteration method. Then, in order to investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the solutions are obtained, and it is found that the steady-state flow turns into periodic flow through chaotic flows if Dn is increased up to 6115. For large Dean numbers Dn 6065 , however, the unsteady flow undergoes through various flow instabilities if, Dn is increased gradually.