Indian Journal of Science and Technology
Year: 2009, Volume: 2, Issue: 8, Pages: 35-42
R. N. Mondal, N. Islam, L. E. Ali and A. K. Datta
Maths. Discipline; Science, Engg. & Technol. School, Khulna University, Khulna-9208, Bangladesh
*Author for the correspondence:
R. N. Mondal,
Discipline; Science, Engg. & Technol. School, Khulna University,
E-mail: [email protected]
In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct. The outer wall of the duct is heated while the inner one is cooled. Numerical calculations are carried out by using the spectral method covering a wide range of the Dean number, Dn , 0 ≤ Dn ≤ 1500 and the curvature, δ , 0 < δ ≤ 0.5 for the Grashof number Gr =100 . First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, six branches of symmetric steady solutions are obtained with two- and multi-vortex solutions. Its linear stability is then investigated. In the unstable region, time evolution calculations as well as their spectral analyses are performed. A typical transition occurs from steady flow to chaos through periodic or multi-periodic flows, if Dn is increased no matter what δ is. Effects of curvature on the unsteady solutions are also obtained. The transition to the periodic or the chaotic state is retarded, if the curvature is increased.
Keywords: Curved rectangular duct, solution flow
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