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This dissertation, Forced Convection in Curved Ducts: Multiplicity and Stability by Fang, Liu, 劉方, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled FORCED CONVECTION IN CURVED DUCTS: MULTIPLICITY AND STABILITY Submitted by Fang LIU for the degree of Doctor of philosophy at the University of Hong Kong in October 2006 Numerical studies are made on fully developed forced convection in slightly / tightly curved ducts of square / rectangular cross-sections, which are encountered in wide applications. The investigation is confined to fully developed flow and heat transfer under peripherally uniform wall temperature. Thermo-physical properties of fluid are taken as the constants. The study focuses on flow bifurcation and stability in curved ducts with different curvature ratios and aspect ratios: slightly curved square ducts, tightly curved square ducts and tightly curved rectangular ducts. Steady bifurcation structures in these curved ducts are obtained. The physical mechanisms and driving forces of the flow structures are discussed. The stability on various branches is determined by direct transient computation on dynamic responses of the multiple solutions. The characteristics of the flow oscillations are revealed by Hilbert spectral analysis. The investigation is divided into three parts according to the curvature ratio and aspect ratio of the curved ducts. In the first part, bifurcation and stability of forced convection in a slightly curved square duct are studied. Six known solution branches are extended to the high Dean number region and four new asymmetric branches are found. As the Dean number increases, fully-developed flows evolve from a stable steady 2-cell solution to a periodic oscillation, another stable steady solution, an intermittent oscillation and a chaotic oscillation. In the second part, bifurcation and stability of forced convection in a tightly curved square duct are studied. Ten solution branches are found, including five asymmetric branches and some sub-branches of the known branches that are new for tightly curved ducts. As the Dean number increases, finite random disturbances lead the flows from a stable steady state to the co-existence of two kinds of periodic oscillations, the co-existence of several kinds of intermittent oscillations, and a chaotic oscillation. In the third part, bifurcation and stability of forced convection in a tightly curved rectangular duct of aspect ratio 10 are investigated. Eleven solution branches are found, seven symmetric and four asymmetric. Ekman vortices are considerably long due to large aspect ratio. As the Dean number increases, finite random disturbances lead the flows from a stable steady state to another stable steady state, a periodic oscillation, an intermittent oscillation, another periodic oscillation and a chaotic oscillation. The mean friction factor and the mean Nusselt number are obtained for all physically-realizable fully-developed flows in these curved ducts. A significant enhancement of heat transfer can be obtained at the expense of a slight increase of flow friction. DOI: 10.5353/th_b3701583 Subjects: Tubes - Fluid dynamicsHeat - ConvectionBifurcation theory

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