Flow In Tubes Of Non-circular Cross-sections

In this thesis steady, laminar, viscous, incompressible flow in tubes of non-circular cross sections is investigated. The specific aims of the investigation are (a) to look at the problems of both developing flow and fully developed flow, (b) to consider non-circular cross sections in a more systematic manner than has been done in the past, and (c) to develop a relatively simple finite element technique for producing accurate numerical solutions of flow in tubes of fairly arbitrary cross sections.;Fully developed flow in tubes is governed by a Poisson type equation for the mainstream velocity. Both analytical and numerical solutions are considered. The cross sections studied include elliptic and rectangular cross sections of different aspect ratios, some triangular cross sections, and a series of crescent-shaped cross sections. The physical characteristics of the flow are examined in a systematic manner in order to determine how these characteristics are affected by certain geometrical features of the cross section. Solutions fall into three basic categories depending on the shape of the cross section. In the first category, which includes circular and elliptic cross sections, solutions are possible in closed form. In the second, including rectangular and some triangular cross sections, solutions are in the form of infinite series. In the third, including cross sections of more complicated or irregular shapes, only numerical solutions are possible. Results of calculations of velocity profiles, flow rate, pumping power, and friction factor are presented in a way which can be useful for engineering applications.;In numerical studies of both developing and fully developed flow finite element techniques are used. Results are obtained for tubes of rectangular and elliptic cross sections of different aspect ratios, for tubes of crescent-shaped cross sections and a tube whose cross section is an oval of Cassini. For fully developed flow, results are compared with the corresponding exact solutions, where available. For rectangular and elliptic cross sections results are also compared with those obtained by using a commercial package (FIDAP). For developing flow finite element results are compared with corresponding theoretical and experimental results from previous work, where available.