**1. Introduction**

468 Biomedical Science, Engineering and Technology

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measurement of the oxygen saturation of retinal vessels in healthy volunteers.

In the study of some industrial, biological and natural fluidic systems it is often necessary to model fluid flow through tubes, channels or passages of complex geometries. The complexity may arise from the cross-sectional shape, or from longitudinal cross-section variation, or from both. Typical cases include flow of molten metals or plastics through dies and moulds, blood flow, microfluidic applications, and flow in porous media, among many others. Characteristics of these flows are laminar state, incompressibility, small rates of flow and varied time patterns. One field where pertinent applications are being developed at a fast rate is Microfluidics (Cetin and Li., 2008; Chen et al., 2008; Forte et al., 2008; Gebauer and Bocek, 2002 ; Mathies and Huang, 1992; Sommer et al., 2008; Srivastava et al., 2005; Woolley and Mathies, 1994; Yeger et al., 2006.) . In this specific field, present microchannel manufacturing techniques produce typically non-circular capillaries (Sommer et al., 2008). Also the introduction of electrical or magnetic field induce plastic behavior in the working fluid.

In particular, it is well known that blood is a biological fluid that behaves as a Newtonian fluid in arteries, veins and large capillaries, but becomes non-Newtonian in the smaller vessels, where the size of suspended particles is big as compared to the vessel´s diameter size (Pedley ,2008). A relevant problem in this field as to the method presented in the next sections is the analysis of diseased arteries and veins for quirurgical interventions. Specifically, stenosed arteries are blood conduits of irregular geometry in which crosssection geometry usually varies along the vessel length.

The above context implies that it is desirable, particularly for modeling and design purposes, to count with analytical techniques that can integrate variables such as the noncircular cross-section of conduits, axial variation of conduit geometry, and plastic flow in some cases.

In this chapter it is presented a method of analysis that allows to address in a general way the problem here outlined.

The standard analytical technique for tube flow problems is usually the search of specific solutions to the momentum equations with associated boundary and initial conditions (Batchelor, 2000). Otherwise numerical solutions are developed for some purposes (Xue et al.,1995).

The main aim of this chapter is, thus, to introduce and explore the potential use of a general analytical approach to irregular conduit flow, which makes it possible to determine velocity field, rate of flow, shear stress, recirculation regions and plug zones, this last when fluid plasticity is operant.

The method already referred to has been developed by the authors through specific applications mainly during the past decade. In this chapter some previous results are organized within a common analytical pattern, together with novel material.

This chapter includes sections for the *general model***,** considering one velocity component and more than one velocity component versions, *applications* related to flow in straight tubes and to axially-varying flows, and a closing *conclusion* section.
