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Fluid flow through flexible tubes is of interest due to its dynamic similarity to that of fluid flow in veins, arteries, bronchial air ways, urethra, vocal codes peristaltic tubes, and flexible micro-fluidic devices. Similar behavior can be observed in diagnostic and therapeutic devices pressurized cuffs, prophylaxis, intra-aortic balloon counterpulsation, prosthetic heart devices, vein cannulation and prosthetic vocal codes. Due to the flexible material that constitutes the tube a state of total collapse is highly likely when the tube is subjected to excessive external forces. Thus, muscle contraction and expansion and external forces that act upon the vessel wall all serve to deform the flexible tube thereby affecting the fluid flow area and fluid flow behavior. It is reasonable to conclude that fluid flow within a flexible vessel is a function of the fluid properties, material prosperities of the flexible structures and any external forces. Furthermore within the flexible tube, the presence of attached internal structures can impose further limitations on the fluid flow. Such systems can be found in vein and valves, heart valves and also in nebulizers.

This study focus on the fluid flow studies in a flexible tube with internal flexible structures. Mathematical formulation of the system considers two dimensional fluid and structure interactions in the presences of Non-Newtonian fluid and isotropic elastic structures. Thus, the mathematical description of this system involves multi-dimensional fluid dynamics and linear solid mechanics resulting in a system of nonlinear partial differential equations with moving boundary conditions. To address the issues associated with moving boundaries in the fluid domain the Arbitrary Lagrangian-Eulerian numerical method is used. Numerical solutions for computational models of Newtonian and

Non-Newtonian fluid flow within and around flexible systems provide a means of predicting the impact of material properties of both the fluid and structure on the system performance. Such knowledge can be used to advance the state-of-the-art in flexible system design and pharmacokinetics which will be of value to the medical, chemical, and pharmaceutical industries. For example, flow predictions within flexible micro-tubes may assist in the design of new tube materials.

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