Exact analytic solutions are obtained for the flow of a viscoelastic fluid with fractional second grade model by peristalsis through a curved channel. The flow has been investigated under the assumptions of long wavelength and low Reynolds number approximation. The streamlines for trapped bolus of Newtonian fluid are analyzed graphically. The fractional calculus approach is used to get analytic solutions of the problem. The influence of fractional parameter, material constant, amplitude, and curvature parameter on the pressure and friction force across one wavelength are discussed numerically with the help of graphs. 1. Introduction Peristalsis is a mechanism of fluid transport through deformable vessels with the aid of a progressive contraction/expansion wave along the vessel. This mechanism appears to be a major mechanism for fluid transport in many physiological systems. It appears in the gastrointestine tract, urine transport from kidney to bladder, bile from the gall bladder into the duodenum, the movement of spermatoza in the ducts efferentes of the male reproductive tract, transport of lymph in the lymphatic vessels, and in the vasomotion of small blood vessels such as arterioles, venules, and capillaries. Peristaltic fluid transport is being increasingly used by modern technology in cases where it is necessary to avoid contact between the pumped medium and the mechanical parts of the pump. A mathematical model to understand fluid mechanics of this phenomenon has been developed using lubrication theory, provided that the fluid inertia effects are negligible and the flow is of the low Reynolds number. The flow of Newtonian and non-Newtonian fluids was described by many researchers in straight vessels (Shapiro et al. [1], Jaffrin and Shapiro [2], Jaffrin [3], Pozrikidis [4], Vajravelu et al. [5], and Li and Brasseur [6]). In recent years it has turned out that the mathematical models in areas like viscoelasticity and electrochemistry as well as in many fields of science and engineering including fluid flow, rheology, diffusive transport, electrical networks, electromagnetic theory, and probability can be formulated very successfully by fractional calculus. In particular, it has been found to be quite flexible in describing viscoelastic behavior of fluids. The starting point of the fractional derivative model of non-Newtonian fluids is usually a classical differential equation which is modified by replacing the time derivative of an integer order by the so-called Riemann-Liouville fractional operator. The fractional derivative models have been used
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