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An unsteady peristaltic transport phenomenon of non-Newtonian fluid – a generalised approach. (English) Zbl 1228.76205
Summary: Peristaltic transport of a non-Newtonian power-law fluid characterised by the streaming blood through an axisymmetric tapered tubular vessel is studied under long wave length approximation. The flow is considered to be unsteady and two-dimensional, so that both the axial and the radial velocity components of the fluid come into play. The generalised constitutive relations for the power-law fluid are thoroughly encountered. The input pressure-radius relationship based on the assumption of incompressibility and viscoelasticity of the vascular wall material in conformity to experimental observations is given much attention in order to have resemblance to the in vivo situation. The nonlinear equations of motion governing the peristaltic transport phenomena are discretised with the use of a suitable finite difference explicit scheme. The resulting difference equations are solved numerically by exploiting initial and boundary conditions resulting from physical and biomechanical points of view. A quantitative analysis is performed through numerical computations of desired quantities in order to estimate the effects of nonlinear inertial forces, wall viscoelasticity, tapering angle and the unsteadiness on flow phenomena in peristaltic transportation.
MSC:
76Z05Physiological flows
76A05Non-Newtonian fluids
76M20Finite difference methods (fluid mechanics)
92C35Physiological flows