An unsteady peristaltic transport phenomenon of non-Newtonian fluid - A generalised approach

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 in the present analysis. The input pressure-radius relationship based on the assumption of the incompressibility and viscoelasticity of the vascular wall material in conformity to the 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 properly discretised with the use of suitable finite difference explicit scheme. The resulting difference equations are solved numerically by exploiting the appropriate initial and boundary conditions resulting from the physical and the biomechanical point of view. An extensive quantitative analysis is performed through numerical computations of the desired quantities of interest in order to estimate the effects of nonlinear inertial forces, the wall viscoelasticity, the tapering angle and the unsteadiness on the flow phenomena indicating their own role of importance in peristaltic transportation.