Separation in the flow through peristaltic motion of a carreau fluid in uniform tube

The problem of separated flow (trapping) through peristaltic motion of an incompressible carreau fluid in uniform tube has been investigated under long wavelength approximation neglecting the wave number and using a perturbation series in the Weissenberg number (Wi) was used to obtain explicit forms for the velocity field, a relation between the flow rate and the pressure gradient and a relation between the friction force and the flow rate, in terms of parameter Weissenberg number (Wi), power-law index (n) and amplitude ratio φ. A condition frequently used to predict separated flow in boundary layer theory is to set the vorticity equal to zero on the boundary. We solve the problem numerically using Newton Raphson method to get separated flow points on the wall surface. From our results, the trapping region at the wall decreases with increasing volume flow rate and we found that there exist two values of longitudinal component of separated flow points one of them approaches to inlet of contraction and the other approaches to outlet of contraction. Also, the magnitude of radial velocity of the fluid at the separated flow points for Newtonian fluid is greater than non-Newtonian fluid and the magnitude of pressure rise at separated flow points approximately has the same values at the two values of the longitudinal component of separated flow points. Moreover, the friction force at separated flow points declare reflux phenomena in the contraction region. We discuss behavior of the vertical velocity, the pressure rise and the friction force at separated flow points for the physical parameters of interest.