The peristaltic flow for Carreau fluid through an elastic channel

The purpose of this study is to investigate the effect of an elastic wall on the peristaltic flow of Carreau fluid between two concentric cylinders, where the inner tube is cylindrical with an inelastic wall and the outer wall is a regular elastic sine wave. For this problem, cylindrical coordinates were used, and a short wavelength “relative to channel width for its length,” as well as the governing equations of Carreau fluid in the Navier–Stokes equations. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the fourth-order in dimensionless Weissenberg number (We{W}_{{\rm{e}}}). The performed computations of various parameter values such as velocity, shear stress, and wave frame streamlines are discussed in detail for different values of the Weissenberg number (We{W}_{{\rm{e}}}). The obtained results demonstrate that the fluid velocity increases with the increase in the value of We{W}_{{\rm{e}}} and some features of the wall, while the opposite behavior is observed with the increase in other features of the wall. Hence, the presented numerical analysis reveals many aspects of the flow by considering a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies. The results were evaluated using the Mathematica software program. The Mathematica program was used by entering various data for the parameters, where the program showed the graphs, then the effect of these parameters became clear and the results were mentioned in the conclusion.