Peristaltic Tube Flow of a Giesekus Fluid

Abstract

The objective of this work is to study the peristaltic motion of an incompressible Giesekus fluid in a circular cylindrical tube. The problem is modeled in a fixed frame of reference and then transformed into a frame that moves with the wave speed. The most widely taken assumptions of long wavelength and low Reynolds number are applied in the wave frame. Both exact and approximate solutions of governing equation for stream function are obtained at each cross-section by solving nonlinear algebraic equations. The comparison of the two solutions is presented graphically. The exact solution is then used to analyze the effects of parameters of interest on velocity profile, pressure rise per wavelength and trapping phenomenon. The results disclose that the magnitude of velocity increases in the middle-most region of the tube whereas it decreases in the vicinity of wall with increasing the Giesekus model parameters. It is also observed that the size and circulation of the trapped bolus decrease with increasing the Giesekus model parameters. Moreover, much greater mixing is realized in a plane channel than in a circular tube.