An analysis of peristaltic motion of compressible convected Maxwell fluid

This paper presents a theoretical study for peristaltic flow of a non-Newtonian compressible Maxwell fluid through a tube of small radius. Constitutive equation of upper convected Maxwell model is used for the non-Newtonian rheology. The governing equations are modeled for axisymmetric flow. A regular perturbation method is used for the radial and axial velocity components up to second order in dimensionless amplitude. Exact expressions for the first-order radial and axial velocity components are readily obtained while second-order mean axial velocity component is obtained numerically due to presence of complicated non-homogenous term in the corresponding equation. Based on the mean axial velocity component, the net flow rate is calculated through numerical integration. Effects of various emerging parameters on the net flow rate are discussed through graphical illustrations. It is observed that the net flow rate is positive for larger values of dimensionless relaxation time λ₁. This result is contrary to that of reported by [D. Tsiklauri and I. Beresnev, "Non-Newtonian effects in the peristaltic flow of a Maxwell fluid," Phys. Rev. E. 64 (2001) 036303]." i.e. in the extreme non-Newtonian regime, there is a possibility of reverse flow.