Peristaltic transport of a visco-elastic fluid in a tube of non-uniform cross section

In this paper, the axi-symmetric peristaltic transport of a viscous incompressible visco-elastic fluid has been investigated through a circular tube whose cross section changes along the length. The wall motion is governed by a wave of contraction propagating along the wall of the tube which contracts in the radial direction and then relaxes up to the boundary of the fully distended tube. The nonlinear convective acceleration terms have been duly considered for non-creeping flow. A perturbation technique has been employed to analyze the problem. This paper is concerned with two particular cases: (i) Reynolds number is small and (ii) the wave number is small. The extensive analysis is based upon second order approximation. The effects of the non-Newtonian parameter relaxation time on the flow rate and the mean axial velocity have been analyzed. The derived analytical expressions have been computed in order to carry out a comprehensive investigation of an important physiological problem, i.e. spermatic flow through the vas deferens, in which peristalsis has a role to play. It is concluded that flow rate decreases with relaxation time and increases with Reynolds number while pressure increases with relaxation time and decreases with Reynolds number at a given tapering.