STEADY LAMINAR FLOW OF VISCO-ELASTIC FLUID THROUGH A PIPE AND THROUGH AN ANNULUS WITH SUCTION OR INJECTION AT THE WALLS

Abstract

The problem of steady laminar flow of visco·elastic fluids through a pipe and through a cylindrical annulus in the presence of suction and injection have been considered in Part A and Part B of the paper respectively. The rate of suction at one wall has been taken to be equal to the rate of injection at the other wall in the case of annulus. For the pipe flow the effect of the visco-elasticity of the fluid on the axial velocity, axial pressure and the bearing stress have been depicted graphically. For the annulus, the perturbation method has been used for the axial velocity regarding K R as the perturbation parameter. For rapid  convergence of the series solution, K R has taken to be equal to 0.1. It has been found that for Reynolds number, R= 1, the axial velocity profile is not symmetrical regardless of the radius ratio of the two boundaries of the annulus. This is in contrast to the Newtonian fluids where the profile is symmetrical for R=1. It bas also been found that tlte points of inflexion in the axial velocity profiles occur after a critical value of Reynolds number, viz., Re= 1.7. Tpe ra :!ial pressure variation depends on the direction of cross flow. In this respect, visco- elastic fluids have been found to differ from Newtonian fluids.