Fahraeus-Lindqvist effect in an Oldroyd 8-constant fluid

A pressure driven axisymmetric flow in a circular tube, having a non-Newtonian Oldroyd 8-constant fluid in the core, is considered in this paper. The Oldroyd 8-constant fluid is surrounded by a Newtonian fluid in the present study. The exact solution of the governing equation is obtained in the form of an integral which is evaluated using Gaussian quadrature. The expression for the apparent viscosity is obtained. The graphical results are presented for the profiles of apparent viscosity for different values of the material parameters plotted against tube radius. It is found that for all the values of the material parameters, the apparent viscosity decreases as the tube radius decreases which is the Fahraeus-Lindqvist effect. The results for the case, when there is no Newtonian fluid present in the periphery, are also deduced.