On the explicit analytic solutions of an Oldroyd 6-constant fluid

This paper deals with some steady unidirectional flows of an Oldroyd 6-constant fluid. The modelled differential equation is non-linear and proposes some new mathematical difficulties. The governing non-linear equation for the steady flow of an Oldroyd 6-constant fluid is different than from the Newtonian fluid and involves the non-Newtonian features. Moreover, the exact analytic solutions are obtained for Couette, Poiseuille and generalized Couette flows for all values of non-Newtonian parameters. The homotopy analysis method (HAM) is used to construct the solutions.