This article presents the steady drag flow problems. The incompressible Oldroyd eight constant fluid flow is considered between two infinite parallel plates. Three flow problems including the Couette flow, Poiseuille flow and Couette–Poiseuille flow are modeled. The source term appearing in the nonlinear differential equation for each case is simplified with the application of modified homotopy perturbation method, and thus the general solution is obtained. The validity of second order approximate analytic solutions is tested with the aid of a numerical technique. The order of accuracy has been obtained in tabular form and the graphs are presented to demonstrate the difference between the three flow regimes.
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