In this paper the steady two-dimensional flow of a Walters-type B' fluid in a vertical channel is investigated. The solutions take into account the behavior of both Newtonian and non-Newtonian fluids. An approximate approach, namely the optimal homotopy asymptotic method (OHAM) is employed to investigate this problem. The proposed algorithm, which is based on a minimization of the residual error by means of several convergence-control parameters, allowed a rigorous determination of an unknown constant, specific to this problem, avoiding artificial assumptions. Numerical simulations were developed for validation purposes and an analysis of the errors is performed, emphasizing excellent accuracy of the approximate analytical results. (C) 2014 Elsevier Ltd. All rights reserved.