The optimal solution for the flow of a fourth-grade fluid with partial slip

The steady flow of a non-Newtonian fluid when slippage between the plate and the fluid occurs is considered. The constitutive equations of the fluid are modeled for a fourth-grade non-Newtonian fluid with partial slip; they give rise to nonlinear boundary value problems. Analytical solutions are obtained using powerful analytic techniques for solving nonlinear problems, homotopy perturbation and optimal homotopy asymptotic methods. The results obtained are compared with the numerical results and it is shown that solutions exist for all values of the non-Newtonian parameters. The solutions valid for the no-slip condition for all values of the non-Newtonian parameters can be derived as special cases of the present analysis. Finally the solutions are discussed using a graphical approach. (C) 2011 Elsevier Ltd. All rights reserved.