Analytical approximations for steady-state boundary-layer flow of a micropolar fluid

In this paper, we consider the nonlinear problem of the steady-state boundary-layer flow of a micropolar fluid near the forward stagnation point of a two-dimensional infinite plane surface. This problem encounters difficulties in obtaining its solutions, not only because it is nonlinear, but also because it contains linear boundary condition. The homotopy analysis method is applied, via a basis which is fractional in most of its terms, to obtain analytic approximations, up to the 10-th order, for this problem. The analytic approximations for both the velocity and the microrotation profiles are investigated and the A-curves which control the convergence of these approximations are plotted. A convergence theorem concerning the application of the homotopy analysis method to this problem is illustrated and the variations in both the velocity and the microrotation profiles due to the changes in the material parameter K and the parameter n, which related to the concentration of microelements, are discussed. The study proved the great ability of the homotopy analysis method to handle such kinds of strongly nonlinear problems which contain linear boundary conditions and obtain their analytic approximations in a direct accurate effective scheme.