  In this paper a problem of stationary flow of generalized Newtonian fluid in
a thin channel is considered. An efficient algorithm of solution is proposed
that includes a flexible procedure for a continuous approximation of the
apparent viscosity by means of elementary functions combined with analytical
integration of the governing equations. The algorithm can be easily adapted to
circular or elliptic conduits. The accuracy and efficiency of computations are
analyzed using an example of the Carreau fluid. The proposed computational
scheme proves to be highly efficient and versatile providing excellent accuracy
of solution at a very low computational cost.
