• analytical solution;
  • Padé approximation;
  • Hankel–Padé method;
  • rational approximation;
  • boundary-layer problems;
  • axisymmetric stretching surface;
  • nano boundary layers


In this paper, a simple and efficient analytical method, Hankel–Padé method, is employed in solving boundary-layer problems. Two important types of boundary-layer problems, the problem of the boundary-layer flow of an incompressible viscous fluid over a nonlinear stretching sheet and the problem of the nano boundary-layer flows with Navier boundary condition, are considered. The analytical solutions of the governing nonlinear boundary-layer problems are developed as rational approximation solutions. The comparison of the obtained results with other available results shows that, in general, the Hankel–Padé is much simpler and more accurate than other approaches that were proposed by other authors recently. Copyright © 2011 John Wiley & Sons, Ltd.