Validation of Navier–Stokes equations for slip flow analysis within transition region

Navier–Stokes equations with first-order and second-order accurate slip boundary conditions are provided to describe the two-dimensional gaseous steady laminar flow between two plates in transition region. A new similarity transformation for the controlling equations with boundary conditions was given so as to obtain the ordinary differential controlling equation. An analytical solution was provided for this strong nonlinear ordinary differential equation using a powerful, easy-to-use analytic technique for nonlinear problems, that is, the homotopy analysis method (HAM). By analyzing solutions and comparing with the results of other investigators, it is proved that the results are not accurate or physically wrong either obtained from calculation of Navier–Stokes equations with first-order boundary condition or second-order slip boundary condition in transition flow region, although some parameters may fit well with the experimental data. So, Navier–Stokes equations cannot govern the gaseous flow in transition region.