THE solution of the incompressible laminar boundary-layer equations under rarefied flow conditions at low Mach numbers has applications to several areas of engineering interest, including aerosol science [1], subsonic flight in extraterrestrial atmospheres [2], and micro and nano air vehicles [3, 4]. Early attempts to solve the boundary-layer equations with a slip boundary condition analytically or using perturbation methods yielded a variety of results. Results assuming that the slip solution was a perturbation of the no-slip solution predicted that the slip condition would not affect shear stress, boundary-layer thickness, or heat transfer [5, 6]. Additional semi-analytic results suggested that the heat transfer would change in the presence of slip flow [7–9]. Additional computations showed that the shear stress would change as well [10, 11]. Several explanations were offered for the contradictory results. The solutions to other viscous flows considered similar to boundarylayer flows, such as Couette, Poiseuille, and Rayleigh flows, showed a change in heat transfer and shear stress [12]. This led to the suggestion that the mathematical and experimental techniques available at the time lacked the accuracy necessary to capture the result.

The suggestion was also made that the boundary-layer equations were not valid for slip flows. Two separate arguments were made. Thefirst was that the second-order slip boundary condition was of the same order as the terms that were discarded from the Navier–Stokes equations to create the boundary-layer equations [13, 14]. A second problem was the Reynolds number scaling of the boundary-layer equations. Using the definitions of viscosity and the speed of sound, the Knudsen number can be found as a function of the Mach number and Reynolds number [15]: