Linearized slip flow past a semi-infinite flat plate

Abstract

Incompressible slip flow past a semi-infinite flat plat at zero incidence is treated in terms of the linearized viscous flow equations. A formal solution is obtained using Fourier transforms and the Wiener-Hopf technique. Explicit inversion of the transform is not possible, but asymptotic expansions are discussed. These reveal the inadequacy of boundary-layer theory in predicting the nature of the solution, even at the plate surface. For example, the local shear forces on the plate are significantly different from boundary-layer values, even far downstream, where slip effects are small. The boundary-layer limit is approached as the Reynolds number based on the mean free path or, equivalently, the free-stream Mach number tends to infinity.