Comment on 'Corrective term in wall slip equations for Knudsen layer'

Abstract

I N a recent Technical Note, Goniak and Duff a obtained an additional term to the surface temperature slip equation of Ref. 2. This term has been referred to as a corrective term in Ref. 1. However, the derivation of this additional term should be viewed from the degree of approximation involved and the validity of continuum methods to treat transition regime. The so-called correction term is, in fact, a higherorder term and may not be significant in the part of transition regime where a continuum flow analysis can be used, i.e., for Kn < 1 and Knudsen layer thickness of order mean free path. In their analysis, Gupta et al. considered only the random thermal velocity and not the mean flow (or drift) velocity (which was considered negligible across the Knudsen layer). This is consistent with the approaches of Shidlovskiy and Patterson, who neglected the convection (or slip) velocity at the edge of Knudsen layer in their velocity distribution functions. Shidlovskiy assumed a nondrifting Maxwellian distribution function, whereas Patterson used a nondrifting Maxwellian with Hermite polynomial perturbation terms. In Ref. 2, a nondrifting Chapman-Enskog velocity distribution function was assumed. The additional (or correction) term of Ref. 1 results from the inclusion of mean flow (or drift) velocity in the analysis. The temperature slip equation with this additional term is