Asymptotic Solution of the Boltzmann-Krook Equation for the Rayleigh Shear Flow Problem

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Abstract
An asymptotic solution of the Boltzmann‐Krook equation is constructed for the Rayleigh shear flow problem. The distribution function is expanded in powers of the square root of the inverse Knudsen number assumed small. If it is required to satisfy boundary conditions on the averaged flow parameters, the first term of the expansion yields a term identical with the solution of the Navier‐Stokes equation with no‐slip condition; subsequent terms yield slip and satisfy a sequence of linear equations whose coefficients are determined by the no‐slip Navier‐Stokes solution. If the boundary condition is specified on the distribution function, there is in addition a molecular sublayer whose thickness is of the order of the mean free path.