A method for solving boundary-value problems of transfer at arbitrary knudsen numbers

TLDR: In this article, the smoothed distribution function (SDF) is proposed to obtain a solution to the system of Maxvell-Boltzmann moment equations, which makes possible a considerable simplification in the procedure for calculating moments of the collision integral.

Abstract: A new method is proposed, called the method of “the smoothed distribution function,” which makes possible a considerable simplification in the procedure for calculating moments of the collision integral, and enables us to obtain a solution to the system of Maxvell-Boltzmann moment equations. The approximating distribution function used in the collision integral in the Boltzmann form ensures a limiting process towards continuous expressions for the flux of molecular characteristics. For the example of the solution to the classical problem of heat transfer between two parallel plates with arbitrary Knudsen numbers, a comparison was made of the theoretical results with the results of other analyses, and also with experiment.