The present review, containing 178 references, is dedicated to one of the largest and most important branches of the rarefied gas dynamics, namely internal flows. A critical analysis of the corresponding numerical data and analytical results available in the literature was made. The most reliable data were selected and tabulated. The review will be useful as a reference for mathematicians, physicists and aerodynamicists interested in rarefied gas flows. In this paper the complete ranges of the main parameters, determining rarefied gas flows through a capillary, are covered. The capillary length varies from zero, when the capillary degenerates into a thin orifice, to infinity when the end effects can be neglected. The Knudsen number, characterizing the gas rarefaction, varies from zero when the gas is considered as a continuous medium to infinity when the intermolecular collisions can be discounted. The pressure and temperature drops on the capillary ends vary from the small values when the linear theory is valid to the large values when the nonlinear equations must be applied. The influence of the gas–surface interaction is considered.

The present review is dedicated to the velocity slip and temperature jump coefficients applied to modeling of gas flows. Such coefficients are used when a moderate gas rarefaction must be taken into account. In this case, calculations of gas flows can be performed on the basis of continuum mechanics equations applying the velocity slip and temperature jump boundary conditions. Thus, the velocity slip and temperature jump coefficients have the same importance in gas dynamics as the transport coefficients such as viscosity, thermal conductivity, and diffusion coefficients. A critical analysis of theoretical and experimental data on the slip and jump coefficients available in the open literature is presented in an accessible form so that it can be easily understandable for nonspecialists in rarefied gas dynamics. The most reliable results are selected and tabulated. The results cover a single gas with the complete and noncomplete accommodation on a solid surface, gaseous mixtures, and polyatomic gases. Many examples of applications of the slip and jump boundary conditions are given. The review will be useful as a reference for mathematicians, physicists, and engineers dealing with flows of moderately rarefied gases.

The mass flow rate of a rarefied gas through a long channel with a rectangular cross section has been calculated based on the model kinetic equation for the whole range of the Knudsen number and in the wide range of the height-to-width ratio. First, the reduced flow rate through a cross section has been calculated as a function of the local rarefaction parameter assuming the pressure gradient to be small. A criterion of the lateral wall influence on the flow rate has been given. Then, the mass flow rate has been calculated as a function of the rarefaction parameters on the channel ends. The last result is obtained for any pressure ratio even if the flow varies along the channel from the hydrodynamic regime to the free molecular one.

The viscous slip coefficient was calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method. The calculations were carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. It was showed that for the mixture of helium and xenon, which has a large ration of the molecular masses, the slip coefficient significantly differs from that for a single gas. A comparison of the present results with those obtained by the moment method applied to the Boltzmann equation showed that the McCormack model equation provides reliable results with modest computational efforts. An example of application of the viscous slip coefficient was given.