Rarefied gas flow through a long rectangular channel of variable cross section

The method, proposed previously by other authors, is applied here to calculate a mass flow rate of rarefied gas through a long rectangular channel of variable cross-section aspect ratio. The gas flow through this channel is generated by the pressure and/or temperature gradient. The method is based on the results obtained previously on the basis of the kinetic equation and it requires very modest computational efforts. As a demonstration of its application some examples of the mass flow rate calculations for the isothermal and non-isothermal flows through the channels with variable rectangular cross sections are given. The analytical expressions in the case of the hydrodynamic and free molecular flow regimes are proposed.