Analysis of rarefied gas flow in microchannels in slip and early transition regimes

In this paper, an analytical solution of two-dimensional, isothermal, compressible, subsonic and rarefied gas flow in a microchannel with slowly varying cross-section is considered. In order to increase the accuracy of the solution for the slip flow regime as well as to obtain solution for the initial part of the transition regime, the second order boundary condition is applied along with governing system of equations. The analytical solution of the differential equation was achieved by expressing the pressure in terms of the local values of the Knudsen number and the channel height, which enable the separation of variables. Thus, the distribution of pressure and velocity field is obtained indirectly based on the distribution of the local value of the Knudsen number. This approach highlights the significance of the Knudsen number as the main characteristic of the rarefied gas flow. The obtained analytical solution is significant because it allows for the accurate calculation of gas flow through microchannels of variable cross-section and can serve as a benchmark for assessing the accuracy and reliability of numerical and experimental approaches to rarefied gas flow problems in microchannels.