Since the size of microsystems is close to the molecular mean free path, the gas rarefaction must be taken into account in modelling of microflows. However, the transition regime represents many difficulties for practical calculations because the Boltzmann equation must be applied. This approach requires great computational efforts and many engineers prefer to substitute such calculations by some estimations, which lead to quite incorrect results in many cases. At the same time, many rigorous results for the transition regime already obtained from the Boltzmann equation can be easily used in practical calculations. A brief survey of many recent books on microflows showed that all of then give just elementary information about the kinetic theory of gases, while the results on the transition flows of gases obtained during the few last decades are omitted. The aim of the present work is to review the recent results of rarefied gas dynamics and to give several examples of their applications in microchannels.

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