The motivation of the current paper is to provide a detailed review of crucial topics in microand nanoscale gas flows, i.e., velocity slip and temperature jump phenomena and their modeling, Knudsen minimum, and thermally-driven flows with application in Knudsen pumps. Non-equilibrium gas flows at the micro and nano scales exhibit peculiarities different from the intuition of macroscopic continuum fluid dynamics and heat transfer. Rarefied gas flows experience unique features such as slip and jump boundary effects, Knudsen paradox, pumping effect, , anti-Fourier heat transfer, thermal critical Knudsen number, and rarefied gas shock polars. This paper reviews the latest advancements and investigations on the gassurface velocity and temperature inequalities, named velocity slip and temperature jump, in rarefied gas flows. Thermodynamic non-equilibrium effects are localized in the Knudsen layer within a width of a few gas mean free path near the surfaces. These particular features result in inequalities between the velocity and temperature of the gas concerning the surface. Experimental investigations of the slip and jump conditions from the first observation to the recent studies are reviewed. Next, a comprehensive review of the different categories of velocity slip models from the Maxwell model up to the recently developed models will be performed. For the first time, all the current models on the viscosity of rarefied gas are classified and compared in the present paper. Progress in the derivation of the models describing the temperature jump of rarefied gas over a solid surface will be performed. Next, a unique behavior of rarefied gas named the Knudsen paradox or Knudsen minimum is introduced and reviewed based on the different viewpoints. Different possible reasons for the origin of the Knudsen paradox phenomena are reviewed. A complete set of experimental and numerical works which detected the Knudsen paradox feature will be historically reviewed. Then, the closed-form relations obtained from the numerical simulations and experimental measurements indicating and predicting the occurrence of the Knudsen paradox phenomenon are reviewed and compared. The end section of this paper focuses on deemed physical and real-world applications of the rarefied flows at small scales utilizing thermally driven gas flows, i.e., the pumping effect of the rarefied gas. The pumping effect of the rarefied gas under temperature gradient leads to the Knudsen pump or Knudsen compressor concept. The main advantage over macro-scale pumps is that these sorts of pumps do not suffer from reduced life cycles due to various modes of mechanical failure because they do not have any rotating and moving parts. Moreover, the pumps mentioned above could find applications in gas chromatography, spectroscopy, moving gases on a chip, forced convection cooling, and micro-nano scale actuators. Different classes of thermally-induced flows with their origins are proposed and discussed, containing the recently detected thermally-driven flows. Based on that, a critical and comprehensive review of the different types and configurations of Knudsen pumps will be presented in detail. The newest published research containing new designs of Knudsen pumps has been considered in this review. Different numerical techniques developed or employed to simulate Knudsen pumps will be extensively reviewed. Besides, all published experimental investigations on Knudsen pumps will be reviewed and classified. Overall, this review will provide insights into the emerging physical science and engineering application of micro- and nanoscale gas flows.

Keywords