Poiseuille Flow of Rarefied Gases Between Concentric Cylinders

Miniaturized devices are used currently in many engineering applications. Nonetheless, despite much progress in their fabrication, the fundamental understanding of fluid flow and heat transfer on the microscale is still not satisfactory. In this study, rarefaction effects in pressure-driven gas flows in annular microchannels are investigated. The influence of Knudsen number, aspect ratio of the annulus, and surface accommodation coefficient on wall friction, mass flow rate, and thermal energy flow rate is discussed. For this, the linearized Navier–Stokes–Fourier (NSF) and regularized 13-moment (R13) equations are solved analytically. The results are compared to available solutions of the Boltzmann equation to highlight the advantages of the R13 over the NSF equations in describing rarefaction effects in the process. Moreover, in order to improve the accuracy of the NSF system a second-order slip boundary condition is proposed.