微槽道是微机电系统（MEMS）的重要组成部件，小尺度特征引起的稀薄效应是影响其流动稳定性不可忽视的重要因素，发展适用于稀薄流的稳定性分析方法，揭示稀薄效应对微槽道流动稳定性的影响规律，对于微机电系统功能的实现和性能的改善具有重要意义。基于Boltzmann Bhatnagar-Gross-Krook（Boltzmann-BGK）方程，结合Maxwell边界条件，通过求解特征值问题的方法对恒温情况下的平板Couette和平板Poiseuille流动的稳定性进行了参数影响分析。另外，现有针对Rayleigh-Bénard流动的研究集中于单原子气体，采用Navier-Stokes方程结合滑移修正边界条件的方法，分析了单、双原子气体对Rayleigh-Bénard流动稳定性的影响，并考虑了不同的分子模型。结果表明，对于平板Couette和平板Poiseuille流动，稀薄效应以及增大适应系数均起稳定作用；增大马赫数对Poiseuille流动起不稳定作用，而对Couette流动稳定性的影响规律与扰动波的形式（驻波或行波）相关，当扰动波形式相同，增大马赫数起不稳定作用，当扰动波形式不同，存在马赫数越大流动越稳定的情况。对于Rayleigh-Bénard流动，相较于变硬球和变软球模型的单或双原子气体，硬球双原子气体具有最大的不稳定参数范围；当波数较大时，稀薄效应起稳定作用，当波数较小时，存在稀薄程度越大增长率越大的情况。

Microchannels are an important component of the microelectromechanical system （MEMS）， and the rarefaction effects caused by small scale characteristics is an important factor that cannot be ignored in affecting the flow stability of microchannels. Developing stability analysis methods suitable for rarefied flows and revealing the influence of rarefaction effects on the microchannel flow stability are of great significance for function realization and performance improvement of the MEMS. Based on the Boltzmann Bhatnagar-Cross-Krook （Boltzmann BGK） equation and Maxwell boundary condition， parameter influence analysis is conducted on the stability of the plane Couette and Poiseuille flow under low-speed isothermal conditions by solving the eigenvalue problem. In addition， existing research on Rayleigh-Bénard flow focuses on monatomic gases. Using the Navier-Stokes equation combined with modified boundary conditions， the effects of monatomic and diatomic gases on the stability of Rayleigh-Bénard flow are analyzed， considering different molecular models. The results show that for the plane Couette and plane Poiseuille flows， the rarefaction effects and the accommodation coefficient increase both play a stabilizing role. Increasing Mach number exhibits a destabilizing effect on the Poiseuille flow， while the rule of influence on the Couette flow stability is related to the form of disturbance waves （standing or traveling waves）. In the same disturbance patterns， an increasing Mach number has a destabilizing effect， while in different disturbance patterns， the flow becomes more stable with a larger Mach number. For the Rayleigh-Bénard flow， the hard sphere diatomic gas has the largest unstable parameter range compared to the monatomic or diatomic gas in the variable hard sphere and variable soft sphere models. With a large wave number， the rarefaction effects play a stabilizing role， while a greater degree of rarefaction leads to a larger growth rate with a small wave number.