This paper presents recent contributions to the development of macroscopic continuum transport equations for micro gas flows and heat transfers. Within the kinetic theory of gases, a combination of the Chapman–Enskog expansion and the Grad moment method yields the regularized 13-moment equations (R13 equations), which are of high approximation order. In addition, a complete set of boundary conditions can be derived from the boundary conditions of the Boltzmann equation. The R13 equations are linearly stable, and their results for moderate Knudsen numbers stand in excellent agreement with direct simulation Monte Carlo (DSMC) method simulations. We give analytical expressions for heat and mass transfer in microchannels. These expressions help to understand the complex interaction of fluid variables in microscale systems. Additionally, we compare interesting analogies such as a mass flux and energy Knudsen paradox. In particular, the R13 model is capable of predicting and explaining the detailed features of Poiseuille microflows.
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