Numerical analysis of the micro-Couette flow using a non-Newton–Fourier model with enhanced wall boundary conditions

Non-equilibrium effects exist extensively in microfluidic flows, and the accurate simulation of the Knudsen layer behind them is rather challenging for the linear Newton–Fourier model. In this paper, a high-order reduced model (nonlinear coupled constitutive relations) from Eu’s generalized hydrodynamic equations is applied for the investigation of the micro-Couette flows of diatomic nitrogen and monatomic argon as well as Maxwell and hard-sphere molecules using the MacCormack scheme. In order to simulate the confined flows accurately, a set of enhanced wall boundary conditions based on this model are derived with respect to the degree of non-equilibrium. Both the 1st-order Maxwell–Smoluchowski model and the Langmuir slip model are also investigated. For a large range of Knudsen numbers, the results show that the enhanced boundary conditions make a significant improvement in the prediction of flow profiles, especially the temperature profile. The reason behind that is analyzed in detail. The numerical predictions obtained from the high-order model in conjunction with the enhanced boundary conditions are also compared with DSMC, regularized 13 moment equations, Burnett-type equations as well as Navier–Stokes solutions, which highlight its excellent capability in describing the underlying mechanism of the Knudsen layer in the Couette flow.