We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the work of Taheri et al. [“Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations,” Phys. Fluids 21, 017102 (2009)], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse-power-law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.

中文翻译：

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平行板之间的流动：逆幂律模型的正则化13矩方程的解析解

我们研究了由正则化13矩方程预测的平稳河道结构。与Taheri等人的工作相比。[“ Couette和Poiseuille微流：正则化13矩方程的解析解，” Phys。流体21，017102（2009）]，我们关注分子满足一般逆幂定律的气体。获得了半线性方程的解析解，并通过将一般解与新推导的边界条件耦合来求解了库埃特，傅立叶和泊瓦依流的结构。结果显示在滑流状态下与参考溶液具有极好的一致性。我们的结果还表明，从逆幂定律模型导出的R13方程比具有改变粘度的Maxwell分子的R13方程具有更好的精度。