The motion of a slightly rarefied gas in a long and straight two-dimensional channel caused by a discontinuous surface temperature is investigated on the basis of kinetic theory with a special interest in the fluid-dynamic description. More precisely, the channel is longitudinally divided into two parts and each part is kept at a uniform temperature different each other, so that the surface temperature of the whole channel has a jump discontinuity at the junction. Under the assumption that the amount of jump in the surface temperature is small, the steady behavior of the gas induced in the channel is studied on the basis of the linearized Boltzmann equation and the diffuse reflection boundary condition in the case where the Knudsen number, defined by the ratio of the molecular mean free path and the width of the channel, is small. Using a matched asymptotic expansion method combined with Sone’s asymptotics, a Stokes system describing the overall macroscopic behavior of the gas inside the channel is derived, with a new feature of the “slip boundary condition” for the flow velocity due to the jump discontinuity in the surface temperature of the channel. This condition takes the form of a diverging singularity with source and sink located at the point of discontinuity, with a multiplicative factor determined through the analysis of a spatially two-dimensional Knudsen-layer (or a Knudsen-zone) problem. Some numerical demonstrations based on the Bhatnagar–Gross–Krook (BGK) equation are also presented.

中文翻译：

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表面温度不连续引起的微稀薄气体运动

基于对流体动力学描述特别感兴趣的动力学理论，研究了由不连续表面温度引起的长而直的二维通道中略微稀薄的气体的运动。更准确地说，将通道纵向分成两部分，每部分都保持在彼此不同的均匀温度下，从而使整个通道的表面温度在接合处具有跳跃不连续性。在表面温度跃变量较小的假设下，在Knudsen数定义的情况下，基于线性化Boltzmann方程和漫反射边界条件研究了通道中诱导气体的稳态行为分子平均自由程与通道宽度的比值很小。使用匹配渐近展开法结合 Sone 渐近性，推导出描述通道内气体整体宏观行为的 Stokes 系统，由于通道中的跳跃不连续性，流动速度具有“滑动边界条件”的新特征。通道表面温度。这种条件采用发散奇点的形式，源和汇位于不连续点，乘法因子通过对空间二维克努森层（或克努森区）问题的分析确定。还介绍了一些基于 Bhatnagar-Gross-Krook (BGK) 方程的数值演示。由于通道表面温度的跳跃不连续性，流动速度具有“滑动边界条件”的新特征。这种条件采用发散奇点的形式，源和汇位于不连续点，乘法因子通过对空间二维克努森层（或克努森区）问题的分析确定。还介绍了一些基于 Bhatnagar-Gross-Krook (BGK) 方程的数值演示。由于通道表面温度的跳跃不连续性，流动速度具有“滑动边界条件”的新特征。这种条件采用发散奇点的形式，源和汇位于不连续点，乘法因子通过对空间二维克努森层（或克努森区）问题的分析确定。还介绍了一些基于 Bhatnagar-Gross-Krook (BGK) 方程的数值演示。通过对空间二维 Knudsen 层（或 Knudsen 区）问题的分析确定乘法因子。还提供了一些基于 Bhatnagar-Gross-Krook (BGK) 方程的数值演示。通过对空间二维 Knudsen 层（或 Knudsen 区）问题的分析确定乘法因子。还介绍了一些基于 Bhatnagar-Gross-Krook (BGK) 方程的数值演示。