Studies on forces on and energy transfer to bodies in a rarefied gas

（1）在过去，我们发展了关于流体力学系统和玻尔兹曼系统的一般理论，在一个稍微稀薄的气体通过物体的定常流中。然而，仅给出了BKW模型方程的滑移系数和Knudsen层修正的显式数据。本文发展了一种新的数值分析方法，对标准Boltzmann方程进行了数值分析，分析了硬球分子气体的滑移系数和Knudsen层，完善了一般理论。（2）在整个Knudsen数范围内，分析了不同温度的非共轴圆柱间的热发散流和诱导流。这是在无外力作用下，由温度场诱导的稀薄气体的典型流动，这在连续介质气体中是看不到的。圆柱上的力随Knudsen数的变化呈现出一个有趣的特征。iii）初始均匀气体的瞬态行为 关于我们 用动力学理论详细研究了蒸发过程中固相的形成。从长时间的解决方案的气体的稳定行为，以及变量之间的关系，在无穷远和凝聚相，澄清。这就为流体动力学方程提供了气体与其凝聚相之间界面上的边界条件。此外，从一个圆柱的稳定的蒸发流的蒸发速率和努森数的范围内进行了准确的分析。在研究过程中，我们提出了几种新的动力学方程分析方法，如数值核方法、分析速度分布函数不连续性的方法、修正的Knudsen数展开法、以及无限域问题的修正Neumann级数方法。v）应用我们的新方法，我们对各种基本稀薄气体流动，如Couette流动，Poiffille流动，狭缝流动，非线性波传播和两个板之间的热传递。少

i) In the past we developed the general theory relating the hydrodynamic system and the Boltzmann system in a steady flow of a slightly rarefied gas past bodies. The explicit data of the slip coefficient and Knudsen layer correction, however, were given only for the BKW model equation. In this study, developing a new method of numerical analysis of the standard Boltzmann equation, we analyzed the slip coefficient and the Knudsen layer for a hard-sphere molecular gas and completed the general theory.ii) The thermal transpiration flow and the flow induced between noncoaxial circular cylinders with different temperatures were analyzed for the whole range of the Knudsen number. These are typical flows of rarefied gas induced by temperature field in the absence of external forces, which are not seen in a continuum gas. The force on the cylinder shows an interesting feature as a function of the Knudsen number.iii) The transient behavior of an initially uniform gas bounded by its plane conden … More sed phase was investigated in detail by the kinetic theory when evaporation took place. From the long-time solution the steady behavior of the gas, as well as the relation among the variables at infinity and on the condensed phase, was clarified. This provides the boundary condition for the fluiddynamic equation on the interface between a gas and its condensed phase. Further, steady evaporation flows from a circular cylinder was analyzed accurately for a wide range of the rate of evaporation and the Knudsen number. The discontinuity of the velocity distribution function in gas was first analyzed accurately in this study.iv) In the course of these studies, we proposed several new methods of analysis of the kinetic equation, such as the numerical kernel method, the method of analyzing the discontinuity of the velocity distribution function, the modified Knudsen number expansion method, and the modified Neumann series method for infinite domain problems.v) Applying our new methods, we made accurate analyses of various fundamental rarefied gas flows for the whole range of gas rarefaction, such as the Couette flow, the Poiseuille flow, a flow through a slit, nonlinear wave propagation, and the heat transfer between two plates. Less