摘要:

Linearized Couette flow is considered for Knudsen numbers ranging from zero to unity using Krook's kinetic model. The velocity and stress are calculated from the numerical solution of an integral equation for the velocity. By comparison with independent calculations the relative error of these results is estimated as less than 0.2%. For the particular case of slip flow, the constant in the boundary condition is evaluated from a numerical quadrature. The accuracy of several analytic methods is compared with particular emphasis on the method of Gross, Jackson, and Ziering and that of Lees.Using previous results obtained for Knudsen numbers greater than unity it is confirmed that some form of iteration, based on an integral equation formulation, is needed to give accurate results in the nearly free molecular regime. Further, such an iteration significantly increases the accuracy of the results over the entire transition regime down to Knudsen numbers as low as one third.

ISSN:0031-9171    

DOI:10.1063/1.1706585

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The descent of small particles or heavy molecules through a stagnant exponential atmosphere has been studied by numerical analysis. Both gravitational fall and molecular diffusion are taken into account. It is found that material injected in an arbitrary but horizontally uniform configuration assumes a constant profile which descends through the atmosphere at the fall rate of particles located at the maximum concentration. Analytic expressions are given which describe the profile descent rate, the constant‐profile shape, and the constant‐profile assemblage criterion. The material retention of an intervening turbulent layer in the atmosphere is examined; it is found that the later history of material is little affected by such a layer.

ISSN:0031-9171    

DOI:10.1063/1.1706586

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A time‐dependent solution of the equation describing the fall of small particles through an infinite exponential atmosphere∂c∂t−∂∂xK1&rgr;∂c∂x+K2&rgr;c=0, where &rgr;=&rgr;0e−x/&lgr;,is found for an arbitrary initial distribution of particles. Qualitative characteristics of the solution including the agreement between this analytic solution and the numerical solutions of Banister and Davis are discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706587

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A formulation of the theorem of minimum entropy production is developed to include the case in which mechanical irreversibility due to viscous forces occurs. We have thus obtained a generalization of the dissipation function of Lord Rayleigh as well as a generalization of Helmholtz' theorem, which states that the dissipation function is a minimum in the stationary state. This generalization refers to the slow movement of a viscous incompressible fluid at nonuniform temperature.

ISSN:0031-9171    

DOI:10.1063/1.1706588

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Stagnation‐point similarity solutions of the laminar boundary‐layer equations are calculated for a thermally and calorically perfect gas with Prandtl number ⅔ and viscosity proportional to a power of the absolute temperature (&mgr; ∝T1−&agr;). The parameter &agr; is varied from 0 to 0.5, and the enthalpy ratio across the boundary layer from 0.01 to 0.80. The results are closely applicable to high‐temperature flows of the five inert gases. Heat‐flux values predicted using these results and Amdur and Mason's viscosity calculations are compared with Rutowski's shock‐tube measurements for argon. The agreement is excellent up to a stagnation temperature of 5400 °K. At higher temperatures, the experimental values gradually rise above the theoretical curve, indicating possible onset of electronic excitation and ionization effects upon the heat transfer.

ISSN:0031-9171    

DOI:10.1063/1.1706589

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The transport properties of dissociating hydrogen gas have been calculated from 1000°K to 15 000°K with the assumption of no ionization or electronic excitation. The rigorous kinetic‐theory formulas, which have recently been modified to take into consideration the multiplicity of interaction curves, were used in the calculations. The transport coefficients at each temperature are tabulated as a function of composition rather than pressure for reasons of compactness and ease of interpolation. The fact that the collision integrals for the H‐H interactions are abnormally large compared to those for the H‐H2and H2‐H2interactions causes the transport properties of the mixtures to exhibit somewhat unusual behavior as a function of composition at constant temperature and pressure. Various approximate formulas for the calculation of transport properties of mixtures have been checked against the results of the rigorous calculations. The errors in the viscosity and thermal conductivity are about 10%. For the Prandtl number, however, which involves the ratio of these coefficients, the error is only about 1%.

ISSN:0031-9171    

DOI:10.1063/1.1706590

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The mean free path of a rigid‐sphere gas has been calculated from the most general form of the equilibrium distribution function. The mean free path depends on stream speed through the flow Mach number and increases monotonically with Mach number. The temperature dependence of the mean free path defined for realistic intermolecular forces through a transport coefficient is justified in molecular dynamics.

ISSN:0031-9171    

DOI:10.1063/1.1706591

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

In the measurement of aerodynamic heat transfer in shock tubes and tunnels utilizing thin‐film resistance thermometers, it is assumed that the thermal properties of the gauge (film and substrate) are constant. Since surface temperatures of bodies in hypersonic flow often reach temperatures of several hundred degrees, the validity of this assumption should be tested. A technique is described for measuring the temperature dependence of the product of the density, thermal conductivity, and heat capacity of various substrates for thin‐film resistance thermometers. The results for Pyrex, quartz, and plate glass, which have been used as backing materials for thin‐film resistance thermometers, indicate that sizable errors may be encountered in inferring heat‐transfer rates from measured surface‐temperature histories if the thermal properties are assumed constant. The corrections which must be applied to account for the temperature dependence of the thermal conductivity and the specific heat have been established through an approximate theoretical solution of the nonlinear one‐dimensional heat‐conduction equation. The magnitude of the correction depends on the material of the substrate and the surface temperature. For Pyrex at 150°C it is about 45% and for fused quartz and glass about 15%.

ISSN:0031-9171    

DOI:10.1063/1.1706592

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A semi‐infinite mass of incompressible, viscous, electrically conducting fluid is bounded by an infinite plane wall with a constant‐strength magnetic field perpendicular to the wall. Either the wall motion is changed indicially parallel to its surface or a constant current is discharged parallel to the surface. The fluid motion and induced magnetic field are discussed for the ratio of kinematic viscosity to magnetic diffusivity &egr; small compared to one and equal to one. For &egr; « 1, it is shown that for the indicial motion of a perfect conductor or for a current discharge there exists a thin viscous boundary layer at the wall; the diffusing Alfve´n wave region extends outside this layer.

ISSN:0031-9171    

DOI:10.1063/1.1706593

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The stability of an arbitrary system is ordinarily determined by means of the variation in its potential energy produced by a displacement of the system from the equilibrium position. In some cases, however, the investigation of stability may be more convenient if it is based on the variation in kinetic energy during a motion of the system past the equilibrium position. In this work it is shown that for magnetohydrodynamic systems such a ``dynamical'' method enables us to very simply obtain a stability criterion equivalent to the well‐known energy principle for the stability of such systems. The proposed method also permits derivation of the criterion of Kruskal and Oberman, who investigated the stability of a plasma on the basis of the kinetic equation in the limit as (m/e) → 0. In this connection it turns out to be superfluous to require the various constants of the motion [of the form ∫dvdV G(L, &mgr;,f)] to be equal to their equilibrium values, as Kruskal and Oberman did.

ISSN:0031-9171    

DOI:10.1063/1.1706594

出版商:AIP    

年代:1962

数据来源: AIP