摘要:

The Maxwell moment method utilizing the two‐sided Maxwellian distribution function is applied to the problem of conductive heat transfer between two concentric cylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders. The predicted heat transfer agrees very well with experiments performed on the heat loss from a fine wire by Bomelburg and Scha¨fer, Rating, and Eucken. Comparison with results given by Grad's thirteen‐moment equations, and with those given by Fourier's ``law'' plus the Maxwell—Smoluchowski temperature‐jump boundary condition, shows that the two‐sided character of the distribution function is a crucial factor in problems involving surface curvature.

ISSN:0031-9171    

DOI:10.1063/1.1706498

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The stability of a rotating cylindrical column of liquid with a concentric solid core is discussed. The critical value of the surface tension is determined for the case of a viscous liquid while, for a nonviscous liquid, the problem is solved for axisymmetric and plane perturbations. The physical significance of the results is also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706499

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Progressive three‐dimensional deformation of an initially parabolic, plane curved vortex due to its own induction is numerically obtained in this paper by the use of the localized‐induction concept instead of through the full Biot—Savart law. It is shown that, after the region near the vertex rises up from the plane of the initial orientation, a helical deformation takes place on the legs of the parabola. The helix, which rotates in the direction opposite to the circulatory rotation around the vortex filament, is found to travel away toward the far ends of the parabola as the vertex keeps rising up, while increasing the amplitude and extent of the helical deformation. Similar computations also carried out with a hyperbolic initial shape resulted in essentially the same conclusions as the parabola but with much better numerical stability, as well as with an exponential initial configuration, which grew into somewhat more complicated patterns, yet maintained the essential feature of the helical deformation.

ISSN:0031-9171    

DOI:10.1063/1.1706500

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The laminar boundary‐layer flow resulting from a wave potential flow of formU= &agr;csin(kx — &ohgr;t), with &agr; a parameter andcthe wave velocity, is considered. It is shown, after suitable transformation, that there is an exact solution of the unsteady boundary‐layer equations which is of the form of a power series in the phasekx — &ohgr;t. The coefficients &phgr;nare functions of a similarity variable, and are the solutions of an infinite set of linear third‐order differential equations with nonlinear forcing terms. The forcing term in the equation for &phgr;nis a function of &phgr;0, &phgr;1, …, &phgr;n−1and their derivatives. Solutions for &phgr;0, &phgr;1, and &phgr;2have been computed and are presented. The theory is applied to the laminar boundary layer under a progressive shallow‐water wave, where &agr; =a/h, and compared to a linearized theory. It is concluded that if &agr; ≪ 1, or for any &agr; in a sufficiently small region nearkx — &ohgr;t= 0, the linearized theory is valid. Otherwise, the linear theory does not provide an adequate description of the flow.

ISSN:0031-9171    

DOI:10.1063/1.1706501

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The boundary layer which is formed as a shock wave propagates down a shock tube causes both shock attenuation and shock curvature. Hartunian studied the curvature effect; however, as he points out, because of the singularities at the leading edge of the boundary layer his solution is not valid where the shock wave touches the tube wall. A detailed study is now made of the flow near the leading edge of this shock‐induced boundary layer for a weak shock wave. The leading‐edge flow can be divided into a shear layer near the wall, and into a free stream or shock region. By expanding the Navier—Stokes equations in the small parameterM1* — 1 and stretching the coordinates, simplified equations for the shear layer and shock region are obtained. The shear layer and shock region flows interact and it is found that the shock region must be a zone of non‐Hugoniot flow where the shock structure is two dimensional. An approximate solution of the shock shape is obtained by replacing the shock region by an oblique shock which is approximately matched to the shear layer.

ISSN:0031-9171    

DOI:10.1063/1.1706502

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The hydrodynamic stability of a steady, plane, step shock through a fluid medium with arbitrary equation of state is investigated through consideration of the initial‐value problem for the time‐dependent hydrodynamic equations, linearized in perturbations from the steady flow. If the stability function,Fs= 1 + &kgr; ‐ &kgr;2(v1‐v)pS/T(with &kgr; the Mach number,vthe specific volume,Tthe absolute temperature,pSthe entropy derivative of pressure at constant volume, and subscript 1 referring to the preshock state) is negative, disturbances grow exponentially with time and the shock is unstable. The character of the shock Hugoniot with respect to stability is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706503

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

In a magnetic annular shock tube the gas is pushed axially by an azimuthal magnetic field. Since this field varies inversely as the radius, there are radial nonuniformities in the resulting flow which are analyzed for small values of the ratio &egr; of annulus spacing to radius. The pressure variation across the annulus at the interface between plasma and driving field results in a tilting of the interface. This flow is analogous to the flow resulting from a dam break in shallow‐water theory; it is characterized by a wave of speed (&egr;p/&rgr;)½. The maximum value of &egr; for which the interface and shock wave remain separated is calculated. Nonuniformities are also produced at the shock front when an azimuthal magnetic field is present ahead of the shock; the shock becomes nonplanar and radial variations in the flow persist far behind the shock. For some cases these nonuniformities are appreciable even for values of &egr; so small that the interface and shock wave remain separated.

ISSN:0031-9171    

DOI:10.1063/1.1706504

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The performance characteristics of an annular‐arc configuration under the influence of a magnetic field have been experimentally analyzed, particularly with respect to the effects of tensor conductivity andj × Bbody forces. In this device the plasma conditions are such that the electrical conductivity is insufficient to prevent the diffusion of the plasma through the magnetic field, i.e., the magnetic Reynolds number was small. Experiments were conducted with this device using helium and argon at power levels up to 50 kW, magnetic field strengths to 10 000 G, and particle densities of the order of 1016/cm3to 1017/cm3. The electron gyroradius was smaller than the electron mean free path, i.e., &ohgr;e&tgr;e> 1, where &ohgr;eis the gyrofrequency, and &tgr;eis the time between collisions for electrons. The impedance of the arc in helium was found to vary linearly with &ohgr;e&tgr;e. The existence of a circulating azimuthal Hall current was also demonstrated. A yaw probe was employed to measure the angle of the flow due to thej × BLorentz forces. A good agreement was found between the measured rotation in argon and the predicted value obtained from momentum considerations.

ISSN:0031-9171    

DOI:10.1063/1.1706505

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The exact solution in a closed form of the hydromagnetic equations for an incompressible, viscous, and electrically conducting fluid flow through an annulus with porous walls in the presence of a radial transverse magnetic field is obtained. The solution is reduced to a simpler form with the use of the plausible conditionv/vH≪ 1 which holds for most of the fluids used in hydromagnetic experiments. The pressure distribution is discussed for this form of the solution. The problem is also extended to include parallel Couette flow.

ISSN:0031-9171    

DOI:10.1063/1.1706506

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A method is presented which, in principle, enables one to calculate higher‐order coefficients for transport in fluids. To illustrate this theory the second‐order terms in the pressure tensor which depend on the mass velocity are presented and evaluated approximately in terms of a microscopic relaxation time. Under certain approximations it is found that it is possible to sum the higher‐order terms to every order.

ISSN:0031-9171    

DOI:10.1063/1.1706507

出版商:AIP    

年代:1962

数据来源: AIP