Similarity solutions for a moving-flat plate thermal boundary layer

In this paper, the thermal boundary-layer problem of a semi-infinite flat plate moving in a constant velocity free stream is studied. The similarity equations with viscous dissipation for the thermal boundary-layer are derived and solved by numerical techniques. Under some specific conditions, the thermal boundary-layer similarity equation can be integrated analytically. The results are analyzed for very small Eckert number case and large Eckert number case. It is found that, for the two cases, wall heat fluxes will increase with the increase of the velocity ratio . With increasing Eckert number, the viscous dissipation heating will become dominant. However, for the Prandtl number when the Eckert number is small, it is found that wall heat fluxes will increase with increasing Prandtl number only for a certain range of velocity ratio . For the other range, the wall heat fluxes will have a maximum at a certain Prandtl number, and, when the Prandtl number is larger than the critical value, wall heat fluxes will decrease with increasing Prandtl number. Some examples of the lower solution branch are also presented to compare with the upper solution branch. It is found that the lower solution branch will result in lower heat fluxes at the wall.     

Measuring concentration: Sampling design issues,as illustrated by the case of perfectly stratified samples

Using the artificial example of perfectly stratified samples, we have shown the effect different sampling designs have on the determination of concentration values. More concretely, we have studied the following four cases: sampling of items in the case the number of sources is known (we have further considered the cases when there are many items in every source and when this is not so); sampling of items in the case the number of sources is unknown, and finally, sampling of sources.     

Random-Matrix Theory: Distribution of Mesoscopic Supercurrents Through a Chaotic Cavity

We investigate the distribution of the supercurrent through a chaotic quantum dot which is strongly coupled to two superconductors when the Thouless energy is large compared to the superconducting energy gap. The distribution function of the critical currents (I_c) is known to be Gaussian in the limit of large channel number, N. For N=1, we present an analytical low-temperature expression for this distribution function, valid both in the presence and in the absence of time-reversal symmetry. It connects directly the distribution of transmission coefficients to the distribution of critical currents. The case of arbitrary channel number (N2) is discussed numerically, and for small critical currents analytically.     

Free convection in h horizontal porous layer with a partly heated or cooled wall

The natural convective flow in a fluid-saturated porous medium is considered for an infinite horizontal channel with the bottom wall being partially heated or cooled. The flow and heat transfer are analysed for a range of values of the two non-dimensional parameters which define the problem, namely the Rayleigh number Ra and aspect ratio . Numerical solutions are obtained for = 1 and = 0.1 for both heated and cooled cases and for a range of values of Ra. In the heated case, the nature of the flow is seen to change from unicellular for smaller values of Ra to multicellular for large Ra, with the value of Ra at this changeover being decreased as is decreased. Also, for this case, a range of values of Ra is found over which both unicellular and multicellular flows are possible. For the cooled case, a boundary layer is seen to develop on the bottom wall as Ra is increased for both the values of taken. Finally, a solution for 1 is obtained and is compared with the numerical solutions for = 0.1.     

Generalized cluster expansions

A unified approach to the cluster expansion of the ground-state energy of a system whose wave function is a product of two factors, one of which is a Jastrow function, is presented. It is shown that several previously derived expansions, notably those of Wu and Feenberg and of Massey and Woo, are special cases of this one. The most general case of this expansion, when applied to crystalline helium, incorporates self-consistent phonons, exchange, and the Massey-Woo treatment of short-range correlations.Work partially supported by U.S. Atomic Energy Commission under Contract No. AT(11-1)1569.     

Measurements of the binding energies for adsorption of 3He and 4He on various substances by dynamic gas diffusion techniques

Dynamic gas-diffusion techniques have been developed for measuring the binding energy for adsorption which are effective even when adsorbents of only small surface area are available. The first technique, first developed by Pollock et al., measures the diffusion time for a pulse of gas to pass in molecular flow through a narrow channel, the walls of which are composed of the adsorbent of interest, as a function of temperature. The second technique measures the changes of molecular flow rate out of such a channel when the temperature of the channel is abruptly altered by small increments. Both techniques yield the binding energy for adsorption and the results obtained with them for adsorption of ³He and ⁴He at low temperatures on copper, gold, and Grafoil surfaces are presented. It is found that the results are in good agreement with data obtained previously by conventional static methods which require much larger adsorbent surface areas.Supported by the NSF.     

Stokes flow for a stokeslet between two parallel flat plates

Summary Velocity and pressure fields for Stokes flow due to a force singularity of arbitrary orientation and arbitrary distance between two parallel plates are found, using the image technique and a Fourier transform. Two alternative expressions for the solution, one in terms of infinite integrals and the other in terms of infinite series, are given. The infinite series solution is especially suitable for computation purposes being an exponentially decreasing series. From the series the far field behaviour is extracted. It is found that a force singularity parallel to the two planes has a far field behaviour of source and image for the parallel components (a two dimensional source doublet of height-dependent strength) whereas the normal component, and all fields due to a force singularity normal to the planes, die out exponentially. Velocity fields are compared with those of the one plane case. An estimate of the influence of the second wall and when its effect can be disregarded is obtained.     

Linearised solution of a free-surface flow over a trapezoidal obstacle

Summary A theoretical study is made, of an irrotational, inviscid incompressible and steady flow over a two-dimensional trapezoidal obstacle; with disturbing height , lying on the bottom of the running stream, in terms of a linearised theory. Particular attention is given to two cases of the flow, the supercritical and the subcritical. The bottom is represented in integral form using Fourier's double-integral theorem. Following the method suggested by Thomson (1886) and Lamb (1932), we obtain a linearised free-surface profile in series form for the two cases of flow. The linearised solution obtained is based on the assumption that the height of the trapezoidal bump, , is small compared to the channel depth,h. The nature of the free-surface formed depends on whether the flow is subcritical or supercritical.The results are plotted for the two cases of the flow for different shapes of the bottom and different values of Froude number,F. The effect of the Froude number, the bottom height and the shape of the bottom are discussed.     

Analysis of the Process of Heat Transfer for Free Steady-State Flow of Liquid in a Flat Channel in View of the Dissipation of Mechanical Energy and of the Temperature Dependence of Viscosity

The steady-state process of heat transfer is analyzed with due regard for the dissipation of mechanical energy and for the temperature dependence of viscosity of liquid under boundary conditions of the first kind. A free steady-state flow is treated for the case when a preassigned constant tangential stress is applied to one of the channel walls. An analysis is performed of the range of permissible values of the Name–Griffiths number, in which a steady-state solution to the heat-transfer equation exists. The distributions of the velocity and temperature of liquid in the channel are obtained for this range, and the effect of the main parameters of the system on these distributions is investigated. The basic regularities of the behavior of the maximum point of temperature are described.     

Elastic wave propagation with kinematic discontinuity along a non-ideal interface between two isotropic elastic half-spaces

The problem of wave propagation along the interface between two elastic, isotropic, and homogeneous half-spaces is studied when the half-spaces are coupled through a vanishingly thin layer of Voigt material. It is assumed that the separation, 2H, between the half-spaces, and the complex rigidity-modulus, , of the layer are both vanishingly small, but the complex quantity /2H remains finite.In a series of experiments in which two blocks of elastic materials with or without lubricant/couplant at the interface are subjected to an external load normal to the interface, the variation of the speed and attenuation of interfacial waves, generated and detected by piezoelectric transducers, was measured as a function of external load. Assuming a nonlinear relation between external load and /2H, the experimental data is interpreted theoretically, and the best-fit parameters of the nonlinear relation are determined.For the 13 cases of interfaces studied, with or without lubricant/couplant, satisfactory agreement was found between experiment and theory, except in one case. Even in this case, the agreement is satisfactory in the lower range of load. It is hoped that this study will be useful in developing nondestructive methods of testing the bonding conditions at an interface between elastic materials by means of interfacial wave properties.     

Peristaltic flow of a non-newtonian viscoplastic liquid in a slot channel

The narrow-band asymptotic method [5] has been used to consider the peristaltic flow of a viscoplastic medium in a slot channel. It is found that the mode of flow differs substantially from that in a channel with rigid walls when the axial pressure gradient is small.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 3, pp. 499–505, September, 1976.     

Electrohydrodynamic pulsatile flow in a channel bounded by porous layer of smart material

Electrohydrodynamic dispersion due to pulsatile flow in a channel bounded by porous layer of smart material is studied considering both steady and unsteady cases using both BJ and BJR-slip conditions. We found that in the case of steady flow, the dispersion coefficient, decreases with an increase in electric number W_e but increases with an increase in porous parameter σ_p in the case of BJ-slip condition. However this nature is different in the case of BJR-slip condition in the sense that the dispersion coefficient, increases for certain values of W_e and then decreases with an increase in W_e. In the case of unsteady flow, the dispersion coefficient, , decreases with an increase in W_e and σ_p for both BJ and BJR conditions. In particular, we found that the value of for steady flow in the case of BJ-slip condition is less than that of unsteady flow. The opposite is true for BJR condition. The findings are useful in the design of robust and efficient artificial organs in the human body.     

Analysis of multiwavelength pyrometry using nonlinear chi-square fits and Monte Carlo methods

An analysis of multiwavelength pyrometry is made using Monte Carlo methods to evaluate the measurement error as a function of temperature for three, four, five, and six channels. Both a graybody and an emissivity with linear wavelength dependence are considered. ² is calculated using the observed intensity in each channel and is minimized with respect to the temperature and the emissivity coefficients, using the Levenberg-Marquardt method. The influence of spectral span of the channels and the weight function used in the ² fit are exmained. For the case of linear wavelength dependence, the solutions are found to be nonunique, even with six channels. The results show little improvement of precision with increasing number of channels beyond four channels when the nonlinear variable T is free. Both the spectral span and the weight function are shown to be important variables.     

Atomistic simulation of grain boundary sliding and migration

Interatomic potentials using Embedded Atom Method (EAM) are used in conjunction with molecular statics and dynamics calculations to study the sliding and migration of [1 1 0] symmetric tilt grain boundaries (STGB) in aluminum, under both applied displacement and force conditions. For equilibrium grain boundaries (without applied displacements and forces), three low energy configurations (corresponding to three twin structures) are found in the [1 1 0] STGB structures when grain boundary energies at 0 K are computed as a function of grain misorientation angle. Pure grain boundary sliding (GBS) without migration is simulated by applying external displacement. When forces are applied, the energy barriers are reduced consequent to the fact that grain boundary sliding of STGB is always coupled with migration. The propensity for pure GBS is evaluated by computing the energy associated with incremental equilibrium configurations during the sliding process and compared to the case when sliding is accompanied by migration. The magnitude of the energy barriers is found to be much higher in pure GBS than when migration accompanies sliding. Relations between the applied force, internal stress field, and displacement field are established and the role of grain boundary structure on the deformation process are examined. It is found that the GBS displacement is proportional to applied force, GB energy, and time.     

A priori evaluation of dynamic subgrid models of turbulence in square duct flow

A priori tests of two dynamic subgrid-scale (SGS) turbulence models have been performed using a highly resolved direct numerical simulation database for the case of turbulent incompressible flow in a straight duct of square cross-section. The model testing is applied only to the homogeneous flow direction where grid filtering can be applied without the introduction of commutation errors. The first SGS model is the dynamic (Smagorinsky/eddy viscosity) SGS model (DSM) developed by Germano et al. [1] while the second is the dynamic two parameter (mixed) model (DTM) developed by Salvetti and Banerjee [2]. For the Smagorinsky model we have used both the Fourier cut-off filter and a modified Gaussian filter which has the property that it removes aliasing errors in consistent a priori model-testing for spectral-based datasets. Results largely consistent with those found for plane channel flow are observed but with some slight differences in the corner regions. As found in prior studies of this sort, there is a very poor correlation of the modelled and exact subgrid-scale dissipation in the case of the DSM. The DSM over-predicts subgrid-scale dissipation on average. Instantaneously, the model provides an inaccurate representation of subgrid-scale dissipation, in general underestimating the magnitude by approximately one order of magnitude. On the other hand, the DTM shows excellent agreement with the exact SGS dissipation over most of the duct cross-section with a correlation coefficient of approximately 09.     

The influence of channelling on radiation damage produced in silicon during ion bombardment

The ion bombardment of silicon results in the formation of an amorphous phase in the vicinity of the bombarded regions. This gives rise to a milky appearance which is easily distinguishable from an adjacent unbombarded region. An experiment is described which was specifically designed to study the influence of channelling of incident 80 keV Ne⁺ ions on the formation of this amorphous phase. It is found that channelling significantly reduces the rate at which this phase is produced, and in the particular case of the 110 axial channel this corresponds to a reduction in radiation damage by a factor of about 8. The results are compared with the current theories of channelling and are found to be in reasonable quantitative agreement.     

Increasing the force with which a shock wave discharged from the channel acts on an obstacle by way of converting a normal pressure shock to a system of oblique shocks

The results are given of experimental and numerical investigations of the effect produced on an obstacle by shock waves discharged from channels of different cross-sectional shapes (circle, square, cross). The pressure distribution on an obstacle mounted normally to the flow axis is measured. The experimental results are compared to the data of numerical calculation for determining the optimal modes as regards the duration of calculation and the cell size that produce the least difference between the experimental and numerical data. Calculations are performed of the gas flow behind a shock wave discharged from a channel of X-shaped cross section, and the distribution of pressure and temperature over the obstacle surface is plotted. It is found that the force with which a flow acts on an obstacle when discharged from a channel of X-shaped cross section is much greater than in the case of being discharged from a channel of round or square cross section. Shadow photographs show that this is due to the reduction of the loss of total pressure in the flow because of the conversion of the normal pressure shock to a system of oblique shocks.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 900–907.Original Russian Text Copyright © 2004 by T. V. Bazhenova, V. V. Golub, A. L. Kotelnikov, A. S. Chizhikov, M. V. Bragin, and S. B. Shcherbak.     

Kinetic equations for neutral Fermi liquids in DC magnetic fields. The nonlinear and particle-hole asymmetric effects

Since nonlinear effects are of the same importance as the particle-hole asymmetry (PHA) effects for normal Fermi liquids, at least for some physical situations, a formalism is presented taking both into account. Moreover, because the nonlinearity or PHA is easiest to induce by strong magnetic fields, weak polarization effects are also included. The kinetic equations for the weakly coupled density and magnetization modes are obtained under these circumstances. They lead to an additional effective mass equation in comparison to the Landau formula, joining the suitable angular average of the effective interaction of triples of quasiparticles with the gradient of the two-quasiparticle interaction with PHA effects included. The equations are investigated in detail for ac magnetic field much smaller than the dc field in two cases: (1) at almost equilibrium magnetization of the sample and (2) at almost equilibrium (in the length) magnetization precessing around a dc field tipped to it by an angle # 0. In the first case, the coupling of the longitudinal magnetization to the density modes should lead to a rather detectable excitation of the zero sound by the ac field longitudinal with respect to the dc field. In the second case, the coupling of the spin waves of the magnetization, transverse with respect to the tipped magnetic moment, to the zero sound by virtue of the polarization effects could lead to the interesting effects discussed. Moreover, the possibility of second harmonic generation in the zero-sound channel by the ac field in the nonlinear regime is also noted.     

Dynamic crack propagation in rubber-modified composite models

The dynamic crack propagation behaviour of several rubber-modified composite models has been studied. In all cases the method of high speed photography along with the method of dynamic caustics was used. Results of crack propagation mode observation, fracture toughness and crack propagation velocity measurements are presented here. Especially in the case of two complex inclusions it was found that the crack propagation mode is highly rate dependent. At low test rates the crack growth tends to follow an almost straight crack path while an increase in strain rate in general results in the formation of a kink in the interparticle area. In the same area a crack propagation delay, and in some cases arrest, was observed while both the crack propagation velocity v and dynamic stress intensity factor K _i ^d showed an intense variation. For the sake of comparison, specimens with one and/or two press-fitting inclusions as well as with two holes were fractured under dynamic loads. In all cases both qualitative and quantitative results were obtained.