Ultrasonic speed in mixtures of monochlorodifluoromethane and monochloropentafluoroethane under high pressures

The ultrasonic speed u of [(1 -) CHClF₂(1) + C₂ClF₅(1)] including the azeotropic mixture [CHClF₂(1) + C₂ClF₅(1)] was measured at pressures up to 51 MPa within the temperature range 283.15 to 373.15 K, using a sing-around technique operated at a frequency of 2 MHz with an estimated uncertainty of less that ±2.4 m·s^–1. For = 0.1537 and 0.6268, measurements of the vapor pressure are also reported.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Coarsening of δ′ (Al3Li) and composite precipitates in an Al-2.5% Li-0.15% Zr alloy

The early stage coarsening behaviour of (Al₃Li) precipitates and composite precipitates, consisting of (Al₃Zr) core enveloped by a shell, in an Al-2.5% Li-0.15% Zr alloy has been studied at 443, 473 and 503 K by conventional transmission electron microscopy using superlattice dark-field images. Coarsening kinetics of precipitates was found to exhibit considerable deviation from the t ^1/3 law corresponding to diffusion control at 473 and 503 K. This deviation may be explained either by the operation of a surface-reaction controlled coarsening mechanism represented by t ^1/2 law, or by the presence of a slower precoarsening stage preceding diffusion-controlled coarsening. The particle-size distributions of precipitates were not in accordance with either the earlier theoretical predictions or the normal distribution. They were symmetrical or slightly skewed to the left, and particle sizes twice the average were observed. The coarsening kinetics of composite precipitates, was found to be rather different from that of ; a diffusion model which yields t ^1/n law with n changing from 1/4 to 1/6 as the coarsening progresses, was predicted. The composite precipitates have exhibited quite a narrow and rather symmetrical size distribution.     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

Anomalous hysteresis of the critical current in long proximity-effect bridges

The critical current hysteresis of long Ag-Sn proximity-effect bridges, observed in the current-voltage characteristics obtained at helium bath temperatures T above and below the point of helium T , shows a jump discontinuity at T = T . The relevance of the observed phenomenon to existing theories of superconductors driven into resistive states by direct currents is discussed.Research carried out at the Tata Institute of Fundamental Research.     

Electron transport properties of palladium-ruthenium alloys from 50 mK to 4.2 K

The thermopowerS, resistivity , thermal conductivity , and thermoelectric ratioG of alloys nominally of 0.1, 0.5, 1.0, and 5 at % Ru in Pd have been measured from 50 mK to 4 K. The thermopowerS varies essentially linearly withT, and is only a slowly varying function of concentration up to 1 at % Ru. The characteristic thermopower of Ru in Pd for the 0.1 at % alloy is (0.23±0.01) T µ V/K. At temperatures below 0.15 K there are departures from linearity, presumably caused by magnetic impurities. In the same temperature rangeG shows large departures from the expected constant value. The Lorenz ratioL obtained from two independent sets of data,S/GT and /T, are in good agreement. Departures ofL from the Sommerfeld valueL ₀ are discussed.Work supported by the National Science Foundation under Grant number DMR-75-01584.     

The spin susceptibility of singlet correlated oxygen band in La2?xSrxCuO4

We have shown that the unconventional temperature dependence of the static susceptibility(T) of the perovskite high-T _c superconductors above the superconducting transition temperatureT _c can be explained in terms of two relevant band models containing the singlet-correlated oxygen band and the copper character band. The usual copper-oxygen Hamiltonian containing hopping and Coulomb repulsion terms has been reduced to an effective Hubbard-liket-t-t-U _eff model to describe the low-energy properties. The unusual behaviour of the susceptibility is due to thermally activated oxygen holes coming into the hybridization singularity peak in the density of states. A possible physical origin ofT _max in the temperature dependence of the susceptibility is discussed.     

Use of the WKB method to investigate connective heat transfer in a micropolar fluid

A general approximate solution is obtained for problems of heat transfer associated with a flow of micropolar fluid in a plane channel with boundary conditions of the first and second kind and its accuracy is determined.Notation T_o and T_w temperatures of entrance section and wall of channel, respectively - dp/dx pressure gradient - x₁, x₂ longitudinal and transverse coordinates, respectively (or x and y) - Pe=2v _m ^N h/a Peclet number - v _m ^N mean velocity of Newtonian fluid with viscosity +/2 in channel of width 2h - boundary condition parameter - 2h width of channel - v_x and v_z nonzero components of velocity and microrotation of micropolar fluid - a and thermal diffusivity and thermal conductivity of fluid - , , and viscosities of micropolar fluid - q_w heat flux density on wall - _n and Y_n(y) eigenvalues and eigenfunctions of Sturm-Liouville problem - C_n constants that can be determined by using orthogonality of eigenfunctions Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 732–738, October, 1980.     

Vibrations of axially compressed laminated orthotropic cylindrical shells,including transverse shear deformation

Summary The free vibrations, buckling and the effect of initial prestress upon the frequency spectrum of orthotropic composite cylindrical shells are examined in the context of a theory that includes transverse shear deformation. Results obtained are compared with the predictions of refined Love-type theory and simplified Donnell-type theory that do not consider shear deformation.The calculated examples indicate that transverse shear deformation can be significant not only for short composite shells but even for longer shells possessing low shear moduli.

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Schwingungen axial gedrückter, laminierter, orthotroper zylindrischer Schalen einschließlich Querschubverformung

Zusammenfassung Es werden die freien Schwingungen, das Beulen und der Einfluß einer Anfangsvorspannung auf das Frequenzspektrum orthotroper, kompositer, zylindrischer Schalen im Rahmen einer Theorie, die die Querschubverformung mitberücksichtigt, untersucht. Die erhaltenen Resultate werden mit den Vorhersagen der verbesserten Loveschen Theorie und der vereinfachten Donnellschen Theorie, welche keine Querschubverformung in Betrach ziehen, verglichen.Die durchgerechneten Beispiele zeigen, daß die Querschubverformung nicht nur für kurze, komposite Schalen sondern sogar für längere Schalen mit niederem Schubmodul Bedeutung gewinnen kann.

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Nomenclature a radius of reference surface of cylindrical shell - A _i amplitudes of displacements - A _ij elastic area - B _ij elastic statical moment - D _ij elastic moment of inertia - E _ij elastic stiffness modulus - h shell thickness - k ₄₄,k ₅₅ shear correction factors - l length of cylindrical shell - L _ij functional operator - m number of half-waves in axial direction - M ,M ,M axial, circumferential and twisting moments, respectively - n number of circumferential waves - N ⁰ axial compression force - N ,N ,N axial, circumferential and shear forces, respectively - Q ,Q transverse shear forces - R ₀,R ₁,R ₂ inertia terms - t time - T matrix defined in Eq. (25) - u, v, w displacements in axial, circumferential and radial directions, respectively - U _i time-independent displacement or rotation - nondimensional axial wave parameter - , , axial, circumferential and shear strains, respectively - radial coordinate, taken positive inward - polar angle - , , curvature changes - circular frequency - nondimensional axial coordinate - density - , , , , stress components - , rotations of normal to undeformed midsurface With 6 Figures     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Rayleigh's problem for compressible viscous flow

Summary Rayleigh's problem for perfect compressible fluid is studied analytically, following the principles outlined by Howarth. It is assumed that the initial temperature jump is small in comparison with the temperature at rest, that is, =|T _w -T _o |/T _o is a small parameter. Moreover, the Mach number is assumed to be of order of ^1/2, and using the requirement of equal order of smallness for important terms of the Navier-Stokes equations one is able to determine the scales of all dimensional variables. The final set of dimensionless equations is obtained by setting a limit 0. Solution for the main component of velocity is expressed in closed form, and that for the variable part of temperature in integral form valid for any Prandtl number. Initial approximations for secondary velocity and density are also expressed in integral form. For a special case of Pr=3/4, using an expansion of a dissipative function in terms of Hermite polynomials, one obtains closed-form expressions for every unknown quantity in any approximation.     

Bending of square aluminium extrusions with aluminium foam filler

Summary An experimental programme consisting of 24 tests was carried out to study the three-point-bending behavior of square AA6060 aluminium extrusions filled with aluminium foam under quasi-static loading conditions. The outer cross section width and span of the beams were kept constant at 80 mm and 800 mm, respectively. The main parameters investigated were the foam density, the extrusion wall strength and the extrusion wall thickness. The experiments showed that the foam filler significantly altered the local deformation pattern of the beams. Simple design formulae were developed in order to predict the load bearing capacity of the foam filled beams.Notation d load cell displacement - total beam rotation - ₀₂ total beam rotation at extrusion flange yielding (non-filled beam) - ₁, ₂ beam end rotations - b outer component cross section width - h component wall thickness - L total beam span length - s central load section of beam - A _e extrusion cross sectional area - A _f foam cross sectional area - P load cell force - M total cross section moment - M _e extrusion moment - M ₀₂ maximum elastic moment capacity of extrusion - M _pl perfect plastic moment capacity of extrusion - M _f foam core moment - M _sf maximum foam core moment - M _s total initial peak moment - M _sa total moment capacity after foam failure - M _u ultimate extrusion moment capacity - M _se calculated moment resistance of extrusion at foam failure - stress, engineering - ₀₂ extrusion wall stress at 0.2% plastic strain - _U extrusion wall ultimate stress - ₀ extrusion wall characteristic stress, 0.5(₀₂+ _U ) - _f foam plateau stress - _s foam tensile failure stress - strain, engineering - ₀₂ extrusion strain corresponding to yield stress ₀₂ - _u extrusion strain corresponding to ultimate stress _U - _s foam tensile failure strain - beam curvature - ₀₂ beam curvature at extrusion flange yielding - _u beam curvature at extrusion ultimate stress - _s beam curvature at foam tensile failure strain - f extrusion section shape factor - k elastic bending stiffness ratio between foam core and extrusion - E extrusion Young's modulus - E _t extrusion tangential modulus - n extrusion material hardening constant - _f foam density - _i foam batch density,i=1, 2, 3 - x, y, z coordinate reference system (x-beam axis) - x _c distance from beam end (change in formula for curvature)     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

On the temperature dependence of the London penetration depth in a superconductor

In the framework of the electron-phonon theory of superconductivity [1], it is shown that the magnetic field penetration depth _L increases like a certain power of temperature atTT _c due to the low-lying excitations in the phonon spectrum. For the acoustic phonons with the density of states ² the penetration depth increases T ⁵. The origin of such a high power ofT is the same as that in the case of resistivity of the normal metal: the phonon corrections to the electromagnetic vertex should be taken into account, and major terms (T ³) cancel, the surviving ones having a higher power ofT. The possibility of linear and quadratic terms in _L(T) is discussed in a model of electrons interacting with two-level centers [2].     

Anomalous Depression of the Debye-Waller Factor and Observations of the Laue Spots Only at Forward X-ray Diffraction in the Light Atom Crystals as Quantum Solid

The ratio of 6·(1/2m)·(E ₀/c)² of 12.9 meV at E ₀=4 keV to k _{B D} of 2.27 meV for hcp-⁴He in the exponent 2M=[6·(1/2m)·(E ₀/c)²/k _{B D} ]·(t)sin² _B of the Debye-Waller factor D=exp(–2M) becomes 5.7, because of the small atomic mass m and the low Debye temperature _D . Conversely that of the heavy atom crystals becomes smaller than 1. An experiment on hcp-⁴He as an example of a light atom crystal at low temperature limit of (t)1 reveals that not only the maximum value of D is significantly reduced below 0.249 (=e ^–1.395) but also the values of D for all other Laue spots except the following observed six spots are crowded into a range of D<0.05. Therefore, only the six Laue spots of at 11.2 keV, (0002) at 20.3 keV, and at 14.4 keV and and at 23.9 keV in a low angular range of _B10.22° were observed over low values of e ^–1.395>De ^–3. At high angle of _B 45°, the values of E ₀ for the above six Laue spots are assigned to the region below 4.07 keV from the Bragg condition under constant values of D. Therefore, detection of them over the higher angular range of _B 45° is not impossible but quite difficult at low temperature X-ray diffraction, considering X-ray absorption by multi-thermal shields of the refrigerator, the thick sample holder as a pressure vessel and massive air in space. Generally this means that the large reduction of the Debye-Waller factor of hydrogen and helium drastically encloses the diffraction intensity and the number of observable Laue spots within lower bounds. This is the reason why definite Laue spots in the light atom crystals of hcp-⁴He could be observed only by forward X-ray diffraction. Conversely the recoil fraction of the diffuse scattering expressed by 1–D concomitantly increases as a major part of the total scattering. A proposal to measure thermal diffuse scattering as well as pressure experiments will provide insight into the wave-like character of constituent atom in solid helium.     

Natural convection flow of a viscous fluid about a truncated cone with temperature dependent viscosity

Summary The two-dimensional natural convection flow of a viscous incompressible fluid with temperature dependent viscosity about a truncated cone is considered. The governing equations for the flow are obtained by using suitable transformations and solved by using an implicit finite difference method. Perturbation solutions are obtained near the leading edge and in the downstream regime, and the results are obtained in terms of the local skin friction coefficient and the local Nusselt number. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The dimensionless velocity profiles and viscosity distribution are also presented graphically for various values of the viscosity variation parameter, , for small values of the Prandtl number appropriate for liquid metals.Nomenclature x Streamwise coordinate - x ^* Distance measured from the leading edge of the truncated cone - x ₀ Distance of the leading edge of the truncated cone measured from the origin - y Transverse coordinate - u Velocity component in thex-direction - v Velocity component in they-direction - f Dimensionless stream function - g Acceleration due to gravity - T Temperature of the fluid - T Temperature of the ambient fluid - T _w Surface temperature - Pr _x Prandtl number - Gr _x Local Grashof number - Stream function - Dimensionless temperature function - Dimensionless distance - Similarity variable - Nu _x Nusselt number - C _f Skin friction - Thermal conductivity - Fluid density - Kinematic viscosity - Viscosity variation parameter - Coefficient of thermal expansion - Viscosity of the fluid - Viscosity of the ambient fluid at infinity - Thermal diffusivity     

Anisotropy in ac losses near the irreversibility field of Bi2Sr2CaCu2O8

The ac susceptibility under a biased dc field near the irreversibility field (H _irr) of a Bi₂Sr₂CaCu₂O₈ single crystal has been measured. The frequency dependence, the ac-power dependence, and the nearly lossless character of the vs.H _dc curve forHa-axis have been roughly explained from a reversible (elastic) fluxoid motion, while those forH c-axis have been explained from a thermally assisted flux-flow (TAFF) model. The obtained parameters are discussed in relation to anisotropic flux-pinning mechanisms in the layered structure of this compound.     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response