Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Study of Broadband Long-Focus Optics for Synchrotron Infrared Diagnosis of Low-Energy Electron Beams

A special optical device for measuring the geometry and current parameters in electron rings by synchrotron infrared radiation is designed, fabricated, and studied. The optical elements of the device are made of an optical ceramic and operate at 1–8 m. The study results are presented.     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Eutectoid decomposition mechanisms in hypoeutectoid Ti-X alloys

A TEM study has been made of the bainite reaction in five hypoeutectoid Ti-X alloys, where X was successively cobalt, chromium, copper, iron and nickel. Rational orientation relationships were demonstrated amongst eutectoid , eutectoid intermetallic compound and the matrix in Ti-Ni, Ti-Co and Ti-Cr. Formation of Ti₂Co at : boundaries was observed. Eutectoid in bainite was found to be slightly misoriented with respect to proeutectoid , indicating that it is separately nucleated, perhaps sympathetically, rather than the result of the continued growth of proeutectoid . Eutectoid Ti₂Co and Ti₂Cu crystals in bainite were approximately equiaxed whereas Ti-Cr₂ crystals were elongated, a result ascribed to a ledge height-to-spacing ratio / at intermetallic compound crystal: boundaries approaching that of eutectoid (: boundaries in Ti-Cr but not in the other two systems. In the Ti-Fe alloy, eutectoid and eutectoid TiFe were directly observed to have ledged interphase boundaries with their matrix, but with different inter-ledge spacings and growth directions. Observation of pearlite lamellae growing normal to the broad faces of proeutectoid plates in the Ti-Ni alloy indicates that this mode of eutectoid decomposition, like that of bainite, can develop from partially coherent interphase boundaries. The suggestion was offered that pearlite forms when approachesh at the nucleating proeutectoid : interface and that bainite develops when h at this interface.     

The anomalous thermal boundary resistance in superfluid4He near Tλ

The anomalous thermal boundary resistance R of superfluid⁴He near the lambda point T was studied in a cell with parallel copper faces and with various fluid layer thicknesses. The study was made as a function of the heat current Q and reduced temperature (T — T)/T = . In all cases, R tends to a maximum value R_itmax at T = T. This value is independent of Q, and is reproducible for various experiments. This contrasts with the regular boundary resistance which can vary considerably between successive experiments. Near T, the limiting slope dR/d¦¦ is found to be proportional to Q^–1, and this leads to a scaled representation of the data. This analysis is extended to data of similar experiments with gold plated copper surfaces by Duncan and Ahlers and by Zhong et al. The measurements of R over the whole range of¦¦ where it is observable are discussed and compared with previous experiments.     

Magnetic penetration depth measurements with the microstrip resonator technique

The microstrip resonator technique is a convenient way to sensitively measure the temperature dependence of the magnetic penetration depth (T) in superconducting thin films. Because the method relies on measuring the resonant frequency of a high-Q transmission line resonator at microwave frequencies, one can very precisely measure small changes in (T). This technique is applied to studying the low-temperature dependence of (T), since that is in principle a measure of the low-lying pair-breaking excitations of the superconductor. We find that the penetration depth in niobium films is consistent with the predictions of weak coupled BCS theory. The low-temperature dependence of (T) inc-axis YBa₂Cu₃O_7– films can be interpreted as either a weak exponential or as a power law. In addition, the measured value of (0) is found to be strongly dependent on the form of the temperature dependence for (T) used in fitting the data. Best fits over the entire temperature range are obtained with a BCS temperature dependence having values for 2(0)/k _BT_c strictly less than 3.5, consistent with our measurements of the temperature dependence of (T) at low temperatures in YBa₂Cu₃O_7– .     

Superfluid density near the lambda point of4He under pressure

The superfluid density in ⁴ He was determined near T from the second-sound velocity as a function of T–T and pressure. The critical exponent of the superfluid density was found to depend, even slightly, on the pressure. Furthermore, the fundamental length ₀ in the coherence length = ₀ [1–(T/T)]^–' seemed to be proportional to the mean interatomic distance. The implications of the results are also discussed.This work was partly supported by The Ito Science Foundation and by The Nishina Memorial Foundation.     

A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands     

Flux-line cutting in type II superconductors

Experimental evidence for flux-line cutting in superconductors (intersection and cross-joining of singly quantized vortices) is briefly reviewed. The interaction energy between two straight vortices tilted at an angle ( 0)is then shown to be finite in the London model, i.e., in the limit of vanishing core radius. Next, the activation energy and maximum interaction force are calculated for the vortices in an analytic approximation to the Ginzburg-Landau theory. Here two competing interactions determine the behavior. Electromagnetic repulsion (0 < < /2) varies as cos and decays over distances scaled by the penetration depth , while core attraction is independent of and varies over distances scaled by the coherence length . The force is always repulsive at large flux-line separation (0 < < /2) and its maximum decreases rapidly as decreases, so that flux-line cutting isexpected to be more probable in low- materials. The calculations provide a basis for explaining longitudinal flux-flow resistance as well as some intriguing magnetization behavior in the same configuration.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division, and by the Deutsche Forschungsgemeinschaft.On leave from Max-Planck-Institut für Metallforschung, Institut für Physik, Stuttgart, West Germany.On leave from New University of Ulster, Coleraine, Northern Ireland.     

Relations Between Transport Coefficients in Lennard–Jones Fluids and in Liquid Metals

Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations performed on Lennard–Jones (LJ) fluids. Typically the individual transport coefficients: self-diffusion coefficients, D, shear viscosity, _s, bulk viscosity, _B, and thermal conductivity, , agree within a factor of two of the exact results over the fluid and liquid parts of the phase diagram, which seems reasonable in view of the approximations involved in the models. We have also considered the ratio, /_s, and the product, D_s, for which simple analytic expressions exist in the hardsphere models. These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functions, Tankeshwar has recently related the ratio /D to thermodynamic quantities, in particular, to the differences in specific heats, C _p – C _V, and to the isothermal compressibility, T. Using D and thermodynamic values taken solely from LJ MD simulations, his relation was tested and found to give typically better than ~20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liquid metals are considered. In this case, is dominated by its electronic contribution, which is related approximately to the electrical conductivity by the Wiedemann–Franz Law. Some theoretical results for the electrical conductivity of Na are referenced, which allow a semiquantitative understanding of the measured thermal conductivity of the liquid metal. Shear viscosity is also discussed and, following the work of Tosi, is found to be dominated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.     

Differential-flow-induced instability in a cubic autocatalator system

The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, A + 2B 3B, B C, with the reactant A being replenished by the slow decay of some precursor P via the simple step P A. The reaction is considered in a differential-flow reactor in the form of a ring. It is assumed that the reactant A is immobilised within the reactor and the autocatalyst B is allowed to flow through the reactor with a constant velocity as well as being able to diffuse. The linear stability of the spatially uniform steady state (a, b) = (µ^–1, µ), where a and b are the dimensionless concentrations of the reactant A and autocatalyst B, and µ is a parameter reflecting the initial concentration of the precursor P, is discussed first. It is shown that a necessary condition for the bifurcation of this steady state to stable, spatially non-uniform, flow-generated patterns is that the flow parameter > _c(µ, ) where _c(µ,) is a (strictly positive) critical value of and is the dimensionless diffusion coefficient of the species B and also reflects the size of the system. Values of _c at which these bifurcations occur are derived in terms of µ and . Further information about the nature of the bifurcating branches (close to their bifurcation points) is obtained from a weakly nonlinear analysis. This reveals that both supercritical and subcritical Hopf bifurcations are possible. The bifurcating branches are then followed numerically by means of a path-following method, with the parameter as a bifurcation parameter, for representatives values of µ and . It is found that multiple stable patterns can exist and that it is also possible that any of these can lose stability through secondary Hopf bifurcations. This typically gives rise to spatio-temporal quasiperiodic transients through which the system is ultimately attracted to one of the remaining available stable patterns.     

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a3He-4He mixture

Measurements of the thermal conductivity are reported for an 80%³He-20%⁴He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of³He. Using again the assumption that the observed conductivity can be decomposed into a sum of a regular and a singular contribution _reg and _sing, it is shown that along two near-critical isochores, _sing diverges. In particular, along the isochore showing the largest at the phase transition, the divergence is nearly the same as for³He and can be roughly characterized by a simple power law (T-T_c)^– with 0.58. This observation is contrary to predictions that foresee _sing0 asT _c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure³He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for³He nearT _c is calculated from heat conductivity, viscosity, and specific heat data.Work supported by Grant DMR 8024056 of the National Science Foundation.     

Principles of heat exchange in evaporation of a liquid film on a smooth horizontal tube

Experimental data are presented for the local heat liberation coefficient for flow of a liquid film on a smooth horizontal tube, permitting refinement of the concept of the heat exchange mechanism.Notation , , ,a kinematic viscosity, thermal conductivity, density, and thermal diffusivity of liquid - liquid film thickness - irrigation density Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 736–739, May, 1988.     

Variational method for measuring dielectric parameters of polar liquids at ultrahigh frequencies

Conclusions Owing to the use of nomograms the above method is universal and rapid. It is independent of the frequency at which the values of and are measured, and it is equally applicable for measuring dielectric parameters of polar liquids which are highly absorbent at ultrahigh frequencies and have one or two clearly expressed minima in the relationship of tol, and for liquids with low dielectric losses in the uhf range, whose measurement with adequate precision is difficult by other methods. Among the deficiencies of the suggested method one should note the two values obtained for _d and tan /2 from the nomogram readings. However, this deficiency can easlly eliminated either by comparing the two values for _d and tan /2 with those obtained for them from a similar nomogram and the second minimum in the relationship of tol, or by an approximate evaluation of _d and tan /2 by means of any other less precise measuring method.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 48–49, October, 1970.     

Specific heat near the lambda point in 4He and 3He-4He mixtures: Test of universality of the critical exponent and the amplitude ratio,and observation of the critical-tricritical crossover effect

The specific heat under saturated vapor pressure of pure ⁴He and of six ³He-⁴He mixtures up to X = 0.545 was measured in the temperature range 3 × 10^–6 <¦T-T ¦ <10^–2 K. The critical exponents and along the path = are independent of X up to X = 0.545, where (= ₃ – ₄) is the difference between chemical potentials. If we take account of higher order terms, the exponent (= ) and the amplitude ratio A /A are independent of X up to X = 0.545. The values of and A /A are –0.023 and 1.090, respectively. The critical-tricritical crossover effect was observed for X = 0.545 and the boundary of crossover region closest to the critical region was at /T = (1–2) × 10^–4, where is the distance ¦T – T ¦ along the path = . This value is in good agreement with the estimated value by Riedel et al. But, remarkably, in the case of X = 0.439 this effect was not observed.     

Gneralized McMillan tunneling model of the superconducting proximity effect. Specific heat jump

The reduced specific heat jumps for the superconducting (S) side and the normal (N) side of a strongly coupled N-S composite have been calculated by using the generalized McMillan tunneling model of the superconducting proximity effect. Both cases _N = 0 and _N 0 (where _N is the BCS interaction constant) have been studied. The results obtained by using the generalized model are significantly different from the ones given by the McMillan tunneling model.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Heat capacity near the lambda point in 4He under pressure. Experimental test of scaling laws and universality

C _p along six isobars was determined near T from measurements of C _v and (P/T) _v along isochores. The critical exponent was independent of pressure, while was dependent on pressure, when the data are fitted to a single power law. The value of A/A was found to be 1.04 ± 0.05 over the entire pressure range by adding a higher order singularity. That is, the results obtained are the best fit using renormalization group theory, but are partly inconsistent with the heat capacity measurement by Ahlers.     

Heat transfer of a semitransparent plate under conditions of a regular regime of the second kind

The kinetics of the cooling of a plane semitransparent layer under conditions of a regular regime of the second kind is analyzed.Notation time - T temperature - T_e temperature of the surrounding medium (the ambient temperature) - T° initial temperature of the layer - h_e coefficient of convective heat exchange - x coordinate - coefficient of absorption of the substance - n index of refraction - B(, T) surface density of radiation of a black body - C bulk specific heat - K thermal conductivity - wavelength of the radiation - _t range of wavelengths in which the material is partially transparent - _op range of wavelengths in which the material is opaque - degree of blackness of the surfaces in the range of _op - R() coefficient of reflection from the inner surfaces of the layer - ⁺ intensity of the rays consisting of acute angles with the inner normal to the surface x = 0 - ^– intensity of rays in the opposite direction - q thermal flux - angle measured from the inner normal to the surface x = 0 Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 541–546, September, 1981.     

Eutectic solidification characteristics of Bridgman grown AI-3Fe-0.1V alloy

Eutectic solidification characteristics of Al-2.85 wt%Fe-0.12 wt% Valloy have been investigated by steady-state growth over the range of solidification front velocity from 51 to 1030m/s and temperature gradient 8 to 15 K/mm. Increasing growth velocity displaced the Al-Al3Fe eutectic by Al-AlxFe eutectic rather than by the Al-Al6Fe eutectic obtained for the binary Al-3 wt%Fe alloy. A fully Al-AlxFe eutectic structure has been obtained for the first time in the vanadium-containing alloy over the growth velocity range from 71 to1030m/s except at 100 and 510m/s where some Al dendrites were present in the eutectic matrix. TheAl-AlxFe eutectic was observed to undergo a morphological transition from lamellar to rod-like with increasing growth velocity concurrently with formation of a cellular eutectic structure. It was found that the relationship = Av–1/2, between eutectic spacing and growth velocity v, was applicable with A = 22.4 ± 1.8 and 13.8 ± 2.1 m3/2s–1/2 for lamellar and rod-like Al-AlxFe eutectics, respectively.