Mutual friction and the thermal conductivity of superfluid helium near Tλ

Temperature gradients in superfluid helium carrying a heat current in a 13.8-mm-wide tube or in a 0.1-mm-wide slit have been measured at 0.09 m°K–T<16 m°K. The results are interpreted in terms of a mutual friction force between the normal component of He II and vortices in its counterflowing superfluid component. This force is found to diverge near T with a mutual friction constant proportional to (T–T)^T 0.35±0.06.     

Aluminum. II. Derivation of C v0from C p and comparison to C v0 calculated from anharmonic models

The specific heat at constant pressure, C _p, of aluminum measured by Ditmars, Plint, and Shukla has been reduced to the volume V ₀ appropriate for 0 K employing the Murnaghan equation. The C _v0 thus obtained is compared with the theoretical C _v0 calculated in the harmonic and the lowest-order anharmonic approximation from three different pseudopotentials (Harrison, Ashcroft, and Dagens-Rasolt-Taylor) as well as a phenomenological Morse potential. The higher-order ( ⁴) anharmonic contributions are calculated from the same nearest-neighbor Morse potential as in the lowest-order anharmonic theory. The role of the vacancy and the higher-order anharmonic contributions to C _v0 has been examined and we conclude that the ⁴ contributions to C _v0 are much smaller than the vacancy contribution. After removal of the vacancy contribution, the reduced C _v0 is found to be in excellent agreement with the Ashcroft and Harrison pseudopotentials as well as the Morse potential including the ² and ⁴ contributions to C _v0.     

Constant-pressure heat capacity of a Bose fluid immediately above the λ point

The heat capacityC _P of a Bose fluid immediately above its point is shown to depend solely on the nature of its low-momentum quasiparticles. If these quasiparticles are only weakly interacting, then it is possible to specify uniquely the limiting behaviorC _P (TT ⁺ ) from a knowledge of the quasiparticle energy-momentum relation '(K) in the low-momentum limit. Thus, phonon-type behavior is shown to result in a finite cusp forC _P (T ⁺ ). The relevance of these results to liquid⁴He is discussed.     

Condensate fraction of liquid 4He

We calculate the fraction C _F of atoms in the ground state of liquid ⁴He for a fluid density of 0.023 atom/»³ at various values of temperature and find a good fit with the law C_F(T)=C_F(0)[1–(T/T)³], where T is the transition temperature; this law gives C _F = 2.3 % at T = 1.2 K, which agrees with the result of a recent high-energy neutron diffraction experiment. We further show that future experiments in the temperature range 1.8 K T T with a statistical error of 1 % or larger will not detect the condensate. A single experiment is suggested to differentiate between our work and an ODLRO type of theory.     

Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity _h of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density and specific heat c as the anisotropic materials, the thermal conductivity _h is shown to be equal to , which is a geometrical mean of the thermal conductivities in the direction of the plane _x and the thickness _y of the anisotropic materials. For an alumina silica blanket (=125 kg·m^–3), the thermal conductivities _h , _x , and _y were measured in the temperature range between –140 and 300°C using the transient hot-wire method for _h and the cyclic heat method for _x and _y . In the same way, the thermal conductivities _h , _x , and _y of a rock wool (=121 kg·m^–3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of _x , it is confirmed that the proposed method can estimate the measured values reasonably well.     

Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed, non-singular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields. The near-field singular stress has the form =C ₀(,z)r ^-/12' +D ₀ (0,)R The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 percent (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second singularity is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer was about 0%, 2%, 4%, and 5% of the total specimen thickness for Poisson's ratio of 0.0, 0.3, 0.4, and 0.45, respectively.Because there are two singular fields near the free surface, the strain-energy-release rate (G) is an appropriate parameter to measure the severity of the crack front. The G-distribution for M-T and bend specimens were different.Nomenclature a crack length, m - E Young's modulus, GPa - G strain-energy-release rate, J/m' - G _p plane-strain, strain-energy-release rate, J/m² - H height of specimen, m - P load per unit length, N/mm - R, O, spherical coordinate system - r, O, z cylindrical coordinate system - S remote tension stress, N/mm² - t specimen thickness, m - t _ti ith layer thickness, m - u, v, w displacements inx-, y-, andz-directions, m - x, y, z Cartesian coordinates, m - W half-width of the specimen, m - power of the stress singularity - power of displacement field - v Poisson's ratio - _y normal stress in y-direction, GPa     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Investigation of the thermophysical properties of fireclay ceramics in the temperature range 80°–1200° K

The thermal conductivity, diffusivity, and specific heat of fireclay ceramics have been investigated over a wide temperature range in various gases. A method of calculating the thermophysical properties of the materials is given, whose use is fully justified by experiment. A method is described of theoretically determining the thermophysical properties of ceramics in various gases on the basis of investigations of these materials in air.Notation _eff effective thermal conductivity of porous material - _sk thermal conductivity of skeleton - _c thermal conductivity of continuous phase of skeleton - _d thermal conductivity of dispersed phase of skeleton - V_d volume fractions of disperse phase of skeleton - P) volume porosity, h/L=f(P) [5] - c) Stefan-Boltzmann constant - T) absolute temperature, °K - d) pore diameter - a thermal diffusivity     

Thermal Diffusivity Measurement of Two-Layer Optical Thin-Film Systems Using Photoacoustic Effect1

In this study, we designed and developed two-layer antireflection (AR) optical coating samples on glass substrates, using different evaporation conditions of coating rates and substrate temperatures for two dielectric materials, MgF₂ and ZnS, with different refractive indices. The through-plane thermal diffusivity of these systems was measured using the photoacoustic effect. The optical thicknesses of MgF₂ and ZnS layers were fixed at 5/4 (=514.5 nm) and , respectively, and the thermal diffusivities of the samples were obtained from the measured amplitude of the photoacoustic signals by changing the chopping frequency of the Ar⁺ laser beam. The results demonstrated that the thermal diffusivity of the sample fabricated under the conditions of 10Å·s^–1 and 150°C had the maximum value and that the results were directly related to the microstructure of the film system.     

Thermal conductivity and heat capacity of solid silver bromide (AgBr) under pressure

The thermal conductivity, , and the heat capacity per unit volume, c _p , have been measured for solid silver bromide (AgBr) using the transient hot-wire method. Measurements were made at temperatures in the range 100–400 K and at pressures up to 2 GPa. c _p was found to be independent of temperature and pressure over these ranges. of AgBr was found to be similar to that of AgCl, which was measured previously. For AgBr, only acoustic phonons needed to be taken into account up to 340 K, but optic phonons probably carried some heat at higher temperatures. The Leibfried-Schlömann (LS) formula could describe the ratio (AgCl)/(AgBr), but not the ratio (1 GPa)/(0) for either substance. An empirical modification of the LS formula could describe the latter ratios but not the former. Further theoretical developments are required for understanding of (P) for even such relatively simple substances as AgCl and AgBr.     

A synthesis of mono-crystalline silicon nitride filaments

A catalytic process for synthesis of pure, mono-crystalline-Si₃N₄ filaments, with iron particles of some micrometres in diameter as catalyst, was investigated. Silicon subhydrides, producedin situ by reaction of silicon powder with hydrogen at 1300° C, were used as the silicon source. Experiments with molecular nitrogen as the nitrogen source failed, but the use of ammonia was successful. At 1300° C mono-crystalline-Si₃N₄ filaments up to some micrometres in diameter and some centimetres in length were successfully produced. These filaments exhibit tensile strength values between 30 and 50 GPa, and Young's modulus values between 550 and 750 GPa.     

Calculation of flow and heat transfer over the radiation section of a fluidized bed furnace-equipped boiler

Calculations of flow and heat transfer in the furnace volume and in the radiation part of the E-160 boiler (under the Russian trademark) for Tash-Kumyrsk coal burning at atmospheric and elevated pressures are made.Notation z boiler height coordinate - d/dz burnout function - t temperature, °C - T absolute temperature, K - C_p gas heat capacity - p gas density - _T, molecular and turbulent thermal conductivity - , _T molecular and turbulent viscosity - q_R radiant energy flux - Q_chem power of chemical heat release - u velocity All-Union Research and Designing Institute of Metallurgical Heat Engineering, Nonferrous Metallurgy and Refractory Materials. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 284–286, March, 1993.     

Critical phenomena of liquid4He in the vicinity of the upper λ point

We determinedC _p along six isobars near T in the vicinity of the upper superfluid transition point (upper point) from measurements ofC _v and (P/T) _v along six isochores.C _p was analyzed with the functionC _p =(A/)^–(1+D^–)+B for T>T, and the same function with primed coefficients for T, whereD denotes the strength of the effect of the irrelevant variable. The present work clarified the effect of the pressure (irrelevant variable) on the critical behavior of ⁴ He near T, that is, the correction term due to the irrelevant variable increases with pressure even in the small range 3×10^–3. This indicates that the pressure depresses the true critical region. The universality of the amplitude ratioA/A was confirmed even in the vicinity of the upper point by specific heat measurements. With constraints ==–0.02, ==–0.5, andB=B the pressure-independent amplitude ratiosA/A=1.088±0.007 andD/D=0.85±0.2 were obtained.AD/AD=0.93±0.2 implies that the pressure has a similar effect onC _p in the normal fluid and superfluid regions, within experimental errors.     

Density correlation function in superfluid helium nearT λ

The previously calculated hydrodynamic form of the density correlation function of liquid helium is written out explicitly forT nearT . This function, which is proportional to the intensity of light scattered from the fluid, has a finite value at =0, which grows asTT from below. In evaluating the precise form of this contribution in terms of transport coefficients, it is important to keep terms of order (C _p /C _v )–1.     

The directional solidification of Pb-Sn alloys

Directional solidification experiments have been carried out on different Pb-Sn alloys as a function of temperature gradient G, growth rate V and cooling rate GV. The specimens were solidified under steady state condition with a constant temperature gradient (50 °C/cm) at a wide range of growth rates ((10–400) × 10^–4 cm/s) and with a constant growth rate (17 × 10^–4 cm/s) at a wide range of temperature gradient (10–55 °C/cm). The primary dendrite arm spacing, ₁, and secondary dendrite arm spacing, ₂, were evaluated. This structure parameters were expressed as functions of G, V and GV by using the linear regression analysis. The results were in good agreement with the previous works.     

Influence of structure on the thermophysical characteristics of porous metals

An experimental investigation of the thermal conductivity and thermal diffusivity of porous copper and iron with different porous structures is made. A dependence of the thermophysical characteristics on the degree of porosity and the mean pore size is established. A correlation with the structural model made it possible to take into account the dependence of the pore size distribution on the parameters.Notation , _com thermal conductivity coefficients of porous and compact materials - ₁, ₂ thermal conductivity coefficients for the cases of isolated and intercommunicating pores - ₁ ^* , ₂ ^* thermal conductivity coefficients of monodisperse structures - a,a _com thermal diffusivity coefficients of porous and compact materials - C _p specific heat - density - P porosity - r, size and mean size of pores - r _str structural parameter - D variance of pore size - R size of an elementary cell - F(r, ,D) differential function of pore size distribution Altai State University, Barnaul. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 720–723, September–October, 1995.     

Thermal conductivity of B2O3 glass under pressure

The thermal conductivity, , of vitreous boron trioxide was measured, using a hot-wire procedure, from 170 to 570 K and under pressures of up to 1.7 GPa. The thermal conductivity at room temperature and zero pressure was found to be 0.52 W · m^–1 · K^–1. The values of the logarithmic pressure derivative, g = d(ln )/d(ln ), where is the density, were found to be 1.1 for uncompacted glass and 0.7 for glass compacted to 1.2 GPa. The variation of with temperature at constant density was approximately linear, with a positive slope of 1.38×10^–3W·m^–1·K^–2.     

Heating of a bulky body by a circular heat source with heat elimination from the surface taken into account

Results of an analytical and numerical solution of the problem, in a form suitable for the determination of material properties, are given.Notation =(t–t_c)/(q₀R) and T= Bi= (t–t_c)/q₀ dimensionless temperature - q₀ heat flux, W/m² - Bi=R/ Blot criterion - R radius of the heating spot, the characteristic dimension, m - ¯r, ¯z radius and depth, m - r=¯r/R, z=¯z/R dimensionless radius and depth - time, sec - Fourier number - criterion - coefficient of heat elimination, W/m²·deg - heat conductivity, W/m·deg - c specific heat, J/kg·deg - density, kg/m³ - a thermal diffusivity, m²/sec - t _c temperature of the external medium Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 524–526, March, 1981.     

Thermal conductivity of solid NaF under high pressure

The thermal conductivity () of solid NaF has been measured over the temperature (T) range 100–350 K and at pressures (P) up to 2.5 GPa, using the transient hot-wire method. Results for (T,P) could be described to a good approximation by the Leibfried-Schlömann formula. It was found that the isochoric temperature derivative of the thermal resistivity W (= ^–1) increased systematically with the mass ratio for the B1-type phases of the sodium and potassium halides.     

Derivation of the thermal resistance of the contact between systems with corrugated surfaces

Contact thermal resistance is considered for joints with corrugated surfaces. Formulas are derived that are confirmed by experiment.Notation R_c total thermal resistance of contact, m₂ · deg/W - R_M, R_cl thermal resistance of real contact and of contactless region, m₂· deg/W - coefficient of contraction of heat flux lines to spots of real contact - S_m, S_c S_o real, contour and nominal areas of contact surfaces, m² - a mean radius of contact spot, m - ¯_M reduced thermal conductivity of contact (1 and 2) materials, W/m · deg - _c thermal conductivity of contact medium, W/m · deg - n number of contact spots of microroughnesses at nominal contact surface - area ratio - b, parameters of support curve of surface - r radius of roughness, m - q_c contour pressure, N/m₂ - N normal load, N - coefficient depending on deformation mechanism - B coefficient characterizing properties - K coefficient depending on and - h_max h_av maximum and mean height of microroughness protrusions, m - P specific normal load to contact surface, N/m² - E Young's modulus, N/m² - R_w wave radius, m - n_w numbers of wave contact spots at nominal surface - L_el, L_p longitudinal and transverse wave pitch, m - _eq equivalent thickness of intercontact laminar, m - H_av mean height of waves, m - relative approach of surfaces under load - c approach of surfaces under load - HB Brinell hardness, N/m₂ - Poisson's ratio - ₂ relative contact surfaces Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 846–852, May, 1971.