An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

Coarsening of precipitates and dispersoids in aluminium alloy matrices: a consolidation of the available experimental data

Experimental data on the coarsening of precipitates and dispersoids in aluminium-based matrices are reviewed. Available data are tabulated as K=(r ³–r ₀ ³ )/t where r ₀ is the initial particle radius and r is its value after time t at temperature T, and then plotted as log (KT) against 1/T for consolidation and assessment. The considerable body of data for -A₃Li in Li-containing alloys is well represented by K=(K ₀/T) exp (–Q/RT) with K ₀=(1.3 _–0.5 ^+3.0 ) × 10^–13m³Ks^–1 and Q=115±4kJ mol^–1. The relatively limited data for and in Cucontaining alloys are representable by the same relationship with K ₀4 × 10^–8 and — 4 × 10^–10 m³ Ks^–1, respectively, and Q — 140 kJ mol^–1. Available data for coarsening of L1₂ ^– Al₃(Zr, V) and related phases in Zr-containing alloys and of Al₁₂Fe₃Si and related phases in Al-Fe based alloys indicate (i) rates of coarsening at 375 to 475 °C (0.7 to 0.8T_m) five to eight orders of magnitude less than would be expected for , and in this temperature range, and (ii) high activation energies of 300 and 180 kJ mol^–1, respectively.     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

High-resolution measurements of the heat capacity of MnBr2·4H2O near its Néel temperature

The heat capacityC _P of the antiferromagnet MnBr₂ ·4H₂O has been measured for polycrystalline and single-crystal samples nearT _N(2.123 K) with temperature resolution of 1×10^–6 K. Similar rounding of the lambda anomaly is found in both cases. For |1 –T/T _N| 10^–1 all data can be well fitted by assuming the samples to consist of many independent subsystems obeying the same power laws but with a Gaussian distribution ofT _N's having a width of 1.1×10^–3 K. ForT>T _N, we findC _P ^–0.12, essentially as predicted for three-dimensional Ising models in the critical region. ForT<T _N and 10^–3 10^–1,C _P ln , which approximates Ising model behavior in this interval but is not expected to be valid for 10^–4. ForT>T _N and 2.5×10^–1, C_P agrees well with predictions for the classical Heisenberg model. This crossover at 10^–1 is consistent with the known anisotropy of the salt and with present theory. The data forT>T _N in the interval 10^–4 10^–3, while not in the range of obvious rounding, appear to be strongly influenced by the mechanism responsible for that rounding.Work supported by the National Science Foundation and the Office of Naval Research. Based on a thesis submitted by L.W.K. to Carnegie-Mellon University in partial fulfillment of the requirements for the Ph.D. degree. A preliminary account of this work was presented at the Atlantic City meeting of the American Physical Society, March 1972 [Bull. Am. Phys. Soc. 17, 299 (1972)].     

Electrical conductivity in hot-pressed nitrogen ceramics

The a.c. and d.c. electrical conductivities of some hot-pressed polycrystalline nitrogen ceramics have been measured between 400 and 1000° C. The materials examined were Si₃N₄, 5.0% MgO/Si₃N₄ and two sialons, Si_(6–z) · Al _z · O _z · N_(8–z) having z 3.2 and z 4.0 respectively. The electrical behaviour of all the materials showed similar general features. The d.c. conductivities were about 10^{–10 –1} cm^–1 at 400° C and rose to between 10^–6 and 10^{–5 –1} cm^–1 at 1000° C. The a.c. Data, taken over the frequency range 15 Hz to 5 kHz showed that below about 500° C the a.c. conductivity ( _a.c.) varied with frequency as _a.c. ^s where 0.7 _d.c.) agreed well with the relation _d.c. = A exp(–B/T ^1/4). Above 700° C both the a.c. and d.c. conductivities followed log T ^–1. Hall effect and thermoelectric power measurements enabled the Hall mobility to be estimated as less than 10^–4 cm² V^–1 sec^–1 at 400° C and showed that the materials were all p-type below 900° C and n-type above 900° C. The electrical properties of all four materials are consistent with the presence of a glassy phase.     

Effect of heat transfer on the limiting characteristics of magnetofluid seals

A procedure is developed for calculating the maximum temperature in the working gap of a magnetofluid seal and the limiting rate of rotation of hermetically sealed shafts.Notation T_max maximum temperature of heating of the sealing fluid, °C - thickness of the sealing layer, m - v₀ linear velocity of rotation of the surface of the hermetically sealed shaft, m/sec - density, kg/m³ - viscosity, N·sec/m² - c specific heat capacity at constant pressure, J/(kg·deg) - coefficient of thermal conductivity, W/(m·deg) - transfer coefficient, W/(m³·deg) - q heat flux, W/m² Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 58–65, January, 1982.     

The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Molar momentum and heat transfer

Universal relations governing the molar transfer of momentum and heat are derived on the basis of a hypothesis about the dependence of the boundaries of the molar transfer region on the flow structure and with the use of a special mathematical transformation.Notation u average longitudinal velocity, m/sec - T average temperature, °K - T_w wall temperature, °K - kinematic viscosity coefficient, m²/sec - density, kg/m³ - c_p specific heat, J/kg·K - tangential stress, N/m² - t_w tangential stress at wall, N/m² - q_w specific heat flux at wall, W/m² - u_*=_w/ dynamic velocity, m/sec - *=q_w/c_pu_* characteristic temperature, °K - thickness of boundary layer, m - ₀ thickness of laminar sublayer, m - l = /u transverse space scale of average mole at wall, m - y⁺ = y/l _22C6; dimensionless coordinate - u⁺=u/u* dimensionless velocity - ⁺=(T_w – T)/* dimensionless temperature - ⁺=/_w dimensionless tangential stress - R=In (y⁺/ _o ⁺ )/In (⁺/ _o ⁺ ) generalized dimensionless co-ordinate - U = (u⁺ - u _o ⁺ )/(u _o ⁺ - u _o ⁺ ) generalized dimensionless velocity - Pr Prandtl number Indices * flow parameters evaluated at y⁺=1 - parameters at y⁺=⁺ - 0 parameters at y⁺= _o ⁺ - w parameters at wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 441–448, September, 1981.     

X-ray studies on the thermal expansion of tellurium dioxide

Using a Unicam 19 cm high temperature powder camera, the precision lattice parameters of tellurium dioxide have been determined at different temperatures in the range 30 to 461 °C. Using this data, the coefficients of thermal expansion, and parallel and perpendicular to the principal axis respectively, have been evaluated. The temperature dependence of the coefficients of thermal expansion is represented by the following equations: =29.673×10^–6+1.552sx10^–8 T+1.069sx10^–10 T ² =9.875sx10^–6–5.440sx10^–9 T+4.572sx 10^–12 T² HereT is the temperature in °C. The thermal expansion of tellurium dioxide has been explained in terms of the interionic distances.     

Preparation of Ultrafine Tetragonal ZrO2–CeO2Solid Solutions

Nanometer-sized tetragonal Zr_{1 – x} Ce _x O_{2 –} powders were prepared by hydroxide precipitation and sol–gel processing. The effects of gel-aging time and solution concentration on the phase composition and particle size of the powders were studied. The ceramics prepared by sintering ultrafine powders at 1500°C had a density of 6.0 g/cm³, open porosity of 4%, and closed porosity below 1%.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Thermal conductivity of argon and argon-neon mixtures at high temperature

The thermal conductivity of neon and argon-neon mixtures is studied in the temperature range 400–1500°K. This is the first recording of such data above 793°K.Notation T_g true temperature drop in gas layer °K - ¯T temperature, °K, Q, effective thermal flux, W - Q_t, Qr thermal flux transmitted by thermal conductivity and radiation, respectively, W - T_sh correction for temperature shift, % - thermal conductivity of gas mixture, W/m·°K - x_i a molar concentration of neon - _i, _i, _ij, _ij potential function parameters for inter molecular interaction of homogeneous and inhomogeneous molecules - slope of exponential repulsion term Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 848–856, November, 1977.     

Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Attenuation of first sound has been measured in ⁴He under saturated vapor pressure near the lambda temperature T at frequencies /2 ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function (, ) = ^1+y F(), where = ₀^–x and = T/T – 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ^x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.Based on a Ph.D dissertation submitted by K. Tozaki to the University of Tokyo (1977).     

Characterization of hydroxyapatite powders prepared by ultrasonic spray-pyrolysis technique

The hydroxyapatite (HAp) powder was prepared by the ultrasonic spray-pyrolysis technique; the characterization of the resulting powders was performed. Five kinds of the starting solutions with the Ca/P ratio of 1.67 were prepared by mixing Ca(NO₃)₂, (NH₄)₂HPO₄ and HNO₃; the concentrations of Ca²⁺ and PO₄ ^3– were in the ranges of 0.10 to 0.90 mol·dm^–3 and 0.06 to 0.54 mol·dm^–3, respectively. These solutions were sprayed into the heating zone to prepare the HAp powders. The heating zone was composed of two electric furnaces; the lower furnace was used for the evaporation of the solvent from the droplets (300–500°C) and the upper furnace for the pyrolysis of the precipitated metal salts (750–900°C). The easily sinterable HAp powder was prepared by spray-pyrolysing the solution with Ca²⁺ (0.50 mol·dm^–3) and PO₄ ^3– (0.30 mol·dm^–3) at the temperatures of 800°C (the upper furnaces) and 400°C (the lower furnaces). The resulting powder was composed of the spherical particles with diameters of 1 m or below. Even without the calcination and grinding operations, the relative densities of the compacts fired at 1150 and 1200°C for 5 h attained maxima 95%. The microstructure of the sintered compacts appeared to be uniform; the average grain size was 3 m. The activation energies for the grain growth of the sintered HAp compacts were 120 to 147 kJ · mol^–1 · K^–1.     

Gas absorptivity in a complete spectrum

Necessary conditions are established for the validity of the Hottel formulas for the absorptivity relative to black radiation. The formulas are used in describing the absorption of a badly mixed medium and for nonblack incident radiation.Notation x ray path in mat - p, P partial and total pressure - P_eff effective broadening pressure - T, T₀ gas and wall temperatures, °K - T_*, T_i selected temperature values - T_c weighted-mean temperature - a₀ absorptivity of the gas for black radiation - a same for a flux with nonblack spectrum - emissivity - m, u, n, , power exponents - i _0j Planck function for the center of the band, cm · W/m² · sr - I_j incident flux intensity at the center of the band j, cm · W/m² · sr - I integrated incident flux intensity, W/m² · sr - A_j integral absorption (equivalent width) of band f, cm^–1 - _j mean absorption in the band - wave number, cm_–1 - ₀ position of the band center - _j width parameter - _effj effective width - _j total width of the band j, cm^–1 - D_j mean transmissivity in the band j - S integrated line intensity, cm–1/mat - d, b spacing between lines and their half-width, cm–1 - S_j integrated intensity of the band j - L Landenburg and Reiche functions - spectral absorption coefficient, mat_–1 - (T) dimensionless function - c_i dimensionless number - R_*, R_c general notation for parameters averaged over the band and for T_c - E Elsasser function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 802–808, May, 1971.     

An analytical investigation of the longitudinal temperature profile developing during the cooling of a cryogenic pipeline

Analytical expressions are obtained for the longitudinal temperature profiles of the wall and the stream of cryogen during the cooling of a cryogenic pipeline. A comparison of the calculated data with experiment gives their good agreement.Notation T temperature, °K - density, kg/m³ - heat-transfer coefficient between wall and stream, W/m²·°K - perimeter wetted by stream, m - c heat capacity, J/kg·°K - F cross-sectional area, m² - G flow rate of cryogen, kg/sec - t time, sec - x longitudinal coordinate, m - coefficient of thermal conductivity of cryogen, W/m·°K - coefficient of dynamic viscosity, m²/sec - Pr Prandtl number - dimensionless time - dimensionless longitudinal coordinate - dimensionless longitudinal coordinate in the moving coordinate system - width of zone of heat exchange - dimensionless temperature - P pressure of cryogen, N/m² - R gas constant, J/kg·°K - dimensionality of temperature - v₁ dimensionless velocity of movement of steady temperature profile - ¯c_w integral-mean heat capacity of wall, J/kg·°K - a b, m, constant coefficients in the approximating equations. Indices: 0, initial value - w wall - g cryogen - r relative value Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 524–531, September, 1981.     

The occurrence of stress-induced α′ martensite in an (α+γ) Fe-Cr-Ni alloy

The interaction of an applied stress with the displacive shear during the martensitic transformation determined theK-S variants which formed in three types of tensile specimens, with tensile directions of 0°, 45° and 90° to a rolling direction respectively. The 3–6, 4–5 and 1–3 variants in a 0°-specimen, 1–5 and 4–5 variants in a 45°-specimen and 4-4 and 3–6 variants in a 90°-specimen are chosen asK-S variants which have the maximum value ofU/ in respective tensile directions. These variants are related to the occurrence of martensite with particular orientations as (100), (110) and (211).     

A thermally stimulated current technique for measuring the molecular parameters of Pebax,a polyether-block amide copolymer

The primary relaxation peaks of Pebax copolymer having a soft segment, poly (tetramethylene glycol) (PTMG) and a hard segment, polyamide 12 (PA12) are located at –69.5 and 18° C for a raw sample and at –71.5 and 4° C when the sample is recrystallized after fusion using the thermally stimulated current (t.s.c.) method. A comparison is made of rapid and slow cooling t.s.c. on hard-segment molecules. Applying the fractional polarization method, the modes _PTMG and _PA have been analysed. The parameters (such as activation energy and relaxation time) associated with the dipolar relaxation process of Pebax have been calculated. The maximum energy observed for modes _PTMG and _PA is 1.47 eV at – 66° C and 1.34 eV at 1° Q respectively. The elementary processes that constitute the modes _PTMG and _PA obey a compensation law with compensation temperatureT _c = –43° C and compensation relaxation time _c, = 3.4 x 10^–2 sec for mode _PTMG, andT _c = 66° C and _c = 2.8 x 1 0^–4 sec for mode _PA.     

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.