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.     

Thermal conductivity of methane

This paper reports thermal conductivity data for methane measured in the temperature range 120–400 K and pressure range 25–700 bar with a maximum uncertainty of ± 1%. A simple correlation of these data accurate to within about 3% is obtained and used to prepare a table of recommended values.Nomenclature a _k ,b _ij ,b _k Parameters of the regression model, k= 0 to n; i =0 to m; j =0 to n - P Pressure (MPa or bar) - Q _kl Heat flux per unit length (mW · m^–1) - t time (s) - T Temperature (K) - T _cr Critical temperature (K) - T _r reduced temperature (= T/T _cr) - T _w Temperature rise of wire between times t ₁ and t ₂ (deg K) - T ^* Reduced temperature difference (TT _cr)/T _cr - Thermal conductivity (mW · m^–1 · K^–1) - ₁ Thermal conductivity at 1 bar (mW · m^–1 · K^–1) - _bg Background thermal conductivity (mW · m^–1 · K^–1) - _cr Anomalous thermal conductivity (mW · m^–1 · K^–1) - _e Excess thermal conductivity (mW · m^–1 · K^–1) - Density (g · cm^–3) - _cr Critical density (g · cm^–3) - _r Reduced density (= / _cr) - ^* Reduced density difference (– _cr )/ _cr      

Thermal conductivity of ethane from 290 to 600 K at pressures up to 700 bar,including the critical region

The paper presents thermal conductivity measurements of ethane over the temperature range of 290–600 K at pressures to 700 bar including the critical region with maximum uncertainty of 0.7 to 3% obtained with a transient line source instrument. A correlation of the data is presented and used to prepare tables of recommended values that are accurate to within 2.5% in the experimental range except near saturation, and in the critical region, where the anomalous thermal conductivity values are predicted to within 5%.Nomenclature a _k , b _ij , b _k , c _i Parameters of the regression model, k=0 to n, i=0 to m, j=0 to n - P Pressure, (MPa or bar) - Q _l Heat flux per unit length (mW · m^–1) - t Time, s - T Temperature, K - T _cr Critical temperature, K - T _r Reduced temperature = T/T _cr - T _w Temperature rise of wire between times t ₁ and t ₂ K - T ^* Reduced temperature difference (T–T _cr)/T _cr - Thermal conductivity, mW · m^–1 · K^–1 - ₁ Thermal conductivity at 1 bar, mW · m^–1 · K^–1 - _bg Background thermal conductivity, mW · m^–1 · K^–1 - _cr Thermal conductivity anomaly, mW · m^–1 · K^–1 - _e Excess thermal conductivity, mW · m^–1 · K^–1 - Density, g · cm^–3 - _cr Critical density, g · cm^–3 - _r Reduced density, = / _cr - ^* Reduced density difference =(- _cr)/ _cr     

Thermophysical Properties of Molten Germanium Measured by a High-Temperature Electrostatic Levitator1

Thermophysical properties of molten germanium have been measured using the high-temperature electrostatic levitator at the Jet Propulsion Laboratory. Measured properties include the density, the thermal expansivity, the hemispherical total emissivity, the constant-pressure specific heat capacity, the surface tension, and the electrical resistivity. The measured density can be expressed by _liq=5.67×10³–0.542 (T–T _m ) kg·m^–3 from 1150 to 1400 K with T _m=1211.3 K, the volume expansion coefficient by =0.9656×10^–4 K^–1, and the hemispherical total emissivity at the melting temperature by _{T, liq}(T _m)=0.17. Assuming constant _{T, liq}(T)=0.17 in the liquid range that has been investigated, the constant-pressure specific heat was evaluated as a function of temperature. The surface tension over the same temperature range can be expressed by (T)=583–0.08(T–T _m) mN·m^–1 and the temperature dependence of the electrical resistivity, when r _liq(T _m)=60·cm is used as a reference point, can be expressed by r _{e, liq}(T)=60+1.18×10^–2(T–1211.3)·cm. The thermal conductivity, which was determined from the resistivity data using the Wiedemann–Franz–Lorenz law, is given by _liq(T )=49.43+2.90×10^–2(T–T _m) W·m^–1·K^–1.     

Thermal conductivity of air in the range 312 to 373 K and 0.1 to 24 MPa

We have used the transient hot-wire technique to make absolute measurements of the thermal conductivity of dry, CO₂-free air in the temperature range from 312 to 373 K and at pressures of up to 24 MPa. The precision of the data is typically ±0.1%, and the overall absolute uncertainty is thought to be less than 0.5%. The data may be expressed, within their uncertainty, by polynomials of second degree in the density. The values at zero-density agree with other reported data to within their combined uncertainties. The excess thermal conductivity as a function of density is found to be independent of the temperature in the experimental range. The excess values at the higher densities are lower than those reported in earlier work.Nomenclature Thermal conductivity, mW · m^–1 · K^–1 - Density, kg · m^–3 - C _p Specific heat capacity at constant pressure, J · kg^–1 · K^–1 - T Absolute temperature, K - q Heat input per unit wire length, W · m^–1 - t Time, s - K(=/C _p) Thermal diffusivity, m² · s^–1 - a Wire radius, m - Euler's constant (=0.5772 ) - p _c Critical pressure, MPa - T _c Critical temperature, K - _c Critical density, kg · m^–3 - R Gas constant (=8.314 J · mol^–1 · K^–1) - V _c Critical volume, m³ · mol^–1 - Z _c(=p _c V _c/RT _c) Critical compressibility factor     

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.     

Excess thermodynamic properties of mixtures of alkyl benzoates withn-heptane

The paper reportsh ^E values at 298.15 K andv ^E and values at various temperatures for binary mixtures of propyl or butyl benzoate andn-heptane. The excess Gibbs energy of viscous flow,g ^*E, and the thermodynamic activation properties were calculated from these values. The results are compared with those for similar mixtures and interpreted on the basis of the characteristic dipole-dipole interactions of alkyl esters.Nomenclature A _i Parameters in Eq. (2) - dg ^*E Gibbs free energy of viscous flow (J · mol^–l) - dg Activation free energy (kJ · mol^–1) - K Parameter in Eq. (2) - h Planck constant - h ^E Excess enthalpy (J · mol^–1) - h Activation enthalpy (kJ · mol^–1) - N Avogadro number - R Universal gas constant (J · K^–1 · mol^–1) - s Standard deviation - s Activation entropy (J · K^–1 · mol^–1) - T Temperature (K) - v Molar volume of pure component (m³ · mol^–1) - v ^E Excess volume (m³ · mol^–1) - x _i Mole fraction of componenti Greek Letters Expansion coefficient (K^–1) - Density (kg · m^–1 ) - Viscosity (mPa · s ) - Apparent excess viscosity (mPa · s)     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure     

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.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

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.     

Evaporation of liquids from cylindrical vessels under conditions of free concentrational convection in a gas phase

An analytical solution is obtained for the axisymmetric problem of free concentrational convection in a vapor-gas mixture with isothermal evaporation of liquids from open cylindrical vessels. Formulas are derived to calculate concentration fields, local and integral mass fluxes of vapor. A comparative analysis of the results of analytical and numerical simulation is carried out for the processes of the evaporation of liquids under the conditions of convective mass transfer.Notation p pressure, Pa - density, kg/m³ - v velocity, m/sec - , dynamic and kinematic viscosity, Pa·sec, m²/sec - D diffusion coefficient, m²/sec - ₁, ₂ mass fractions of vapor and gas in a mixture - g free fall acceleration, m/sec² - M ₁,M ₂ molar masses of vapor and gas, kg/kmole - _r , _z radial and axial components of the velocity of a gas-vapor mixture, m/sec - r, z cylindrical coordinates, m - R, H radius and height of vessel, m - j local mass flux of vapor, kg/(m²·sec) - j vessel cross-sectional area-averaged mass flux of vapor, kg/(m²·sec) - j vessel cross-sectional area-averaged mass flux Chelyabinsk State Technical University, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 403–407, May–June, 1995.     

Transient processes of heat exchange in an air-plasma jet

The results of an experimental investigation of transient processes of nonsteady heat exchange in a high-temperature air stream are presented.Notation R radius of thermocouple junction, m - a thermal diffusivity, m²/sec - _th thickness of thermal boundary layer, m - thermal conductivity of gas, J/m·sec·deg - heat-transfer coefficient, W/m²·deg Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 520–523, September, 1981.     

Deviation from Wiedemann–Franz Law for the Thermal Conductivity of Liquid Tin and Lead at Elevated Temperature

The thermal conductivities of tin and lead in solid and liquid states have been determined using a nonstationary hot wire method. Measurements on tin and lead were carried out over temperature ranges of 293 to 1473 K and 293 to 1373 K, respectively. The thermal conductivity of solid tin is 63.9±1.3 Wm^–1K^–1 at 293 K and decreases with an increase in temperature, with a value of 56.6±0.9 Wm^–1K^–1 at 473 K. For solid lead, the thermal conductivity is 36.1±0.6 Wm^–1K^–1 at 293 K, decreases with an increase in temperature, and has a value of 29.1±1.1 Wm^–1K^–1 at 573 K. The temperature dependences for solid tin and lead are in good agreement with those estimated from the Wiedemann–Franz law using electrical conductivity values. The thermal conductivities of liquid tin displayed a value of 25.7±1.0 Wm^–1K^–1 at 573 K, and then increased, showing a maximum value of about 30.1 Wm^–1K^–1 at 673 K. Subsequently, the thermal conductivities gradually decreased with increasing temperature and the thermal conductivity was 10.1±1.0 Wm^–1K^–1 at 1473 K. In the case of liquid lead, the same tendency, as was the case of tin, was observed. The thermal conductivities of liquid lead displayed a value of 15.4±1.2 Wm^–1K^–1 at 673 K, with a maximum value of about 15.6 Wm^–1K^–1 at 773 K and a minimum value of about 11.4±0.6 Wm^–1K^–1 at 1373 K. The temperature dependence of thermal conductivity values in both liquids is discussed from the viewpoint of the Wiedemann–Franz law. The thermal conductivities for Group 14 elements at each temperature were compared.     

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.     

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.     

Temperature-enthalpy approach to the modelling of self-propagating combustion synthesis of materials

A new temperature-enthalpy approach has been proposed to model self-propagating combustion synthesis of advanced materials. This approach includes the effect of phase change which might take place during a combustion process. The effect of compact porosity is also modelled based on the conduction, convection and radiation in the local scale. Various parametric studies are made to analyse numerically the effects of activation energy, non-reacting phase content, porosity, Biot number, etc. The model predictions of the combustion pattern are in close agreement with those observed in experiments.Nomenclature c Concentration (wt %) - B _i Biot number =hL/k - f Fractional value - c _p Specific heat (J kg^–1 K) - h Heat-transfer coefficient (W m^–2 K) - L Height of material,m - Q Heat of reaction (J kg^–1) - H _SL ^* Latent heat of fusion (J kg^–1) - H _SE ^* Latent heat of fusion at eutectic (J kg^–1) - k Thermal conductivity (W m^–1 K) - k Equilibrium partition coefficient - Reaction kinetic function - t Time (s) - Non-dimensional time - T Temperature (K) - T ₀ Initial temperature (K) - Non-dimensional temperature - H Enthalpy (J kg^–1) - Kinetic function - Non-dimensional enthalpy - v _f Volume fraction of non-reactive phase - V Volume (m₃) - k ₀ Pre-exponential constant to reaction rate (s^–1) - z Cartesian co-ordinate - z^* Non-dimensional co-ordinate - Non-dimensional reacted fraction - Density (kg m^–3) - A non-dimensional temperature - Pore surface emissivity - Planck's constant - i Initial state - r Reacted state - l, L Liquid state - s Solid state - E Eutectic - M Melting point of pure material - P Centre of control volume - s Southern side of central volume - S Southern control volume - n Northern side of central volume - N Northern control volume - * Non-dimensional term - n New time level - o Old time level - m Iteration level     

Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

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.