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      

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.     

Thermophysical Property Measurements of Supercooled and Liquid Rhodium

The density, the isobaric heat capacity, the surface tension, and the viscosity of liquid rhodium were measured over wide temperature ranges, including the supercooled phase, using an electrostatic levitation furnace. Over the 1820 to 2250 K temperature span, the density can be expressed as (T)=10.82×10³–0.76(T–T _m ) (kgm^–3) with T _m =2236 K, yielding a volume expansion coefficient (T)=7.0×10^–5 (K^–1). The isobaric heat capacity can be estimated as C _P (T)=32.2+1.4×10^–3(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid remains constant at 0.18 over the 1820 to 2250 K interval. The enthalpy and entropy of fusion have also been measured, respectively, as 23.0 kJmol^–1 and 10.3 Jmol^–1K^–1. In addition, the surface tension can be expressed as (T)=1.94×10³–0.30(T–T _m ) (mNm^–1) and the viscosity as (T)=0.09 exp[6.4×10⁴(RT)] (mPas) over the 1860 to 2380 K temperature range.     

Noncontact Measurements of Thermophysical Properties of Molybdenum at High Temperatures

Four thermophysical properties of both solid and liquid molybdenum, namely, the density, the thermal expansion coefficient, the constant-pressure heat capacity, and the hemispherical total emissivity, are reported. These thermophysical properties were measured over a wide temperature range, including the undercooled state, using an electrostatic levitation furnace developed by the National Space Development Agency of Japan. Over the 2500 to 3000 K temperature span, the density of the liquid can be expressed as _L(T)=9.10×10³–0.60(T–T _m) (kg·m^–3), with T _m=2896 K, yielding a volume expansion coefficient _L(T)=6.6×10^–5 (K^–1). Similarly, over the 2170 to 2890 K temperature range, the density of the solid can be expressed as _S(T)=9.49×10³–0.50(T–T _m), giving a volume expansion coefficient _S(T)=5.3×10^–5. The constant pressure heat capacity of the liquid phase could be estimated as C _PL(T)=34.2+1.13×10^–3(T–T _m) (J·mol^–1·K^–1) if the hemispherical total emissivity of the liquid phase remained constant at 0.21 over the temperature interval. Over the 2050 to 2890 K temperature span, the hemispherical total emissivity of the solid phase could be expressed as _TS(T)=0.29+9.86×10^–5(T–T _m). The latent heat of fusion has also been measured as 33.6 kJ·mol^–1.     

Non-contact measurements of thermophysical properties of niobium at high temperature

Four thermophysical properties of both solid and liquid niobium have been measured using the vacuum version of the electrostatic levitation furnace developed by the National Space Development Agency of Japan. These properties are the density, the thermal expansion coefficient, the constant pressure heat capacity, and the hemispherical total emissivity. For the first time, we report these thermophysical quantities of niobium in its solid as well as in liquid state over a wide temperature range, including the undercooled state. Over the 2340 K to 2900 K temperature span, the density of the liquid can be expressed as _L (T) = 7.95 × 10³ – 0.23 (T – T _m)(kg · m^–3) with T _m = 2742 K, yielding a volume expansion coefficient _L(T) = 2.89 × 10^–5 (K^–1). Similarly, over the 1500 K to 2740 K temperature range, the density of the solid can be expressed as _s(T) = 8.26 × 10³ – 0.14(T – T _m)(kg · m^–3), giving a volume expansion coefficient _s(T) = 1.69 × 10^–5 (K^–1). The constant pressure heat capacity of the liquid phase could be estimated as C _PL(T) = 40.6 + 1.45 × 10^–3 (T – T _m) (J · mol^–1 · K^–1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the temperature range. Over the 1500 K to 2740 K temperature span, the hemispherical total emissivity of the solid phase could be rendered as _TS(T) = 0.23 + 5.81 × 10^–5 (T – T _m). The enthalpy of fusion has also been calculated as 29.1 kJ · mol^–1.     

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.     

Thermodynamic Properties of Sulfur Hexafluoride

We present new vapor phase speed-of-sound data u(P, T), new Burnett density–pressure–temperature data (P, T), and a few vapor pressure measurements for sulfur hexafluoride (SF₆). The speed-of-sound data spanned the temperature range 230 KT460 K and reached maximum pressures that were the lesser of 1.5 MPa or 80% of the vapor pressure of SF₆. The Burnett (P, T) data were obtained on isochores spanning the density range 137 mol·m^–34380 mol·m^–3 and the temperature range 283 KT393 K. (The corresponding pressure range is 0.3 MPaP9.0 MPa.) The u(P, T) data below 1.5 MPa were correlated using a model hard-core, Lennard–Jones intermolecular potential for the second and third virial coefficients and a polynomial for the perfect gas heat capacity. The resulting equation of state has very high accuracy at low densities; it is useful for calibrating mass flow controllers and may be extrapolated to 1000 K. The new u(P, T) data and the new (P, T) data were simultaneously correlated with a virial equation of state containing four terms with the temperature dependences of model square-well potentials. This correlation extends nearly to the critical density and may help resolve contradictions among data sets from the literature.     

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     

Non-Contact Measurements of Surface Tension and Viscosity of Niobium, Zirconium, and Titanium Using an Electrostatic Levitation Furnace

The surface tension and viscosity of liquid niobium, zirconium, and titanium have been determined by the oscillation drop technique using a vacuum electrostatic levitation furnace. These properties are reported over wide temperature ranges, covering both superheated and undercooled liquid. For niobium, the surface tension can be expressed as (T)=1.937×10³–0.199(T–T _m) (mN·m^–1) with T _m=2742 K and the viscosity as (T)=4.50–5.62×10^–3(T–T _m) (mPa·s), over the 2320 to 2915 K temperature range. Similarly, over the 1800 to 2400 K temperature range, the surface tension of zirconium is represented as (T)=1.500×10³–0.111(T–T _m) (mN·m^–1) and the viscosity as (T)=4.74–4.97 ×10^–3(T–T _m) (mPa·s) where T _m=2128 K. For titanium (T _m=1943 K), these properties can be expressed, respectively, as (T)=1.557×10³–0.156(T–T _m) (mN·m^–1) and (T)=4.42–6.67×10^–3(T–T _m) (mPa·s) over the temperature range of 1750 to 2050 K.     

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     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

On the analysis of the thermal diffusivity measurement method with modulated heat input

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(t) Energy of modulation per unit surface deposited on surface x=l, W · m^–2 - Q(t) Total energy per unit surface deposited on surface x=l, W · m^–2 - q Complex energy modulation amplitude, W · m^–2 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(x, t) Modulation temperature at any distance x and at time t, K - t Time, s - x Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1     

Welding of thin steel plates: a new model for thermal analysis

A mathematical model for the transient heat flow analysis in arc-welding processes is proposed, based on a unique set of boundary conditions. The model attempts to make use of the relative advantages of analytical as well as numerical techniques in order to reduce the problem size for providing a quicker solution without sacrificing the accuracy of prediction. The variation of thermo-physical properties with temperature has been incorporated into the model to improve the thermal analysis in the weld and heat-affected zones. The model has been evaluated using a five-point explicit finite difference method for analysing the welding heat flow in thin plates of two different geometric configurations. The temperature distribution closer to the heat source, primarily in the weld zone and the heat-affected zones, are predicted by the numerical technique. The thermal characteristics beyond the heat-affected zone are amenable to standard analytical techniques. The behaviour of the boundary condition in the model has been investigated in detail.Nomenclature q Rate of heat per unit thickness (Wm^–1) - d Plate thickness (m) - v Velocity of source (m s^–1) - t Time (s) - T Temperature value at the desired point (K) - T ₀ Initial temperature (K) - K Thermal conductivity (W m^–1 K^–1) - Density (kg m^–3) - c _p Specific heat (J kg^–1 K^–1) - Thermal diffusivity (m² s^–1) - n - Distance of point considered from the source (=x–vt) (m) - K ₀ Modified Bessel function of second kind and zero order - r Radial distance from the source (r=(x ²+y ²)^1/2) (m) - Model width (m) - a Plate width (m) - Distance from the source =(²+4 ×10^–4)^1/2 (m) - _n      

Glassy behavior of low-temperature energy relaxation in YBa2Cu3O7 and YBa2Cu3O6

Measuring the power release after rapid cooling a YBa₂Cu₃O₇ sample (m=42.85 g, T_c=91 K) from the equilibrium temperature T₁ (2.35 KT₁15.1 K) to T₀=1.5 K, we observed a time dependence typical of a glass: is proportional to t^–1. The results allow us to determine the linear term of the heat capacity (0.8 mJ/mole · K²) due to the two-level systems. While the low-temperature heat capacity anomaly noticeably decreases, the power release is essentially unchanged after oxygen reduction of the sample.     

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.     

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.     

The critical constants of long-chain normal paraffins

Because of the recent availability of the critical constants of normal alkanes up to octadecane, some modifications in the estimation procedures for the critical constants have become necessary. It has been shown that the equation of Ambrose for the critical temperature of normal alkanes leads to the result that as n , the limiting value for the critical temperature is equal to the limiting value for the normal boiling point and the limiting value for the critical pressure is 1 atm. Currently, the CH₂ increment for the critical volume is considered constant. The recent data of Teja have shown that the CH₂ increment increases indefinitely in a homologous series until the critical volume reaches its limiting value. This has made the current procedure for estimating the critical volume obsolete. Taking into account the new measurements of Teja, we have now developed new equations for estimating the critical constants. The limiting values for an infinitely long alkyl chain for T _b, T _c, P _c, and V _c have been found to be 1021 K, 1021 K, 1.01325 bar, and 18618 cm³ · mol^–1, respectively. These new concepts have been applied to the estimation of various properties other than the critical constants.Nomenclature M Molar mass, kg·mol ^–1 - V _c Critical volume, cm³·mol^–1 - V ₁ Saturated liquid volume, cm³·mol^–1 - P _c Critical Pressure, bar - T _c Critical temperature, K - T _b Normal boiling point, K - T _B Boyle temperature, K - T _A Temperature at which the third virial coefficient is zero, K - V _c Limiting value of critical volume = 18,618 cm³ · mol^–1 - P _c Limiting value of critical pressure=1.01325 bar - T _c Limiting value of critical temperature = 1021 K - T _b Limiting value of normal boiling point = 1021 K - P _b Pressure at the normal boiling point, 1 atm - Z _c Critical compressibility factor - Z _c Limiting value for the critical compressibility factor = 0.22222 - R Gas constant, 83.1448×10^–6m³ · bar · K^–1 · mol^–1 - Acentric factor - X (T _c–T _b)/T _c - X ₁ (T _c–T)/T _c - X ₂ 1–(T _B/T)^5/4 - X ₃ 1–(T _A/T)^5/2 - Y P _c/RT _c - Surface tension, mN · m^–1 - B Second virial coefficient, cm³ · mol^–1 - B Limiting value for the second virial coefficient = –30,463 cm³ · mol^–1 - C Third virial coefficient, cm⁶ · mol^–2 - C _b Third virial coefficient at the normal boiling point, cm⁶ · mol^–2 - C _c Third virial coefficient at the critical temperature, cm⁶ · mol^–2 - C _B Third virial coefficient at the Boyle temperature, cm⁶ · mol^–2 - H _vb Enthalpy of vaporization at the normal boiling point, kJ · mol^–1 - n Number of carbon atoms in a homologous series - p Platt number, number of C-C-C-C structural elements - a, b, c, d, e, etc Constants associated with the specific equation - T _c ^* , T _b ^* , P _c ^* , V _c ^* , etc. Dimensionless variables     

Heat transfer in hydrocarbon fuel boiling under conditions of natural convection

Data on the heat-transfer coefficient in boiling of five jet fuels, two automotive gasolines, and a diesel fuel are presented over a wide range of regime parameters. The obtained results are described by a unified similarity equation.Notation heat-transfer coefficient, W/(m²·K) - P _s pressure, MPa - q heat flux density, W/m² - V volume, m³ - T _s temperature, K - ₁ and ₂ density of the liquid and vapor phases, kg/m³ - thermal conductivity, W/(m·K) - viscosity of the liquid, m²/sec - surface tension, N/m - C _p heat capacity, J/(kg·K) - r vaporization heat, J/kg - Nu Nusselt number - P Pecklet number.l=C _p T _{s 1}/(r₂)² serves as a governing dimension Kazan' State Techological University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 438–443, May–June, 1995.     

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

An assessment of expressions for the apparent thermal conductivity of cellular materials

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.Nomenclature a Absorption coefficient - C _v (Jmol^–1 K^–1) Specific heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E ₀ Boundary surfaces emissivity - f Fraction of solid normal to heat flow - fics Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(W m^–1 K^–1) Effective thermal conductivity of foam - k _cd(W m^–1 K^–1) Conductive contribution - k _cr(W m^–1 K^–1) Convective contribution - k _g(W m^–1 K^–1) Thermal conductivity of cell gas - k _r(W m^–1 K^–1) Radiative contribution - k _s(W m^–1 K^–1) Thermal conductivity of solid - L(m) Thickness of sample - L _g(m) Diameter of cell - L _s(m) Cell-wall thickness - n Number of cell layers - r Reflection coefficient - t Transmission coefficient - T(K) Absolute temperature - T _m(K) Mean temperature - T _N Fraction of energy passing through cell wall - T ₁(K) Temperature of hot plate - T ₂(K) Temperature of cold plate - V _g Volume fraction of gas - V _w Volume fraction of total solid in the windows - w Refractive index - (m) Effective molecular diameter - (Pa s) Gas viscosity - Structural angle with respect to rise direction - (W m^–2 K^–4) Stefan constant