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 _itv(J mol^–1 K^–1) Specinc heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E _o Boundary surfaces emissivity - f Fraction of solid normal to heat flow - f _s Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(Wm^–1 K^–1) Effective thermal conductivity of foam - k _cd(Wm^–1 K^–1) Conductive contribution - k _cr(Wm^–1 K^–1) Convertive contribution - k _g(Wm^–1K^–1) Thermal conductivity of cell gas - k _r(Wm^–1 K^–1) Radiative contribution - k _s(Wm^–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 - (Wm^–2 K^–4) Stefan constant     

Analytical technique for the determination of solidification rates during the inward freezing of cylinders

An analytical/experimental approach which permits the determination of solidification rates during the inward solidification of cylinders is proposed. The technique is based on a previous analytical solution that treats the generalized problem of solidification of slabs. This solution is modified by a geometric correlation to compensate for the cylindrical geometry. A number of experiments have been carried out with a special experimental set-up, designed to simulate the inward solidification of cylinders in a water-cooled mould. A series of comparisons of experimental results, numerical predictions and calculations furnished by the proposed technique were made, showing good agreement for any case examined.Nomenclature a _s Thermal diffusivity of solid metal = k _s/c _s d _s (m² sec^–1) - A _i Internal surface area of the mould (m²) - b _s Heat diffusivity of solid metal = (k _s c _s d _s ^1/2(J m^–2 sec^–1/2 K^–1) - c _s Specific heat of solid metal (J kg^–1 K^–1) - d _s Density of solid metal (kg m^–3) - h Newtonian heat transfer coefficien (W m^–2 K^–1) - H Latent heat of fusion (J kg^–1) - k _s Thermal conductivity of solid metal (W m^–1 K^–1) - q Heat flux (W m^–2) - r Radial position (m) - r _o Radius of cylinder (m) - r _f Radius of solid/liquid interface (m) - S Thickness of solidified metal (m) - S _o Thickness of metal side adjunct (m) - t Solidification time (sec) - T Temperature (K) - T _i Surface temperature (K) - T _f Freezing temperature of metal (K) - T _o Temperature of the coolant (K) - T _s Temperature at any point in the solidified metal (K) - V ₁ Volume of remaining liquid metal during the solidification (m³) - V _s Volume of solidified metal (m³) - V _T Total volume of metal in the mould (m³) - x Distance from metal/mould interface (m) - Dimensionless solidification constant.     

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.     

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.     

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.     

The influence of surface kinetics in modelling chemical vapour deposition processes in porous preforms

The isothermal chemical vapour infiltration (ICVI) process is a well known technique for the production of composites and the surface modification of porous preforms. Mathematical modelling of the process can provide a better understanding of the influence of individual process parameters on the deposition characteristics such as final porosity or deposition profiles in the pore network. The influence of different rate expressions for several binary compounds on the ICVI process is discussed. Experimental work is used to validate the importance of correct kinetic expressions in a continuous ICVI model for cylindrical pores. The predicted infiltration characteristics are compared with experimental results. The final densification and Thiele modulus, i.e. a number which is a measure for the diffusion limitations in a pore, are used for the evaluation of the presented model, and conditions are given for an optimal densification of a porous preform by the ICVI process for several binary compounds. The deposition profiles as predicted by the model calculations are in agreement with the experimentally determined deposition profiles of TiN and TiC in small tubes. Moreover, it can be concluded that the shape of the deposition profiles is determined by the heterogeneous reaction kinetics. There is only a qualitative agreement between the predicted densification and measured densification for the synthesis of TiN and TiB₂ in sintered porous alumina. This mismatch can be explained in terms of a complexity of the pore network and differences in reaction kinetics. Model calculations reveal that there is a scattering for the predicted residual porosity as a function of the Thiele modulus for TiN. Moreover, this Thiele modulus can not fully account for the changes in densification at different temperatures. Given these uncertainties it is likely that a residual porosity of less than one percent can be obtained if the Thiele modulus is smaller than 1 × 10^–4. However, a CVI process with such a small Thiele modulus will not be practical, because of the concomitant long process times. Therefore, more precise conditions for the individual process parameters, i.e. concentration, reactor pressure, and temperature are deduced from the model calculations.Nomenclature a, b, c reaction order constants - C _i(x, t) concentration of species i at axial position x and time t (mole m^–3) - C _i ^o bulk concentration of species i (mole m^–3) - C _i ^* (x, t) dimensionless concentration of species i at axial position x and time t - D _e(x, t) effective diffusion coefficient at axial position x and time t (m²s^–1) - D _ij(x, t) binary diffusion coefficient (m²s^–1) - D _K(x, t) Knudsen diffusion coefficient at position x and time t (m²s^–1) - F correction factor for effective diffusion coefficient - k growth rate constant (ms^–1(m³mole^–1)^a+b-1) - K _i adsorption-desorption equilibrium constant (m³mole^–1) - L length of a pore (m) - M _i molecular weight of species i (g mole^–1) - M _ij harmonic mean of the molecular weights of species i andj (g mole^–1) - M _s molecular weight of deposit (g mole^–1) - m _t measured mass increase (g) - n _i stoichiometric number - P reactor pressure (Pa) - R(C _i) growth rate (mole(m^–2s^–1)) - r(x, t) pore radius at position x and time t (m) - r ^o initial pore radius (m) - r ^* dimensionless pore radius - S geometrical surface area (m²) - s ^t fraction of free titanium sites at the surface of TiN - s ⁿ fraction of free nitrogen sites at the surface of TiN - T temperature (K) - t time (s) - t _p process time (s) - U K _HCl/(K _{H 2} C _{H 2})^1/2 (m³ mole^–1) - V volume of alumina substrate (m³) - W K _TiCl3(m³ mole^–1) - X volume of infiltrated deposit relative to initial pore volume - x axial distance (m) - x ^* dimensionless axial distance - z number of time steps - dummy variable for integration - porosity of sintered porous alumina substrate - ratio of the volume over the surface area perpendicular to the flux (m) - density deposit (kg m^–3) - _ij a characteristic length (Å) - tortuosity factor of substrate - Thiele modulus - _D collision integral     

The structural degradation and lamellar to rod transition in the Bi-Cd eutectic during unidirectional growth

The Bi-Cd eutectic system is a prototype quasi-regular eutectic in which the bismuth-rich phase has a volume fraction of 57%. It shows a high degree of regularity but, clearly, is not a normal (regular) eutectic. Microstructural observations of unidirectionally-grown specimens show that the minor cadmium-rich phase degrades at small temperature gradients and small growth rates. However, the structural refinement resulting from rapid freezing or chemical addition is found to be analogous to that of the F/NF eutectics. A lamellar rod transition has been achieved at intermediate growth rates by adding 2.0 wt % Sn as a modifier to the eutectic alloy. However, this was accompanied by the bismuth phase showing cellular facets of the solid-liquid interface.Nomenclature G _L temperature gradient in the melt ahead of the solid/liquid interface (° C cm^–1) - G _S temperature gradient in the solid behind the solid-liquid interface (° C cm^–1) - R growth rate of solid (cm sec^–1) - S cooling rate (° C sec^–1, ° C h^–1) - K _S thermal conductivity in the solid (W m^–1 K^–1) - K _L thermal conductivity in the melt (W m^–1 K^–1) - L latent heat of fusion (J mol^–1) - T temperature difference, undercooling (° C) - K ₁ constant in Equation 2 - K ₂ constant in Equation 3 - D diffusion coefficient of solute in solid (m² sec^–1) - C solubility in solid (wt %, at %) - M molecular weight (g mol^–1) - density (g cm^–3) - interfacial energy, surface tension (J mm^–2) - R gas constant, 8.314J mol^–1 K^–1 - r radius of curvature (m) - T temperature (K) - t time (sec) - F faceted - NF non-faceted     

Estimation of the unknown parameters in the melt-spinning process

The free-surface temperature history of the melt spinning of copper measured by Tenwick and Davies [3] is compared with those calculated using a thermokinetic model assuming different parameters. The heat-transfer coefficient, nucleation temperature and the crystal-growth kinetics were thus estimated for the melt spinning of copper at a wheel speed of 35 ms^–1 as follows: heat-transfer coefficient during liquid cooling stage HL=1.0 × 10⁷ W m^–2K^–1, heat-transfer coefficient after solidification finished HS=1.0 × 10⁵ W m^–2K^–1, heat-transfer coefficient during solidificationH= 1.0 x 10⁷- 1.2 x 10¹¹ (t-t _n) (W m^–2K^–1), the nucleation temperatureT _n 1233 K and the crystal-growth kinetic lawV=4.0 × 10^–3 T^1.1 (ms^–1).     

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     

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     

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.     

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 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     

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.     

Non-Contact Measurements of the Thermophysical Properties of Hafnium-3 Mass% Zirconium at High Temperature

Several thermophysical properties of hafnium-3 mass % zirconium, namely the density, the thermal expansion coefficient, the constant pressure heat capacity, the hemispherical total emissivity, the surface tension and the viscosity are reported. These properties were measured over wide temperature ranges, including overheated and undercooled states, using an electrostatic levitation furnace developed by the National Space Development Agency of Japan. Over the 2220 to 2875 K temperature span, the density of the liquid can be expressed as _L (T)=1.20×10⁴–0.44(T–T _m ) (kgm^–3) with T _m =2504 K, yielding a volume expansion coefficient _L (T)=3.7×10^–5 (K^–1). Similarly, over the 1950 to 2500 K span, the density of the high temperature and undercooled solid -phase can be fitted as _S (T)=1.22×10⁴–0.41(T–T _m ), giving a volume expansion coefficient _S (T)=3.4×10^–5. The constant pressure heat capacity of the liquid phase can be estimated as C _PL (T)=33.47+7.92×10^–4(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the 2250 K to 2650 K temperature interval. Over the 1850 to 2500 K temperature span, the hemispherical total emissivity of the solid -phase can be represented as _TS (T)=0.32+4.79×10^–5(T–T _m ). The latent heat of fusion has also been measured as 15.1 kJmol^–1. In addition, the surface tension can be expressed as (T)=1.614×10³–0.100(T–T _m ) (mNm^–1) and the viscosity as h(T)=0.495 exp [48.65×10³/(RT)] (mPas) over the 2220 to 2675 K temperature range.     

Aerobic composting of tobacco industry solid waste—simulation of the process

Solid waste accumulated during the processing of tobacco for cigarette manufacture mostly contains tobacco particles and flavoring agents. Its main characteristics are a high content of nicotine (2,000 mg per kg of total solids), which is a toxic compound, and high value of total organic carbon of the aqueous extract (12,620.0 mg l^–1). Because of this fact tobacco waste cannot be disposed of with urban waste.The aim of this work was to stabilize tobacco solid waste by aerobic composting. The experiments were carried out in closed thermally insulated column reactors (1.0 l and 25 l) under adiabatic conditions and at an airflow rate of 0.9 l min^–1 kg^–1 of volatile solids for 16 days. During the process, temperature changes in the reactor, CO₂ production and the numbers of mesophilic and thermophilic organisms in the mixed microbial culture were closely monitored. Nicotine concentration in the samples was analyzed at the start and at the end of process. It was estimated that at the end of composting the volume and mass of total solids in the tobacco waste were reduced by about 50% and those of nicotine by 80%. A simple empirical model was used to simulate the biodegradation rate of the organic fraction of the solid waste. It was found that the selected model describes aerobic composting fairly well, although only two kinetic parameters (k₀ and n) were estimated.List of symbols c_pS specific heat capacity of the substrate, kJ kg^–1 K^–1 - c_pz specific heat capacity of air, kJ kg^–1 K^–1 - F_Ku and F_Ki molar airflow at the reactor inlet and outlet, mol h^–1 - H_r reaction enthalpy, kJ kg^–1 of dry substrate - k specific rate, Eqs. (5) and (9), h^–1 - k_o constant in Eq. (9), day^–1 - m_o initial mass of the substrate, kg - m_S mass of dry substrate, kg - n order of the reaction in Eq. (5) - n_K molar amount of oxygen, mol - Q_v airflow volume, m³ h^–1 - r_K oxygen depletion rate, mol kg^–1 h^–1 - r_S degradation rate, kg kg^–1 h^–1 - _z air density, kg m^–3 - SD mean square deviation - t time, h - T temperature in reactor, °C - T_o temperature of substrate at the beginning of reaction, °C - T_K temperature of compost at the end of reaction, °C - T_u temperature of air at the reactor inlet - space time, day - w_S mass fraction of compost, m_sm_o^–1, kg kg^–1     

Thermoelastic stress analysis with standard thermographic equipment by means of statistical noise rejection

A statistical method of signal processing allows for the quantification of small periodic temperature changes, using a standard IR camera and short image sequences without the necessity of any synchronization device. The attenuation of the signal in a high emissivity coating such as a black paint has been quantified by means of a 1D thermal model. This same model is used to analyze the heat conduction effects on thermoelastic stress measurements. By analogy with the resolution power of optical systems, a thermal spatial resolution power is calculated. The spatial resolution appears to be limited by the heat conduction at low frequencies and by the performance of the radiometer at high frequencies.

Nomenclature

Roman letters a Thermal diffusivity (m².s^–1) - c_p Specific heat at constant pressure (J.kg^–1.K^–1) - f Frequency (Hz) - h Surface exchange coefficient (W.m^–2.K^–1) - k Thermal conductivity (W.m^–1.K^–1) - q Heat source (W.m^–3) - t Time (s) - T Instantaneous temperature (K) - T₀ Initial specimen temperature (K) Greek letters Coefficient of thermal expansion (K^–1) - = 2f - Phase difference (rd) - Density (kg.m^–3) - _kl Components of Cauchy's stress tensor (MPa)     

Designing and upgrading model of pre-denitrification systems

This paper reports a three-substrate steady-state integrated model, whose unknowns are expressed in explicit terms once concentrations of nitrogen compounds in the effluent flow are fixed. The model can be applied both to design and to upgrade wastewater treatment plants. The model is also able to evaluate the flexibility of existing wastewater treatment plants, which represents the capacity of the system to operate under different working conditions caused by increases in influent load or reductions in effluent quality standards. In this case the admissible variation of influent load or effluent concentration can be measured using suitable dimensionless flexibility indexes.List of symbols Q influent flow [L³ T^–1] - R₁ sludge recycle flow ratio - R₂ aerated mixed liquor recycle flow ratio - V_D denitrification reactor volume [L³] - V_N nitrification reactor volume [L³] - S biodegradable organic substrate concentration [M L^–3] - N-NH₄ ammonia nitrogen concentration [M L^–3] - N-NO₃ nitrate nitrogen concentration [M L^–3] - N_tot total nitrogen concentration [M L^–3] - O₂ oxygen concentration in the nitrification reactor [M L^–3] - X_H heterotrophic biomass concentration [M L^–3] - X_AUT autotrophic biomass concentration [M L^–3] - maximum removal rate of biodegradable organic substrate for an assigned value of temperature [T^–1] - maximum removal rate of nitrate for an assigned value of temperature [T^–1] - maximum removal rate of ammonia nitrogen for assigned values of pH and temperature [T^–1] - _S removal rate of biodegradable organic substrate [T^–1] - _D removal rate of nitrate [T^–1] - _N removal rate of ammonia nitrogen [T^–1] - K_S saturation coefficient for biodegradable organic substrate [M L^–3] - K_D saturation coefficient for nitrate [M L^–3] - K_SD saturation coefficient for organic substrate in the denitrification kinetic [M L^–3] - K_N saturation coefficient for ammonia nitrogen [M L^–3] - saturation coefficient for oxygen [M L^–3] - Y_H yield coefficient for heterotrophic microorganisms in the biodegradable organic substrate removal process - Y_D yield coefficient for heterotrophic microorganisms in the nitrate nitrogen removal process - Y_AUT yield coefficient for autotrophic microorganisms in the ammonia nitrogen removal process - (X_H)_r heterotrophic biomass concentration in the recycle sludge [M L^–3] - (X_AUT)_r autotrophic biomass concentration in the recycle sludge [M L^–3] - biodegradable organic mass consumption for unitary nitrate nitrogen mass reduction in the denitrification reactor - nitrogen consumption in the biodegradable organic oxidation process by mean of heterotrophic biomass     

Thermal boundary resistance at interfaces between sapphire and indium

The Kapitza thermal boundary resistanceR _K has been measured above 1 K on several sapphire-indium boundaries prepared with different methods. By vapor-deposition of indium on sapphire and subsequent cold-welding with bulk indium, reproducible results were obtained. With the indium superconducting, we foundR _KT ^–3 within a certain temperature range, andR _K(1K)=42–44 and 30–36 cm² K/W for polished and rough sapphire surfaces, respectively. The calculation according to the acoustic mismatch theory yieldsR _K(1K)20 cm² K/W. Samples prepared by ultrasonic soldering also follow the relationR _KT ^–3 approximately, and giveR _K(1K)=14–17 cm² K/W. However, it is doubtful whether the calculation presuming a smooth boundary can be applied to the latter samples. Furthermore, we found that the method of vapor deposition and subsequent pouring on molten indium does not give good contacts. Moreover, the electronic contribution to the heat transfer across the boundary has been proved by ruling out other effects.