Pool boiling heat transfer to hydrocarbons and ammonia: A state-of-the-art review

Interest has grown in recent years to extend the use of hydrocarbons and ammonia as working fluids in refrigeration to new domains of application, despite their flammability. In the context of pool boiling heat transfer, this has created increasing research activities, particularly with regard to hydrocarbons. In contrast with this, only a few new experimental results have been added to the data set existing for ammonia in the literature. So this review will concentrate on hydrocarbons, while ammonia will be treated in a comparatively brief part.The review starts with the state-of-the-art that had been reached at about 1990. It continues with the data set for propane being taken as an example to highlight various reasons for the experimental data scatter that is found when different sources are compared for the same substance. In the main part, new results of 12 (aliphatic) hydrocarbons are discussed regarding the influence of heat flux q and reduced saturation pressure p^* = p_s/p_c on the heat transfer coefficient α, and also the variation in α₀ caused by the differences in the thermophysical properties of the 12 hydrocarbons at constant q₀ and . It is shown that the dependencies of the heat transfer coefficient α on heat flux q and reduced pressure p^*, and on the thermophysical properties of the various fluids at constant values q₀ and can be correlated by general semi-empirical functions with comparatively narrow limits of error that do not reach far beyond the experimental scatter occurring when different sources are compared for the same substance. Before treating ammonia in a final section, the review on hydrocarbons closes with short discussions for mixtures of hydrocarbons, for the bundle effect, and for the behaviour of enhanced tubes.     

Two-phase flow heat transfer of CO2 vaporization in smooth horizontal minichannels

Experiments were performed on the convective boiling heat transfer in horizontal minichannels with CO₂. The test section is made of stainless steel tubes with inner diameters of 1.5 and 3.0 mm and with lengths of 2000 and 3000 mm, respectively, and it is uniformly heated by applying an electric current directly to the tubes. Local heat transfer coefficients were obtained for a heat flux range of 20–40 kW m⁻², a mass flux range of 200–600 kg m⁻² s⁻¹, saturation temperatures of 10, 0, −5, and −10 °C and quality ranges of up to 1.0. Nucleate boiling heat transfer contribution was predominant, especially at low quality region. The reduction of heat transfer coefficient occurred at a lower vapor quality with a rise of heat flux, mass flux and saturation temperature, and with a smaller inner tube diameter. The experimental heat transfer coefficient of CO₂ is about three times higher than that of R-134a. Laminar flow appears in the minichannel flows. A new boiling heat transfer coefficient correlation that is based on the superposition model for CO₂ was developed with 8.41% mean deviation.     

Flow boiling heat transfer to carbon dioxide: general prediction method

An updated version of the Kattan–Thome–Favrat flow pattern based, flow boiling heat transfer model for horizontal tubes has been developed specifically for CO₂. Because CO₂ has a low critical temperature and hence high evaporating pressures compared to our previous database, it was found necessary to first correct the nucleate pool boiling correlation to better describe CO₂ at high reduced pressures and secondly to include a boiling suppression factor on the nucleate boiling heat transfer coefficient to capture the trends in the flow boiling data. The new method predicts 73% of the CO₂ database (404 data points) to within ±20% and 86% to within ±30% over the vapor quality range of 2–91%. The database covers five tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m⁻² s⁻¹, heat fluxes from 5 to 36 kW m⁻², saturation temperatures from −25 °C to +25 °C and saturation pressures from 1.7 to 6.4 MPa (reduced pressures up to 0.87).     

Studies on the presence of copper in the galvanized coating on weathering steel and the adherence characteristic of the protective copper complex formed on galvanized weathering steel

Following the hot-dip process for zinc coating on weathering steel, the galvanizing bath was found to have picked up copper. The galvanizing bath was observed to pick up Cu from the weathering steel at an average rate of 1.83×10^–3% s^–1m^–2 at 452±2C. EDAX/SEM studies exhibited a concentration gradient of copper to exist across the thickness of the galvanized coating on weathering steel. XRD studies revealed the formation of a protective copper complex, {Cu[(OH)₂Cu]₃}SO₄, on galvanized coating containing 0.739% Cu, when exposed in marine and industrial atmospheres. The adherence characteristic of the copper complex to the galvanized coating was found to be very satisfactory.     

The surface diffusion coefficients of MgO and Al2O3

From the measurement of neck size and neck curvature during the sintering of two spheres the surface diffusion coefficients of MgO and Al₂O₃ were determined. The spheres of both materials were machined from single crystals. The following values of surface diffusion coefficients were found: for MgO,D _{s s} = 3.7 × 10^–4 exp (407.8 kJ mol^–1/RT m³ sec^–1; for Al₂O₃,D _{s s} = 1.5 × 10^–2 exp (518.7 kJ mol^–1/RT) m³ sec^–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.     

Magnetic properties of hydrothermally synthesized strontium hexaferrite as a function of synthesis conditions

Fine particles of strontium hexaferrite, SrFe₁₂O₁₉, with a narrow size distribution have been synthesized hydrothermally from mixed aqueous solutions of iron and strontium nitrates under different synthesis conditions. The relationship between the synthesis variables (temperature, time and alkali molar ratio) and the magnetic properties has been investigated. The results have shown that, as the synthesis temperature increases, the saturation magnetization of the particles increases up to a plateau and the coercivity decreases. As the alkali molar ratio R(=OH^–/NO ₃ ^– ) increases, the coercivity decreases and goes through a local minimum, while the saturation magnetization increases and goes through a local maximum. Increasing the synthesis time from 2 h to 5 h has no significant effect on the saturation magnetization, but decreases the coercivity. An anisotropic sintered magnet with a high saturation magnetization value of 67.26 e.m.u g^–1 (4320 G) has been fabricated from the hydrothermally synthesized powders.Relationship between the c.g.s and S.I.units which are used in this paper are as follows: 1 erg = 10^–7 J, 1 e.m.u. cm^–3 = 12.57×10^–7 Wom^–2 (tesla), 1 oersted (Oe) = 79.6 A m^–1, 1 G = 10^–4 tesla (T).     

Two-dimensional pressure-temperature phase diagram and latent heats of neon adsorbed on exfoliated graphite

A two-dimensional pressure-temperature phase diagram was constructed for neon adsorbed on exfoliated graphite using the heat capacity data obtained in our laboratory for this system. The two-dimensional pressures at the triple and critical points were found to be _t=64×10^–6 N/m and _c=128×10^–6 N/m, respectively. From Clapeyron's equation and assuming an ideal behavior for the two-dimensional gas phase, the latent heat of sublimation was calculated as a function of temperature. The latent heat of vaporization was also calculated at the triple point and consequently the latent heat of fusion was found. The following values were obtained at the triple point:l _s/k=86 K,l _v/k=24 K, andl _f/k=62 K.     

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.     

Saturation curve equations for normal and heavy water

Compact and precise equations are obtained for the saturation curves of normal and heavy water.Notation p saturated vapor pressure - p_c critical pressure - T absolute temperature - T_c critical temperature - =T/T_c dimensionless temperature - =1 – ; r heat of vaporization - c _p ⁰ isobaric heat capacity of vapor in ideal gas state - c_s liquid heat capacity along saturation curve - v specific volume of vapor - a _i coefficients of Eq. (1) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 894–897, May, 1981.     

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     

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     

Influence of heat flux and pressure on heat transfer associated with fully developed nucleate pool boiling

Heat transfer in the pool boiling of helium is investigated experimentally. The dependence of the heat-transfer coefficient on the heat flux and pressure is determined for the fully developed nucleate boiling regime.Notation q heat flux, W/m² - T temperature differential, °K - heat-transfer coefficient, W/m²·°K - P pressure, N/m² - P_cr critical pressure, N/m² - P_* reference pressure, N/m² - n a power exponent - C a proportionality factor - , F₁ special functions Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 828–831, November, 1977.     

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     

Thermal properties of high-temperature superconductors

The specific heat and thermal conductivity measurements of YBa₂Cu₃O_7– high-T _c superconductors were performed by an a.c. calorimetry method. Investigations of the specific heat of YBa₂Cu₃O_7– ceramics in magnetic fields show that an increase in the magnetic field reduces the jump in the specific heat, broadens the transition region, and shifts the transition temperature downward by about 0.5 K, Temperature dependence of the specific heat of a YBa₂Cu₃O_7– high-T _c superconducting ceramic reveals that fluctuation affect the specific heat near the superconducting transition, Critical exponents = = 0.5, the critical amplitudesC ⁺ =C ^– = 0.5 J · mol^–1 K^–1, the space dimensionalityd = 3, and the number of components in the order parametern = 3 is calculated, The specific heat and the along-c-axis thermal conductivity of YBa₂Cu,₃O_7– single crystal were simultaneously measured.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, 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     

Superheating and bubble formation in Helium II

Heat transport experiments with superfluid helium in pipes of 60–400 cm length and diameters between 0.3 and 1.0 cm show the existence of a critical heat current when superfluidity breaks down and vaporization onset starts. In all measurements of the critical heat flux density where breakdown of superfluid cooling occurred, the maximum temperature for the start of bubble formation proved to be not the thermodynamic limit or saturation temperature T _s (temperature at which the coexistence curve is reached), but a temperature T _m which was 0.1–0.4 K higher. The magnitude and temperature dependence of the measured metastable superheating T₁=T_m–T_s can be explained by the assumption that nucleation occurs on the superfluid vortex lines or vortex rings.     

Low temperature sintering and crystallisation behaviour of low loss anorthite-based glass-ceramics

Anorthite-based glass-ceramics including TiO₂ as nucleating agent were melted and quenched in this study. The effect of particle size on the sintering behaviour of glass powders was investigated in order to obtain low-temperature sintered glass-ceramics. Anorthite glass-ceramic starts to densify at the transition temperature of glass (T _g = 770°C) and is fully sintered before the crystallisation occurrence (880°C). Therefore, a dense and low-loss glass-ceramic with predominant crystal phase of anorthite is achieved by using fine glass powders (D ₅₀ = 0.45 m) fired at 900°C. The as-sintered density approaches 99% theoretical density and the apparent porosity is as low as 0.05 Vol%. The dense and crystallized anorthite-based glass-ceramic exhibits a fairly low dielectric loss of 4 × 10^–4 at 1 MHz and a thermal expansion coefficient of 4.5 × 10^–6°C^–1. Furthermore, the microwave characteristics were measured at 10 GHz with the results of K = 9.8, Q _f = 2250, and temperature coefficient of resonant frequency _f = –30 ppm/°C.     

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).