Showing papers on "Thermal diffusivity published in 1972"

Nonlinear water diffusion in nonsaturated concrete

Abstract: The equations governing drying and wetting of concrete are formulated, assuming the diffusivity and other material parameters to be dependent on pore humidity, temperature and degree of hydration. By fitting of computer solutions for slabs, cylinders and spheres against numerous test data available in the literature it is found that the diffusion coefficient decreases about 10 to 20 times when passing from 0.9 to 0.6 pore humidity. The problem is thus strongly nonlinear. Dependence on temperature is found to agree satisfactorily with the rate process theory. Effect of temperature on equilibrium pore humidity is also studied. The aging effect is defined by means of an equivalent hydration period. To enable easy prediction of drying of simple bodies, charts for the solution in terms of nondimensional variables are presented. Finally, correlation to the diffusion in a saturated concrete is discussed.

Thermal conductivity of Earth materials at high temperatures

Abstract: The total thermal conductivity (lattice plus radiative) of several important earth materials is measured in the temperature range from 500 to 1900 K. A new technique is used in which a CO2 laser generates a low-frequency temperature wave at one face of a small disk-shaped sample, and an infrared detector views the opposite face to detect the phase of the emerging radiation. Phase data at several frequencies yield the simultaneous determination of the thermal diffusivity and the mean extinction coefficient of the material. The lattice, radiative, and total thermal conductivities are then calculated. Results for single-crystal and polycrystalline forsterite-rich olivines and an enstatite indicate that, even in relatively pure large-grained material, the radiative conductivity does not increase rapidly with temperature. The predicted maximum total thermal conductivity at a depth of 400 km in an olivine mantle is 0.020 cal/cm/sec/deg C, which is less than twice the surface value.

The diffusivity and solubility of oxygen in liquid tin and solid silver and the diffusivity

Abstract: The diffusivity and solubility of oxygen in liquid tin and solid silver in the temperature range of about 750° to 950°C (1023 to 1223 K) and the diffusivity of oxygen in solid nickel at 1393°C (1666 K) were determined using the electrochemical cell arrangement of cylindrical geometry: Liquid or Solid Metal + O (dissolved) ¦ ZrO2 + (3 to 4%)CaO ¦ Pt, air The diffusivity and solubility of oxygen in liquid tin are given by:DO(Sn) = 9.9 × 10−4 exp(−6300/RT) cm2/s (9.9 × 10−8 exp − 6300/RT m2/s) andNOS(Sn) = 1.3 × 105 exp(−30,000/RT) at. pct The diffusivity and solubility of oxygen in solid silver follow the relations:DO(Ag) = 4.9 × 10−3 exp (−11,600/RT) cm2/s ( 4.9 × 10−7 exp − 11,600/RT m2/s) andNOS(Ag) = 7.2 exp (−11,500/RT) at. pct The experimental value for the preexponential in the expression forDO(Ag) is lower than the value calculated according to Zener’s theory of interstitial diffusion by a factor of 11. The diffusivity of oxygen in solid nickel at 1393°C (1666 K) was found to be 1.3 × 10−6 cm2/s (1.3 × 10−10 m2/s).

Application of the convolution equation to stream-aquifer relationships

Abstract: Flow and head variations in stationary linear stream-aquifer systems are obtained through application of the convolution equation. Four highly idealized cases involving finite and semi-infinite aquifers, with and without semipervious stream banks, are considered. Equations for the instantaneous unit impulse response function, the unit step response function, and the derivative of the unit step response function are given for each case. Head fluctuations in the aquifer due to an arbitrarily varying flood pulse are obtained for the cases involving a finite aquifer with and without a semipervious stream bank. Flow in and out of the aquifer at the stream bank is determined for the same cases and demonstrates the value of the convolution equation in evaluating the base flow. Head variations, and to a lesser extent flow variations, are apparently relatively insensitive to variations in aquifer diffusivity.

Heat Flow and Convection Demonstration Experiments Aboard Apollo 14

Abstract: A group of experiments was conducted by Apollo 14 astronaut Stuart A. Roosa during the lunar flyback on 7 Fehruary 1971 to obtain information on heat flow and convection in gases and liquids in an environment of less than 10-(6)g gravity. Flow observations and thermal data have shown that: (i) there are, as expected, convective motions caused by surface tension gradients in a plane liquid layer with a free upper surface; (ii) heat flow in enclosed liquids and gases occurs mainly by diffusive heat conduction; and (iii) some convective processes, whose characteristics are not fully known, add to the heat transfer.

Thermal Diffusion and Convective Stability

Abstract: The stability of a two‐component fluid layer subjected to a temperature gradient has been studied, and the associated thermal diffusion separation has been found to exert a large influence even when the separations are small. The most unexpected and perhaps important result is that an instability has been found which can give rise to convection currents even though the density gradient is not adverse. Thus, a system heated from above can become unstable even when the fluid is less dense at the top of the system provided the more dense substance rises to the upper plate. Many measurements of the Soret coefficient could be subject to this instabilitity.

Diffusivity and solubility of oxygen in platinum and Pt-Ni alloys

Abstract: The diffusivity and solubility of oxygen in metal specimens were determined from measurements of permeation through thin wall tubes containing oxygen and heated by electrical resistance. The permeating oxygen desorbed in vacuum as monoatomic oxygen and the flux was monitored mass-spectrometrically. A known helium leak rate and experimentally-determined sensitivities of the two gases were used for flow calibration. The diffusion coefficient of oxygen in pure platinum, calculated from the time lag to reach a steady state flux, is: {fx065-01} in the temperature range of 1435∮ to 1504°. The solubility of oxygen in pure platinum was obtained from the steady-state flux using the previously determined diffusivity. The solubility is proportional to p1/2O2 and at 1 atm of oxygen the solubility is: CsO = (0.2 ± 0.1) × 1012 exp {fx065-02}, wt pct. Small amounts of nickel, less than required for internal oxidation, had a negligible effect on the oxygen solubility and diffusivity in platinum alloys.

Enhanced diffusion in Si and Ge by light ion implantation

Abstract: This paper presents theoretical and experimental results of investigations of impurity‐atom diffusion enhancement in Si and Ge crystals under light ion bombardment. Using existing ion range and displacement mechanism theories, a continuity equation for bombardment‐generated defects is written and solved to give an expression for the steady‐state excess defect concentration as a function of depth in the crystal. With the aid of existing diffusion theory, this is interpreted as a spatially varying atomic diffusivity which is a function of the bombarding beam parameters, temperature, the atomic species, and an experimentally measurable defect diffusion length. This spatially varying diffusivity, inserted in an appropriate diffusion equation, determines the evolution of the distribution of any impurity species diffusing by a defect‐related mechanism. Some numerical solutions of this equation and some analytic solutions of interest are given, and a comparison of theory and experiment is presented. Among the results of this comparison are (i) defect diffusion length measurements of 0.27 μ in p‐type Ge, and 0.086 μ in n‐type Si, (ii) a measured yield of approximately 25 mobile defects/proton in either Ge or Si, mostly clustered at the end of the proton's track. A simple method is presented for the experimental measurement of the required defect diffusion length. Impurity concentration profiles of the proton‐enhanced diffusion of P31 in Ge and B in Si were measured, and experimental checks of several theoretical predictions were carried out. There are some indications of a diffusivity saturation at high beam currents in Si which may result from the generation of immobile defect clusters. Impurity diffusivity enhancement by a factor of greater than 105 was observed in Si. Several physical parameter values of interest are calculated. Transmission electron microscopy measurements were undertaken to observe the effects of the bombardment on crystalline order in Si, and V‐I and C‐V characteristics of p‐n diodes produced using enhanced diffusion of B in Si were examined. The uses of bombardment‐enhanced diffusion as a device fabrication tool are discussed, and some unresolved topics are indicated.

Predicting gas-liquid diffusivities

Abstract: Diffusion in liquids has been studied for many years (14, 16). Available expressions for calculating diffusion coefficients in liquids, however, only partially have been successful. There is no one equation which predicts diffusivities for all systems involving a liquid solvent. The object of this investigation was to compare the existing diffusivity expressions for systems involving a gas solute diffusing through a liquid solvent. Dissolved gases form a special class of molecules of small size and low enthalpy of vaporization in the broad category of liquid diffusion and thus provide a good means of comparing the accuracy of the various equations. The first equation used is the Stokes-Einstein equation developed as early as 1905 (4).

Dielectric behaviour in a vanadium phosphate glass

Abstract: The dielectric constant and conductivity of 80% V 2 O 5 : 20% P 2 O 5 glass has been measured in the frequency range 10 2 to 10 9 Hz and in the temperature range 80 to 350°K. It is shown that the dielectric behaviour over these ranges is described by a Debye type relaxation process with distribution of relaxation times. A method is proposed to determine the width of distribution from the data at fixed frequencies and different temperatures. The width of distribution increases at frequencies ω > 10/ τ , which leads to an a.c. conductivity at these frequencies almost linearly proportional to frequency and independent of temperature. The estimated value of the static dielectric constant of about 30 was found to decrease with temperature while the infinite frequency dielectric constant of 10 was independent of temperature. The carrier concentration calculated from the dielectric relaxation time and the d.c. conductivity through a thermal diffusion model shows reasonable agreement with direct measurement using electron paramagnetic resonance.

Thermal Diffusion and Convective Stability. II. An Analysis of the Convected Fluxes

Abstract: The stability of a horizontal, two‐component fluid layer subjected to a positive vertical temperature gradient (heating from above) is investigated taking advantage of the fact that the time scales for thermal relaxation and concentration relaxation are widely separated. Based on this hypothesis a buoyancy driven instability owing to the separation by thermal diffusion is found even when the density gradient favors stability. This is in agreement with the previous findings of Schechter, Prigogine, and Hamm thus verifying that the difference in time scales is the essential feature giving rise to this unexpected instability. A convective state in which rolls are assumed to be stable is then studied by solving the nonlinear problem. The analysis shows that the contribution of the convective heat flux to the total heat flux vanishes to the approximation studied here, but that the convective mass flux is an important part of the total. Thus, the separation by thermal diffusion tends to be destroyed by the instability.

Heat-Flow Microcalorimetry and Its Application to Heterogeneous Catalysis

Abstract: Publisher Summary This chapter reviews heat-flow calorimetry as a new tool in adsorption and heterogeneous catalysis research. Heat-flow calorimeters are adapted to the investigation (1) of slow adsorption or reaction processes, (2) at moderate or high temperatures, and (3) on solids that present a poor thermal diffusivity. Heat-flow calorimetry allows the study of adsorption or reaction processes that cannot be studied conveniently with the usual adiabatic or pseudoadiabatic, adsorption calorimeters. The chapter describes the general principles of heat-flow calorimetry, the specific advantages of heat-flow microcalorimeters for the determination of heats of adsorption. It illustrates the use of this calorimetric technique in the study of heterogeneous catalysis reactions. All heat-flow microcalorimeters described in the chapter have been applied to the study of gas–solid interactions. In heat-flow calorimeters, it is important that the heat sink remain, throughout the experiment, at a constant temperature.

Methods for thermal well logging

Abstract: A method for thermal well logging of earth formations in cased or open boreholes to produce logs of temperature, specific heat and formation thermal conductivity is disclosed. A well logging tool employing a constant output heat source and three temperature sensors is utilized. A first temperature sensor measures the ambient borehole temperature at a given depth level. The constant output heat source then heats the formation at the investigated depth level. A second temperature sensor located relatively near the heat source then measures the temperature increase at the depth level due to the heating. This provides a measure of the formation specific heat. A third temperature sensor located a spatially separated distance from the second temperature sensor is then moved past the depth level being investigated some time interval later and the amount of cooling since the heat source has passed is measured. This provides a measure of the formation thermal conductivity. A further embodiment which utilizes the three temperature sensors and a heat source which is utilized also as a drilling tip is also disclosed.

Stability of a Two‐Component Fluid Layer Heated from Below

Abstract: In connection with recent experimental results, the stability of a two‐component fluid layer heated from below is examined taking into account the concentration gradient due to thermal diffusion. With the use of a variational method (local potential technique) developed by Glansdorff and Prigogine, an approximate solution is proposed for dilute solutions. The critical Rayleigh number increases for negative thermal diffusion factors and decreases for positive ones.

An Improved Form of Soil-Water Diffusivity Function

Abstract: The soil-water diffusivity D(θ) is expressed by a functional form which becomes infinite as the soil-water content approaches a constant value, such as the saturated or near-saturated value. The function begins at the origin, and shows an approximately exponential rise in the intermediate soil-water content range. When combined with a previously suggested form of unsaturated hydraulic conductivity function K(θ), qualitatively reasonable forms for the relationship between water content and suction head can be inferred. A computer program was developed to determine the characterizing parameters in the function by a least-squares fit to experimental data for horizontal water absorption. The program used an optimum seeking technique with numerical solutions of the flow equations as obtained by Philip's method. For different types of soils and several bulk densities, the new functional form was compared with the commonly used exponential expression for D(θ), and was found to be more representative, particularly for soils which show a very rapid increase in D(θ) as saturation is approached.

Measurement of the Thermal Conductivity of Argon, Krypton, and Nitrogen in the Range 800–2000°K

Abstract: The thermal conductivities of argon, krypton, and nitrogen were measured at 760 mm Hg in the temperature range 800–2000°K. Two thermal conductivity columns of different outside diameters were used in the experiments to provide an assessment of the convective heat transfer. In addition, potential leads were employed to minimize convection and end effects. The thermal conductivity values obtained were compared with existing data, with results of viscosity measurements, and with theoretical predictions.

Gaseous reduction of iron oxides: Part IV. mathematical analysis of partial internal reduction-diffusion control

Abstract: In this mathematical analysis of gaseous reduction of iron oxides, the partial internal reduction of the porous oxide and gas diffusion in the porous iron layer are considered simultaneously in deriving the rate equation. The rate equation, derived by partly analytical and partly numerical solutions, is well substantiated by the experimental results obtained previously. The following parameters, determined previously, are used in the application of the rate equation: i) specific rate constant for the gas reaction on the pore walls of wustite, ii) pore surface area of wustite, iii) effective gas diffusivity in the porous wustite formed during reduction of hematite, and iv) effective gas diffusivity in the porous iron layer. The effective depth of the internal reduction zone at the wustite-iron diffuse interface increases steeply with the progress of reduction beyond about 50 pct O removal. For reduction of 1 to 2 cm diam hematite spheroids in 100 pct H2, the gas composition at the diffuse iron-wustite interface is within 10 to 20 pct of that for the iron-wustite equilibrium; beyond about 50 pct O removal, the rate of reduction is controlled primarily by gas diffusion in the porous iron layer. From the mathematical analysis it is found that the relative depth of internal reduction increases with decreasing particle size and increasing temperature.

The moon's thermal state and an interpretation of the lunar electrical conductivity distribution

Abstract: Heat convection, being a more general theory than conduction theory, compels one to give reasons for using the latter theory as the basis of thermal evolution studies. Such reasons are supplied by considerations of material rheology.

A Laser Flash Technique for Determining Thermal Diffusivity of Liquid Metals at Elevated Temperatures

Abstract: The laser flash technique has been frequently employed in many laboratories as a relatively fast and easy technique of modest accuracy for measuring the thermal diffusivity of solids at ordinary and elevated temperatures. We have refined this technique and extended it to measurements of the thermal diffusivities of liquid metals. In both solid and liquid metallic specimens we have found, on both experimental and theoretical grounds, that the accuracy of the results is very sensitive to the degree of uniformity of the laser pulse. By introducing appropriate optics between the laser and the specimen we have been able to obtain a very uniform laser pulse and thus considerably enhance the accuracy of our measurements. In particular in measuring the thermal diffusivity of liquid mercury at temperatures from 13 to 300°C the difference between our values and values derived from published results of steady state measurements was never more than 5%. A cinematographic study of the impact of the laser beam on the su...

Thermal Diffusivity of Heterogeneous Materials. II. Limits of the Steady-State Approximation

Abstract: In the first paper of this series, the concept of the thermal diffusivity as a characteristic constant of a heterogeneous material was examined by considering the derivation of the heat conduction equation. In this second paper, a specific transient thermal problem with periodic boundary conditions is treated for two model heterogeneous materials: spheres imbedded in a matrix, and a two‐phase material composed of roughly spherical particles with neither phase continuous. In the steady‐state limit (low frequency or small particle size), it is shown that the material may be considered homogeneous and the proper value of thermal conductivity and heat capacity are those developed from a steady‐state development of thermal conductivity and the equilibrium heat capacity. A criterion for determining when a material of this type may be treated as homogeneous for a given transient thermal problem is also developed.