Showing papers on "Thermal diffusivity published in 1968"

The influence of molecular diffusivity on turbulent entrainment across a density interface

Abstract: The rate of mixing across a density interface between two layers of liquid has been measured in a laboratory experiment which allows a direct comparison between heat and salinity transports over the same range of density differences. Low Reynolds number turbulence was produced by stirring mechanically at a fixed distance from the interface, either in one or in both layers, and the results for these two sets of experiments are also compared. The measurements cover a factor of two in stirring rate and twenty in density. Over this range of conditions the ratio of entrainment velocity to stirring velocity can be expressed as functions of an overall Richardson number Ri, and in this form the results of the one and two stirred layer experiments are indistinguishable from one another. For density differences produced by heat alone, the functional dependence is close to Ri−1 except at small values of Ri where it approaches a finite limit. For experiments with a salinity difference across the interface, the mixing rate is the same as in the heat experiments at low values of Ri, but falls progressively below this as Ri is increased, with the approximate form .An interpretation of these results has been attempted, using a dimensional analysis and qualitative mechanistic arguments about the nature of the motion. The Ri−1 dependence implies a rate of change of potential energy proportional to the rate of working by the stirrer. The decreased mixing rates for salt have been attributed to a slower rate of incorporation of an entrained element into its surroundings by diffusion, which increases the tendency for it to return to the interface and dissipate energy in wave-like motions.

Thermal diffusivity measurement of rock-forming minerals from 300° to 1100°K

Abstract: Measurement of thermal diffusivity, K, of fused silica, quartz, olivine, periclase, jadeite, garnet, spinel, corundum and alkali feldspar was made at 1-atm pressure and over the temperature range from 300° to 1100°K. All the samples are of gem quality but of millimeter size. The Angstrom method was slightly modified to be applicable to small samples. For all the minerals except feldspar 1/κ increases almost linearly with temperature up to 700°K, as expected from the theory of lattice conduction. Tightly packed minerals, such as periclase, spinel, and corundum, have a diffusivity 3 to 10 times as large as that of other minerals. At temperatures higher than 700°K, 1/κ decreases with temperature for some minerals. This decrease can be interpreted as being due to radiative heat transfer within the crystals, if the opacity of the minerals is in the range 6 to 20 cm−1. High-temperature optical data are essential for a detailed discussion of the radiation effect.

A Model for Magnetic Instabilities in Hard Superconductors: The Adiabatic Critical State

Abstract: The isothermal critical‐state model of hard superconductors is extended to include the effects of heating when the applied field is changed suddenly and magnetic flux enters adiabatically into the bulk. We consider the following specific situation. A semi‐infinite slab of superconductor is cooled in a magnetic field lying in its surface plane. Next, the external field is raised isothermally by an amount Hs. This excess field decreases linearly to a depth δ= 10Hs/4πJc from the surface. Finally, the field is raised by an infinitesimal amount ΔH in a time short compared to the thermal diffusion time and long compared to the electromagnetic diffusion time. Each element of volume exposed to the changing field receives a thermal impulse proportional to the local‐flux‐change times Jc. This thermal impulse, in turn, lowers the critical current and allows more flux to penetrate. We find that if Hs exceeds some critical value Hfj, then the isothermal critical state is not the only allowed state of the superconductor. This instability field is given in terms of the critical current density Jc, derivative of the critical current density with temperature, ∂Jc/∂T, and the volume specific heat C by the formula Hfj= [−π3CJc/(∂Jc/∂T)]1/2. The application of the incremental field ΔH can initiate an avalanching process, or a flux jump, that terminates in an adiabatic critical state. Immediately following the flux jump the internal field, the induced supercurrent, and the temperature rise at each position are associated in a self‐consistent way with the avalanche of flux that has entered the superconductor. In this framework a flux jump is viewed as a switching from the isothermal critical state to an adiabatic critical state. The magnitude of the jump is related to Js and is calculated.

Flame structure and flame reaction kinetics II. Transport phenomena in multicomponent systems

Abstract: The transport fluxes in multicomponent flame systems due to diffusion and thermal conduc­tion, and to thermal diffusion and its reciprocal effect, are considered from the standpoint of the extension of the Chapman–Enskog kinetic theory to polyatomic gases by Wang Chang, Uhlenbeck & de Boer (1951, 1964) and the subsequent development by Mason, Monchick and coworkers (1961-66). Equations are given for the various diffusional, thermal diffusional and thermal fluxes which it is necessary to derive in order to obtain reaction rates from experimental temperature and composition profiles in flames; and the organization of com­puter programs for calculation of the multicomponent diffusion and thermal diffusion coefficients and the thermal conductivity is described. The use of matrix partitioning tech­niques in suitable circumstances to reduce the amount of computation is also discussed. The expressions for the transport fluxes are next used to derive equations for the mole fraction and temperature gradients in flowing reaction systems such as flames where trans­port processes and reaction occur side by side. From the mole fraction and temperature at one point in the system it is then possible by a numerical integration method such as the Runge–Kutta procedure to compute the complete composition and temperature profiles. Two methods of obtaining the mole fraction and temperature gradients are described, one of which, the Stefan–Maxwell formulation, leads to the more economical computation. A hydrogen–oxygen–nitrogen–steam mixture was chosen under conditions which simu­lated the pre-reaction region of a hydrogen–oxygen–nitrogen flame that had been studied experimentally, and the detailed composition profiles due to diffusion were computed. The experimental method of measurement involved continuous sampling from the flame and mass spectrometric analysis, a technique which had not previously been checked on a flame system itself. Good agreement between theory and experiment was found when thermal diffusion was considered in the calculation, although the computed hydrogen profile was slightly displaced with respect to the experimental one. This last observation is possibly due to diffusion effects in the pressure gradient at the probe tip. Otherwise the experimental technique seemed to be satisfactory. The computed profiles also showed a number of interesting features such as a maximum in the nitrogen concentration profile caused by thermal diffusion effects.

The effect of structural changes on dye diffusion in poly(ethylene terephthalate)

Abstract: The diffusion of a disperse dye, 1-amino-4-hydroxyanthraquinone (C.I. Disperse Red 15) into poly(ethylene terephthalate) fibers has been studied as a function of heatsetting temperature and draw ratio. It was found that the dynamic loss modulus E″, measured under the dyeing conditions, was related to the dye diffusivity D. This indicates that the diffusion is controlled by the mobility of the polymer chain segments. Both the diffusivity and dye saturation values do not vary monotonically with heatsetting temperature but exhibit a minimum at a heat-setting temperature near 175°C. X-ray diffraction measurements were used to show that this behavior is attributable to crystallinity and crystal size changes resulting from heat-setting.

Thermal diffusivity of Mg2SiO4, Fe2SiO4, and NaCl at high pressures and temperatures

Abstract: The pressure and temperature variations of thermal diffusivity of poly crystalline Mg2SiO4 have been measured for the range 24 to 50 kb and 400° to 1300°K. Effect of the olivine-spinel phase transition on thermal diffusivity of Fe2SiO4 was studied at 48.5 kb for the temperature range 350° to 650°K. Synthetic samples with grain size 1 to 5 microns were used. For the pressure range studied, the reciprocal of thermal diffusivity 1/κ of Mg2SiO4 increases almost linearly with temperature up to about 1200°K, as expected from the theory of phonon conduction, but is nearly constant above that temperature. The 1/κ versus temperature curve of Fe2SiO4 (olivine) is nearly straight up to 700°K, where it becomes slightly convex. The thermal diffusivity of NaCl is measured under similar conditions for comparison with Bridgman's data. The agreement is reasonably good. The pressure derivative ∂κ/∂P, at P = 40 kb is 1.8 × 10−4 cm2/sec kb (at 700°K) and 0.8 × 10−4 cm2/sec kb (at 1100°K) for Mg2SiO4, and 4.7 × 10−4 cm2/sec kb (at 700°K) for NaCl. This pressure dependence can be explained by the theory of phonon conduction. The thermal diffusivity of Fe2SiO4 (spinel) is about 1.5 times that of Fe2SiO4 (olivine) over the range 350° to 650°K. The effect of radiative heat transfer in Mg2SiO4 is discussed. The photon mean free path is estimated to be 0.3 mm at 1400°K.

The Thermal Diffusivity of Ice and Water Between -40 and + 60 ~ C

Abstract: The thermal diffusivity αs of triply-distilled deionised water, and αL of single-crystal ice along the c-axis, have been measured by Angstrom's method. The temperature range covered was −40 to +60° C. The results for water compare well with published data for the thermal conductivity, but for ice there are unexplained discrepancies. The linear relationships αs=(8.43−0.101 T) 10−3 cm2/sec and αL=(1.35+0.002 T) 10−3 cm2/sec where T° C is the temperature, fit the data obtained.

An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 4 - A unified approximation for mixture transport properties for multicomponent boundary-layer applications

Abstract: Bifurcation approximation for binary and thermal diffusion coefficients, mixture viscosity, and thermal conductivity of laminar boundary layer

Some Diffusion and Solubility Measurements of Cu in CdTe

Abstract: The diffusivity and solubility of Cu in CdTe has been measured between 97° and 300°C using radiotracer techniques. The system studied involved chemically formed Cu2Te films on undoped zone‐purified CdTe single crystals. The solubility was found to vary from approximately 3×1016 to 2×1018 cm−3 in the temperature range studied. The diffusivity corresponding to these solubilities is given by D(cm2·sec−1) =3.7× 10−4 exp (−0.67 eV/kT). A much faster diffusing ``tail'' involving about 1015 cm−3 Cu is also observed.

Laminar liquid jet diffusion studies

Abstract: A rigorous analysis of jet hydrodynamics is used to develop a technique for determining diffusion coefficients from laminar liquid jet absorption experiments, and the influence of the jet fluid mechanics on the absorption process is clarified. The new technique is used to determine the diffusivities of carbon dioxide, oxygen, argon, nitrous oxide, ethylene, and propylene in water within the temperature range 25° to 40°C. A critical analysis of available diffusivity data for these gases indicates that there is no conclusive evidence that demonstrates the existence of a significant interfacial resistance in uncontaminated laminar jet experiments. In addition, comparison of existing data shows that the commonly accepted diffusivities for the oxygen-water system may be significantly higher than the actual values. It is concluded that the laminar jet experiment is a rapid, accurate method of obtaining diffusion coefficients of dissolved gases in liquids.

Kinetics of sorption and volume change in clay-colloid pastes

Abstract: The present paper analyses one-dimensional absorption (swelling) and desorption (shrinkage or consolidation) in two-component pastes of clay-colloid and electrolyte solution. The work deals specifically with the case where solution exchange with the paste column is possible only through its base. The extension to systems with 'top drainage' and 'double drainage' is trivial. The analysis combines Darcy's law applied to the flow of solution relative to the colloid particles with the continuity requirement. The hydraulic conductivity K and the moisture potential (i.e. minus the 'swelling pressure') O are taken to be arbitrary known functions of the volumetric solution content e. The fundamental flow equation which follows is basically a nonlinear partial integrodifferential equation. It can be restated as a Fokker-Planck equation with e-dependent 'diffusivity' and the 'drift velocity' spatially constant but unknown and time dependent. The dependent variable is conveniently taken as e, although it can be made O if this is desired. The specific problem is that of sorption consequent on a step-function change in applied load (i.e. of the value of O (or e) at the base of the column). The column is taken to be effectively semi-infinite, so that the solution applies only until swelling or shrinkage at the upper surface of the column first becomes significant. Under these conditions, the solution is of the similarity form x(e, t) = O(e)t1/2 where x is the space coordinate, t is time, and O is a function of e which is found by the solution of a nonlinear, ordinary, integrodifferential equation. With O(e) known, it is an elementary matter to deduce a great variety of properties of the sorption process: the instantaneous distribution of colloid content; the instantaneous rate of total volume change; the cumulative total volume change; the instantaneous local velocity and volume flux density of colloid; the instantaneous local mean velocity and volume flux density of solution relative to colloid; the instantaneous local absolute mean velocity and volume flux density of solution; the instantaneous local volume flux density of solution due to mass flow; and the displacement history of colloidal particles initially at various positions in the column.

Measurement by the Flash Method of Thermal Diffusivity, Heart Capacity, and Thermal Conductivity in Two‐Layer Composite Samples

Abstract: The well‐known flash method of measuring thermal diffusivity, heat capacity, and thermal conductivity in single‐layer samples has been extended to measurements in two‐layer composite samples. The analysis presented allows these measurements to be made for the material in one of the layers if the corresponding values are known for the material in the second layer. An analytical solution is obtained as the basis of a computer data‐reduction procedure devised for calculating the thermal diffusivity from flash‐technique data. Replication of the diffusivity measurements is accomplished, in effect, by utilizing the information contained in an arbitrary number of points distributed over a wide range of the experimental temperature transient. Through the use of an empirical function closely representing the actual waveform of the heat pulse produced by a flash lamp, the measurements remain valid in thin samples for which heat losses are small. Experimentally, the method is demonstrated with data obtained for some commercial samples of bimetallic composites.

Tables of Collision Integrals for the (m,6) Potential Function for 10 Values of m.

Abstract: Tables of collision integrals are presented for the (m, 6) potential function for 87 reduced temperatures for each of 10 values of m. The exponents m used were m = 9, 12, 15, 18, 21, 24, 30, 40, 50, and 75. Comparisons are made with five other calculations for the case m = 12. The accuracy of the calculation appears to be at least several parts in 10,000.

Heat transfer through a three-phase porous medium

Abstract: Experimental values of the effective thermal conductivity obtained by Sugawara on calcareous sandstone partially filled with water are compared with values calculated by using the geometric mean equation of Lichteneker extended to a system having three phases and also with values obtained from a relation given by Brailsford and Major. The calculated values disagree with the experimental values. A weighted geometric mean of the maximum (weighted arithmetic mean of the individual thermal conductivities) and minimum (weighted harmonic mean of the individual thermal conductivities) values of the thermal conductivity of the sample is proposed here for obtaining its effective thermal conductivity. It is held that such an equation can demonstrate the structure and distribution of phases in the sample.

Light Scattering from a Chemically Reactive Fluid. I. Spectral Distribution

Abstract: The spectral distribution of light scattered by fluctuations about equilibrium in a chemically reactive fluid is calculated from the time dependence of the fluctuations predicted by the linearized hydrodynamic equations of irreversible thermodynamics. The theory treats a system with an arbitrary number, n, of independent chemical reactions which are coupled to the hydrodynamic processes involving viscosity and thermal conductivity. However, diffusion and any frequency dependence of the transport coefficients are neglected. The scattered light as a function of frequency has a central component and two side or Brillouin components. The central component is analyzed as a sum of n + 1 Lorentzian lines, one associated with a thermal diffusion relaxation process and n lines associated with the relaxation of the chemical reactions. In the limit of zero angle of scattering the widths of all Lorentzian lines associated with transport properties (thermal conductivity, viscosity, etc.,) vanish, and the entire width ...

The Thermal Interaction between the Atmosphere and the Earth and Propagation of Diurnal Temperature Waves

Abstract: The thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, is investigated through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter. The virtual thermal diffusivity is assumed to vary both in time and in space in order to represent the various physical processes involved in accomplishing the actual heat transfer. It is shown that a mean upward transport of heat is maintained through the diurnal variation of the transfer process although the mean lapse rate is stable, thereby removing a long-standing difficulty in evalutating the turbulent heat flux from the mean potential temperature distribution. The solar energy received at the surface is found to be partitioned into the two media a...

Convective Instability in Fluids of High Thermal Diffusivity

Abstract: The problem of the onset of thermal instability in heated layers of fluid is investigated in a linear approximation, assuming the confining planes to be surfaces of constant heat flux. It is shown that in the absence of time dependence a limiting point of the neutral stability curve can be obtained exactly by analytical methods. This point is evaluated for a variety of boundary conditions on the fluid motion, and it is verified that the results give criteria for the onset of instability as stationary convection. Similar calculations are made for an idealized fluid in the time‐dependent case, and it is established that the combined effects of buoyancy and surface‐tension gradients may lead to overstable oscillations in certain circumstances.

Measurement of the Thermal Conductivity of Neon Using Hot-Wire-Type Thermal Diffusion Columns

Abstract: The thermal conductivity of neon is measured on two hot‐wire‐type thermal diffusion columns which are alike except for length. This has enabled a more explicit analysis of the so‐called “end effects.” Convection and temperature jump effects are investigated experimentally by taking measurements for several values of gas pressure. The data are reported in the temperature range from 100° to 1200°C and these can be correlated by a quadratic polynomial in temperature (T), viz., λ × 105 = 4.68 + 2.62 × 10−2T − 4.40 × 10−6T2. Here λ is in cal cm− 1·sec− 1·deg− 1 and T is in degrees Kelvin. The present data are estimated to have an error of about ±2% and within this scatter these agree with the predictions of the theory and also with most of the available measurements. This technique appears very promising for generating data in a temperature range where none of the established techniques work satisfactorily.

Dispersion in Porous Mediums Due to Oscillating Flow

Abstract: The existence of irregularly oscillating air flow in soils, induced by turbulence in the atmosphere, and the possible effect of such flow on the transport of water vapor and oxygen in soil, make dispersion in porous materials owing to oscillating gas flow of interest. Theoretical study indicated that, for oscillating flow in geometrically similar porous mediums, the rate of dispersion of miscible fluids can be expressed as a function of two dimensionless parameters, the Peclet number and the dimensionless amplitude of the displacement. Experiments designed to test this prediction included the measurement of the dispersion of oxygen in nitrogen in beds of randomly packed spheres subjected to oscillating gas flow. It was found that defining a dispersivity, analogous to a diffusivity, is meaningful, and that the dispersivity was strongly dependent on both the Peclet number and the dimensionless amplitude of the displacement. Data obtained using different sized spheres verified the conclusions deduced from the similarity analysis. (Key words: Dispersion; evaporation; porous mediums)