Showing papers on "Thermal diffusivity published in 1991"

Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials

Abstract: The general theory of the transient plane source (TPS) technique is outlined in some details with approximations for the two experimental arrangements that may be referred to as ‘‘hot square’’ and ‘‘hot disk.’’ Experimental arrangements and measurements on two materials, Cecorite 130P and Corning 9606 Pyroceram, using a hot disk configuration, are reported and assessed.

Observing the general circulation with floats

Abstract: The prospect for describing advection and eddy transport of tracers in the general circulation using floats is examined This is done within the context of a recently proposed generalization of the advection-diffusion equation for passive scalars in which eddy transport is governed by a time-dependent eddy diffusivity tensor κ(t) which at large t approaches the constant κ(∞) appropriate to pure advection-diffusion models A minimal description of the general circulation would include the Eulerian mean velocity U(x) and the diffusivity κ(t) Given sufficient numbers of current-followers which adequately follow ideal fluid particles, both the horizontal components of U and the purely horizontal components of K could be measured The connection between these transport parameters and statistics of ideal particles shows that if the mean density of the float array is nonuniform then the mean velocity deduced from it will be in error by an array bias produced by downgradient diffusion of floats; this same phenomenon is responsible for the bias of Lagrangian mean velocity away from U toward high eddy diffusivity A bias also affects diffusivity estimates when the sampling array is not uniform in the mean The effects of nonuniform sampling make it difficult to piece together an accurate description of the general circulation from floats deployed in localized regional arrays Both horizontal and vertical separations develop between initially paired floats and fluid particles because floats do not follow vertical water motion The effect of this on the U and κ measured with floats is examined and is found to be negligible outside of strong currents With floats, Eulerian statistics must be estimated from a combination of space and time averaging The uncertainty, σU, of a measured U then depends on the spatial averaging scale A The trade-off between accuracy and resolution is at the analyst's control by adjusting the averaging scale, but the product σU·λ is fixed by the sampling density and eddy field properties The measurement uncertainty of the diffusivity κ(t) increases with t, even after κ has reached its asymptote κ∞ Numerical simulation of particle motion is used to test the generalized advection-diffusion equation upon which the development is based, to study how the diffusivity depends on properties of the eddy field, and to explore problems in mapping the general circulation in the presence of statistically inhomogeneous eddies, boundaries and strong currents When the mean float density is reasonably uniform, then measurements of mean flow and the fully horizontal components of the eddy diffusivity are accurate and are equally useful in strong boundary currents and in broad interior flows

The thermal behaviour of oscillating gas bubbles

Abstract: Several aspects of the oscillations of a gas bubble in a slightly compressible liquid are discussed by means of a simplified model based on the assumption of a spatially uniform internal pressure. The first topic considered is the linear initial-value problem for which memory effects and the approach to steady state are analysed. Large-amplitude oscillations are studied next in the limit of large and small thermal diffusion lengths obtaining, in the first case, an explicit expression for the internal pressure, and, in the second one, an integral equation of the Volterra type. The validity of the assumption of uniform pressure is then studied analytically and numerically. Finally, the single-bubble model is combined with a simple averaged-equation model of a bubbly liquid and the propagation of linear and weakly nonlinear pressure waves in such a medium is considered.

An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows

Abstract: Precise necessary and sufficient conditions on the velocity statistics for mean field behavior in advection-diffusion by a steady incompressible velocity field are developed here. Under these conditions, a rigorous Stieltjes integral representation for effective diffusivity in turbulent transport is derived. This representation is valid for all Peclet numbers and provides a rigorous resummation of the divergent perturbation expansion in powers of the Peclet number. One consequence of this representation is that convergent upper and lower bounds on effective diffusivity for all Peclet numbers can be obtained utilizing a prescribed finite number of terms in the perturbation series. Explicit rigorous examples of steady incompressible velocity fields are constructed which have effective diffusivities realizing the simplest upper or lower bounds for all Peclet numbers. A nonlocal variational principle for effective diffusivity is developed along with applications to advection-diffusion by random arrays of vortices. A new class of rigorous examples is introduced. These examples have an explicit Stieltjes measure for the effective diffusivity; furthermore, the effective diffusivity behaves likek0(Pe)1/2 in the limit of large Peclet numbers wherek0 is the molecular diffusivity. Formal analogies with the theory of composite materials are exploited systematically.

Cosmic-Ray Heating of Cooling Flows: A Critical Analysis

Abstract: It is shown that a combination of MHD wave-mediated cosmic ray heating and thermal conduction could balance cooling in intracluster media and substantially reduce the rate of inflow. The appropriate system of steady state equations is solved, including a new self-consistent formulation for the cosmic-ray diffusivity. Models which can produce substantial positive temperature gradients in static configurations are found when conduction is reduced by a factor of 10 or more. These models have too-flat thermal pressure profiles compared with observations. It is found that cosmic-ray heating is unlikely either to stabilize positive density perturbations against condensation or to contribute appreciably to the powering of the optical filaments.

Thermal diffusivity measurements in solids by the ‘‘mirage’’ technique: Experimental results

Abstract: This work provides the experimental confirmation of a generalized theory for thermal diffusivity measurements of solid samples using the ‘‘mirage’’ technique presented by the authors in a previous paper [A. Salazar, A. Sanchez‐Lavega, and J. Fernandez, J. Appl. Phys. 65, 4150 (1989)]. Moreover the influence of different effects on such determinations has been analyzed, and the limits of validity of the method have been established. The most important influence relies on the finite nature of two parameters: the height of the probe beam above the sample surface h and the radius of the exciting beam a. Such effects in all solids are discussed in detail according to their bulk thermo‐optical properties and for two ways of measuring: ‘‘bouncing’’ (probe beam sent to the sample surface at a small angle) and ‘‘skimming’’ (probe beam parallel and grazing the surface). The first way of measuring gives reliable results while the second one must be managed with care. In any case, significant shifts in the thermal di...

Dispersion, convection, and reaction in porous media

Abstract: The problem of transport of a reactive solute in a porous medium by convection and diffusion is studied for the case in which the solute particles undergo a first‐order chemical reaction on the surface of the bed. Assuming that the geometry is periodic, the method of homogenization is applied, showing explicitly that the effective equation is given by a Kramers–Moyal expansion, i.e., a partial differential equation of infinite order in which the nth term is the product of the nth gradient of the mean concentration by an nth‐order constant tensor. The effective values of reactivity, solute velocity, diffusivity, and of all the tensorial coefficients in the expansion are independent of the initial solute distribution and are expressed in terms of Peclet’s and Damkohler’s numbers, Pe=aV/D and Da=ak/D, respectively, where a is the cell size, V is the solvent mean velocity, D is the solute molecular diffusivity, and k is the surface reactivity, showing that they are independent of the initial solute distributi...

Fluctuations and transport in a stirred fluid with a mean gradient

Abstract: The effective thermal diffusivity D* and the probability distribution of temperature fluctuations are measured in a stirred fluid across which a temperature gradient is maintained. A distinct mixing transition is observed for D* as a function of Reynolds number R. Above the transitions, the distribution is strongly non-Gaussian and approaches an exponential exp(-‖δT‖/βξ), where β is the local temperature gradient and ξ the correlation length.

Chaotic advection in a Rayleigh-Bénard flow

Abstract: We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number scrR slightly above the scrRt at the onset of the even oscillatory instability for Rayleigh-Benard convection rolls. By modeling the flow with a stream function, we show how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity. This approach and symmetry considerations allow us to write explicit formulas that describe the tracer transport for finite times. In the limit of small amplitude of the oscillation, i.e., when (scrR-scrRt)1/2 is small, we show that the amount of fluid transported across a roll boundary grows linearly with the amplitude, in agreement with the experimental and numerical findings of Solomon and Gollub [Phys. Rev. A 38, 6280 (1988)]. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.

Molecular dynamics simulations of pressure and temperature effects on MgSiO 3 and Mg 2 SiO 4 melts and glasses

Abstract: Ab-initio interionic potentials for Mg2+, Si4+, and O2− have been used in molecular dynamics (MD) simulations to investigate diffusivity changes, pressure-induced structural transitions, and temperature effects on polymerization in MgSiO3 and Mg2SiO4 melts and glasses. The potential gives reasonable agreement with the 0.1 MPa radial distribution function of MgSiO3 glass. Maxima in the diffusion coefficients of Si4+ and O2− occur as pressure is increased on the MgSiO3 melt. The controlling structural mechanism for this behavior is the Q1 species of SiO4 tetrahedra. Mg2+ diffusion coefficients decrease monotonically with pressure in both melt compositions. Increasing Mg2+ coordination number and population of 3- and 4-membered SiO4 rings with pressure combine to hinder translation of the Mg2+ ions. The dominant changes in structure with pressure are a decrease in the intertetrahedral (Si-O--Si) angle up to approximately 4 g/cm3 and coordination changes of the ions above this density. Temperature effects on viscosity in these simulated melts are indirectly studied by analyzing polymerization changes with temperature. Polymerization and coordination numbers increase with decreasing temperature and a small quench rate effect is observed. Fair agreement is found between the MD simulations and experimental equation of state for Mg2SiO4, but the equation of state predictions for MgSiO3 melts are much less accurate. The zero pressure volume, V 0, is significantly higher and K 0 is lower in the simulations than empirical values. The inadequacies reflect error in using the ionic approximation for polymerized systems and a need to collect more data for a variety of molecular configurations in the development of ab-initio potentials.

The thermal conductivity of AISI 304L stainless steel

Abstract: A compilation and critical analysis of the thermal conductivity (γ) of AISI 304 stainless steel (SS) between 100 and 1707 K has been given in the literature. The author represented his “recommended” values of λ by an inflection in the A versus temperature relationship between 300 and 500 K. Because a physical mechanism had not been identified that would produce such a temperature dependence in γ of 304 SS, interest was generated in the possible existence of an as yet undiscovered phenomenon that might cause such an inflection. Consequently, experimental verification of the inflection was sought. The present paper presents recent measurements of λ, the electrical resistivity, and the absolute Seebeck coefficient of 304L SS from 300 to 1000 K and of the thermal diffusivity (α) from 297 to 423 K. The λ values computed from the a measurements were within ± 1.6% of the directly measured λ An inflection was not observed in the temperature dependence of λ between 300 and 500 K. After careful evaluation and because a physical mechanism still has not been identified which would produce such an inflection, the authors conclude that the inflection in the λ vs T relationship reported in the literature was caused by the data analysis technique.

Thermomechanical and thermo-optical properties of the LiCaAlF 6 :Cr 3+ laser material

Abstract: Measurements of the intrinsic thermomechanical and thermo-optical properties of the new laser material LiCaAlF6:Cr3+ (known as Cr:LiCAF) are performed. Thermal diffusivity, heat capacity, thermal expansion, elastic constants, fracture toughness, and dispersion and temperature variation of the refractive index are all characterized for this material. In addition, the magnitude of the thermal lensing induced in a flash-lamp-pumped laser rod of Cr:LiCAF is measured and compared with the results obtained for an alexandrite laser rod in the same laser head. We find that the thermal lensing of Cr:LiCAF is favorably small and that the thermomechanical properties are expected to be adequate for applications at low and medium average power.

A High-Temperature Transient Hot-Wire Thermal Conductivity Apparatus for Fluids.

Abstract: A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 µm diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hot-wire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ± 0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ± 5%. From the measured thermal conductivity and thermal diffusivity, we can calculate the specific heat, Cp , of the fluid, provided that the density is measured, or available through an equation of state.

Heat flux transients at the casting/chill interface during solidification of aluminum base alloys

Abstract: Heat flow at the metal/chill interface of bar-type castings of aluminum base alloys was modeled as a function of thermophysical properties of the chill material and its thickness. Experimental setup for casting square bars of Al-13.2 pct Si eutectic and Al-3 pet Cu-4.5 pct Si long freezing range alloys with chill at one end exposed to ambient conditions was fabricated. Experiments were carried out for different metal/chill combinations with and without coatings. The thermal history at nodal locations in the chill obtained during the experiments was used to estimate the interface heat flux by solving a one-dimensional Fourier heat conduction equation inversely. Using the data on transient heat flux q, the heat flow at the casting/chill interface was modeled in two steps: (1) The peak in the heat flux curve qmax was modeled as a power function of the ratio of the chill thickness d to its thermal diffusivity a, and (2) the factor (q/qmax) X α0.05 was also modeled as a power function of the time after the solidification set in. The model was validated for Cu-10 pct Sn -2 pct Zn alloy chill and Al-13.2 pct Si and Al-3 pct Cu-4.5 pct Si as the casting alloys. The heat flux values estimated using the model were used as one of the boundary conditions for solidification simulation of the test casting. The experimental and simulated temperature distributions inside the casting were found to be in good agreement.

Thermal diffusivity of MgSiO3 perovskite

Abstract: Thermal diffusivity of MgSiO3 perovskite has been measured in the temperature range of 160 K to 340 K using a sample synthesized in a uniaxial split-sphere high-pressure apparatus. At 300 K the thermal diffusivity of perovskite is 1.72 × 10−6 m2s−1, from which the thermal conductivity is evaluated to be 5.1 Wm−1K−1. Our model calculation shows that lattice thermal conductivity of the perovskite increases by a factor of 4 with depth throughout the lower mantle and reaches to 12 Wm−1K−1 in the vicinity of the mantle-core boundary. The D″ layer might not be a thermal boundary layer insulating the high core-temperature, if this layer mainly consists of the perovskite.

Diffusion in fluid-bearing and slightly-melted rocks: experimental and numerical approaches illustrated by iron transport in dunite

Abstract: Bulk diffusion of iron in synthetic dunites containing 1–6 vol.% fluid or melt at 10 kbar (1 GPa) and 900°–1300° C was examined by encapsulating the samples in platinum, which served as a sink for iron. The rate of iron loss from the dunite was found to depend strongly upon the identity of the fluid, which was varied from CO2 and H2O to melts of basaltic and sodium carbonate composition. Carbon dioxide in amounts up to 4 vol.% has no effect upon bulk iron diffusion because it exists in the dunite are isolated pores. The interconnected nature of H2O, basaltic melt, and carbonate melt, on the other hand, results in marked enhancement of bulk-rock Fe diffusion that is correlated with the diffusivity and solubility of olivine components in the fluid. At 1300° C, 4–5 vol.% of either water or basaltic melt increases the effective bulk diffusivity from the fluidabsent value of ≈10-10 cm2/s to ≈10-8 cm2/s. A single experiment involving a similar volume fraction of carbonate melt yielded a minimum bulk diffusivity of 10-7–10-6 cm2/s. This remarkably high value is attributable to the concurrent high diffusivity and high solubility of olivine components in molten carbonate H2O has a high diffusivity, estimated at ≈10-4 cm2/s in this study, and basaltic melt can dissolve large amounts of olivine, but neither possesses these two qualities in combination. Bulk transport of Fe in dunite containing <2 vol.% of pure H2O is independent of olivine grain size for samples having an average grain diameter of <10 μm to ≈60 μm. This is probably because bulk diffusion specifically in these H2O-bearing samples is ratelimited by the flux (which is proportional to concentration) of olivine components in the fluid. Given a constant fluid volume fraction, the effect of reducing the grain size is to increase the number of fluid-filled channels, but at the same time to decrease their average aperture, thus keeping constant the cross-sectional area through which the diffusional flux occurs. (Independence of bulk diffusivity from grain size is not anticipated for rocks containing melt, in which the silicate components are much more soluble.) In numerical (finite difference) simulations of selected laboratory experiments, the bulk Fe transport process was modeled as diffusion in fluid-filled tubules of triangular cross-section that are supplied by volume diffusion from contacting olivine grains with which they are in surface equilibrium. Applying a tortuosity factor of 1.7 brings the numerically computed diffusional loss profiles for experiments containing basaltic melt into near-coincidence with the experimentally-determined curves. This success in reproducing the experimental results lends credence to the interpretation of the bulk diffusional loss profiles as composites of gradients due to volume, grain-boundary and fluid-phase diffusion.

The space potential in the tokamak text

Abstract: A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self‐consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur during periods of magnetic island overlap. These calculated changes in diffusivity are interpreted in terms of a stochastic layer width, which is itself used to predict a potential change for comparison with the experimental results.

Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media

Abstract: Experimental results for natural convection in a horizontal porous cavity of aspect ratio A = 5 and heated from below are reported. A wide range of governing parameters are covered by careful selection of bead size, solid material, and fluid. These results fully support the effects of fluid-flow parameters (Rayleigh and Prandtl numbers), porous matrix-structure parameters (Darcy and Forchheimer numbers), and the conductivity ratio as predicted by the formulation based on the Darcy-Brinkman-Forchheimer (DBF) equations of motion. The DBF flow model, with variable porosity and variable thermal conductivity in the wall regions, predicts reasonably well in comparison with the experimental data. However, the difference between the predictions and the measurements increases as the ratio of solid-to-fluid thermal conductivity becomes very large. 32 refs.

Hydrogen diffusion in crystalline semiconductors

Abstract: The diffusion of hydrogen in semiconductors is complicated by the existence of several charge states (notably H+ in p-type material and H- or H0 in n-type material, at least for Si) and also that hydrogen is present in a number of different forms, namely atomic, molecular or bound to a defect or impurity. Since the probability of formation of these different states is dependent on the defect or impurity type and concentration in the material and on the hydrogen concentration itself, then the apparent hydrogen diffusivity is a function of the sample conductivity and type and of the method of hydrogen insertion. Under conditions of low H+ concentration in p-type Si, for example, the diffusivity is of the order of 10-10 cm2 · s-1 at 300 K and is consistent with the value expected from an extrapolation of the Van Wieringen and Warmoltz expression DH = 9.4 × 10-3exp[-0.48 eV/kT] cm2 · s-1. The characteristics of hydrogen diffusion in n- and p-type Si and GaAs are reviewed in this paper, and the retardation of hydrogen permeation by molecular formation and impurity trapping is discussed. The measurement of several key parameters, including the energy levels for the hydrogen donor and acceptor in Si and the diffusivity of the H0 and H- species, would allow a more quantitative treatment of hydrogen diffusion in semiconductors.

Liquid jet method, recording head using the method and recording apparatus using the method

Abstract: A liquid jet method for ejecting liquid using a bubble created by heating the liquid in a passage, characterized in that a non-dimensional number Z which is determined by the nature of the liquid, a heat flux and a configuration of the passage and which is specific to a recording head is not less than 0.5 and not more than 16; where z ≡ (π/6) 1/2 Tgk(p g /q₀) 3/2 /(ρ g Lg·a·S H A) 1/2 ; Tg is as superheat limit temperature of the major component of the liquid; Pg is a saturated vapor pressure of the major component of the liquid at temperature Tg; ρg is a saturated vapor density of the major component of the liquid at temperature Tg; Lg is a latent image of vaporization of the major component of the liquid at temperature Tg; k is as heat conductivity of the major component of the liquid at the temperature of the recording head before heating, a is a thermal diffusivity of the major component of the liquid at the temperature of the recording head before heating; q₀ is a flux of the heat which heats the liquid; S H is an area of that part (heating surface of the heat generating element which heats the liquid; A is an inertance of the passage under the conditions that the heating surface is a pressure source, that the liquid supply opening and the liquid ejection opening are open boundaries, and that the wall defining the passage is a wall (fixed) boundary; π is the number π; W is the work done by a bubble on the liquid, and Q is the heat applied from the heat generating element to the liquid from the start of the heating to the creation of the bubble.

Low-temperature electrical conductivity of highly conducting polyacetylene in a magnetic field

Abstract: The temperature dependence of the electrical conductivity and the low-temperature magnetoresistance for iodine-doped highly conducting polyacetylenes are reported. The overall behavior of the temperature dependence is explained in terms of the phenomenological Sheng model, but the selection of parameter values is not unique, suggesting that the model is not sufficient to characterize the samples. The temperature dependence changes rather drastically with the conductivity, which is determined by the doping concentration and chemical reactions within (CH${)}_{\mathit{x}}$. The magnetic-field effect is rather insensitive to the field direction. This indicates that the classical orbital effect is not the principal cause. The magnetoresistance is negative for the sample with the highest conductivity, and its magnitude exceeds by far the upper bound arising from the quantum correction based on weak-localization theory for isotropic media. We evaluate the effect of the anisotropy in the electron diffusivity on the magnitude. With a decrease in conductivity, positive magnetoresistance emerges at low magnetic fields. The drastic variations of the temperature and the magnetic-field dependence with the conductivity show that the highly conducting polyacetylene is close to the metal-nonmetal transition boundary.

EFFECT of PHYSICAL STRUCTURE of STARCH MATERIALS ON WATER DIFFUSIVITY

Abstract: The physical structure, developed during drying, affects the transport of water and the quality of processed solid foods. the effective diffusivity of water in starch-based systems was estimated from drying data at moisture 3–50% and temperatures 40-100°C. Hydrated granular or gelatinized starches and their mixtures with sugars or inert particles were used to produce different structures during air drying. the physical structure was characterized by the bulk porosity, estimated from the bulk and solid densities of the samples. the water diffusivity was influenced strongly by the porosity, developed during drying. Mechanical compression, starch gelatinization or addition of water-soluble sugars reduced the water diffusivity in granular starches. Incorporation of inert particles or extrusion cooking resulted in higher water diffusivities, due to higher porosities of the starch/inert mixtures or the expanded extrudates.

Overview of TFTR transport studies

Abstract: A review of TFTR plasma transport studies is presented. Parallel transport and the confinement of suprathermal ions are found to be relatively well described by theory. Cross-field transport of the thermal plasma, however, is anomalous with the momentum diffusivity being comparable to the ion thermal diffusivity and larger than the electron thermal diffusivity in neutral beam heated discharges. Perturbative experiments have studied nonlinear dependencies in the transport coefficients and examined the role of possible nonlocal phenomena. The underlying turbulence has been studied using microwave scattering, beam emission spectroscopy and microwave reflectometry over a much broader range in k perpendicular to than previously possible. Results indicate the existence of large-wavelength fluctuations correlated with enhanced transport.