Showing papers on "Thermal diffusivity published in 1985"

Dispersion in fixed beds

Abstract: A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Peclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Peclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Peclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Peclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Peclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.

Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors

Abstract: This paper presents an experimental method to measure the thermal conductivity and thermal diffusivity of biomaterials. Self-heated thermistor probes, inserted into the tissue of interest, are used to deliver heat as well as to monitor the rate of heat removal. An empirical calibration procedure allows accurate thermal-property measurements over a wide range of tissue temperatures. Operation of the instrument in three media with known thermal properties shows the uncertainty of measurements to be about 2%. The reproducibility is 0.5% for the thermal-conductivity measurements and 2% for the thermal-diffusivity measurements. Thermal properties were measured in dog, pig, rabbit, and human tissues. The tissues included kidney, spleen, liver, brain, heart, lung, pancreas, colon cancer, and breast cancer. Thermal properties were measured for 65 separate tissue samples at 3, 10, 17, 23, 30, 37, and 45°C. The results show that the temperature coefficient of biomaterials approximates that of water.

Thermal evolution models for the Earth

Abstract: Thermal evolution models for the earth which are based on a parameterization of the convective heat transport are critically reexamined. Traditionally, it has been assumed that the temperature dependence of the mantle viscosity implies that internal temperature and convective heat loss are strongly coupled. Recent numerical work on the heat transport by variable viscosity convection demonstrates that the dependence of the heat flow on the mantle temperature may in fact be much weaker than expected. I compare thermal evolution models with strong and weak dependence of the heat loss on the temperature. With the weaker dependence, plate velocities and heat flow in the Archean were not more than 50% higher than today, while with the strong dependence, much larger differences are predicted. In the former case the Archaean mantle temperatures are somewhat higher, and the present-day ratio of radioactive heat production over heat loss (Urey ratio) is 50% or slightly less. The Urey ratios in the traditional parameterized evolution models are >70%. The predictions of both kinds of models are compared with the independent geological, geochemical, and palaeomagnetic evidence. Although this evidence is subject to some uncertainties, it favors in every case the evolution models based on a weak coupling of heat loss to the interior temperature.

Thermal diffusivity measurement of thin films by means of an ac calorimetric method

Abstract: A new method to measure thermal diffusivity of a thin sample was developed using a light‐irradiated ac calorimetric technique. The experimental conditions and the fundamental equations for the measurement are discussed. In principle, this method can be applied no matter how thin a sample may be. This method was tested for samples of nickel, silicon, stainless steel, and alumina in the range from 50 to 300 μm in thickness. The measured thermal diffusivities coincide satisfactorily with the values reported for bulk materials. It is concluded that this method is useful in the measurement for thin materials with a variety of thermal diffusivities, and the sample mounting is easy in comparison with other methods.

Enhanced heat conduction in oscillating viscous flows within parallel-plate channels

Abstract: The hydrodynamics of enhanced longitudinal heat transfer through a sinusoidally oscillating viscous fluid in an array of parallel-plate channels with conducting sidewalls is examined analytically. Results show that for fixed frequency the corresponding effective thermal diffusivity reaches a maximum when the product of the Prandtl number and the square of the Womersley number is approximately equal to α2 Pr = π Under such tuned conditions the axial heat transfer achievable is considerable and can exceed that possible with heat pipes by several orders of magnitude. The heat flux between different temperature reservoirs connecting the parallel-plate-channel configuration is shown, under tuned conditions, to be proportional to the first power of both the axial temperature gradient and the flow oscillation frequency and to the square of the tidal displacements. A large value for the fluid density and specific heat is also found to be beneficial when large heat-transfer rates are desired. The process discussed involves no net convection and hence achieves large heat-transfer rates (in excess of 106 W/cm2) without a corresponding net convective mass transfer. A discussion of the physical origin for this new heat-transfer process is given and suggestions for applications are presented.

Some observations of turbulence structure in stable layers

Abstract: SUMMARY Three days of measurements in stable conditions (Monin-Obukhov length L between 15 and 300 m) at the Boulder Atmospheric Observatory tower are presented. Winds came off the Rocky Mountains on two days and off the plains on the other day. Vertical profiles of the mean horizontal velocity and Brunt-Vaisala frequency N, and the standard deviation of the vertical component, a,, fluxes, spectra, cospectra, quadspectra, correlations and length scales are examined in this study. The measurements indicate that wave motion was present on all occasions, but which varied in strength, from weak to strong. New theoretical arguments are tested, which suggest that where the Richardson number is less than one, the velocity gradient dV/dz rather than N determines the integral scales L?) of the vertical velocity fluctuations, i.e. Ly) - a,/(dU/dz). But theory also suggests that it is not this scale, but the larger buoyancy scale uw/N that determines the temperature variance and thermal diffusivity. On this basis, dimensionless parameters are developed for plotting the measurements of temperature variance and thermal diffusivity. They are found to be in reasonably good agreement with other observations and with theory, even though the relative strength of wave motion to turbulence varied considerably. Low frequency wave motion appeared to be associated with significant heat flux, a possibility that has been excluded or overlooked in some previous studies.

The Diffusivity and Solubility of Oxygen in Silicon

Abstract: The diffusivity and solubility are two key parameters required for understanding and modeling the behavior of oxygen in silicon. This paper gives an up to date review of experimental determinations of these parameters, including some recent unpublished data. There is very good agreement within the long-range diffusivity results determined by secondary ion mass spectrometry (SIMS), charged particle analysis (CPA), and x-ray diffraction. The oxygen diffusivity is independent of [O], orientation, ambient, or crystal doping. The data also extrapolate well to the diffusivities obtained by the intrinsic oxygen atomic hop frequency at low temperature to give a combined expression of D = 0.13 exp(−2.53eV/kT) cm2s−1. There is somewhat poorer agreement on the solubility measurements, in part due to inconsistent calibration factors and the observation of a processing-dependent extrinsic oxygen solubility. The intrinsic solubility derived from SIMS, CPA, and infrared absorption is described by [O] = 9E22 exp (−1.52 eV/kT) cm−3. Finally, the above diffusivity and solubility parameters are compared to modeling of oxygen related phenomena in silicon, such as thermal donor and precipitate formation kinetics, and interaction with point defects during the relaxation of stress-aligned dichroism.

Enhanced Heat Conduction in Fluids Subjected to Sinusoidal Oscillations

Abstract: Analyse mathematique de l'augmentation du transfert de chaleur par conduction provoque par un ecoulement oscillatoire sinusoidale dans des tubes circulaires reliant 2 reservoirs maintenus a des temperatures differentes. Determination des variations temporelle et spatiale de temperature dans les tubes pour de faibles valeurs du produit du nombre de Womersley et du nombre de Prandtl du fluide. Calcul de la diffusivite thermique effective et determination du transfert de chaleur du reservoir chaud au reservoir froid

Thermal conductivity, thermal diffusivity, and thermal capacity of some Nigerian soils

Abstract: Thermal conductivity increased with increasing soil water content. Clayey soils had lower thermal conductivity than sandy soils at all water levels studied. Thermal conductivity ranged from 0.37 to 1.42 for sandy loam, from 0.37 to 1.90 for loam, from 0.38 to 1.71 for sandy clay loam, and fr

Thermal conductivity behavior of boron carbides

Abstract: Knowledge of the thermal conductivity of boron carbide is necessary to evaluate its potential for high temperature thermoelectric energy conversion applications. We have measured the thermal diffusivity of hot-pressed boron carbide B1-xCx samples as a function of composition (0.1 ≤ x ≤ 0.2), temperature (300 K to 1700 K) and temperature cycling. These data in concert with density and specific heat data yield the thermal conductivities of these materials. We discuss these results in terms of a structural model that has been previously advanced by two of us (D.E. and C.W.) to explain the electrical transport data. Some novel mechanisms for thermal conduction are briefly discussed.

Thermal diffusion fluid flow sensor

Abstract: A miniature solid state fluid flow sensor having a low diffusivity substrate (10), such as a polymer film, which is optionally mounted on a thermally conductive base. A resistor strip (12) on the substrate is connected to an electrical oscillator (16) and thus emits thermal waves which are propagated through the fluid at a rate dependent on a fluid flow component perpendicular to the strip. A thermoelectric detector (20), spaced from one side or each side of the strip, senses the thermal waves; and detector circuitry (26, 28, 30, 31) determines the time or phase shift due to fluid flow.

Experimental determination of the thermal conductivity of molten pure salts and salt mixtures

Abstract: The thermal conductivity of some molten salts was measured at atmospheric pressure, using the coaxial cylinder method. The pure compounds NaCO3, KNO3, and NaNO2, the equimolar mixture NaNO3-KNO3, and HITEC, which is a three-component mixture, NaNO3-NaNO2-KNO3 (0.07-0.40-0.53 in weight), were investigated. For mixtures, it was found that the experimental thermal conductivity coefficients are in agreement with calculated values using a simple linear mixing law. The thermal diffusivity was calculated and compared with experimental data.

Influences of thermal spikes in ion beam mixing

Abstract: Guided by the results of molecular dynamics simulations, we develop a thermal spike model for the relaxation of collision cascades in which the hot zone has mobile, reacting defects and cools by thermal diffusion. Marker atoms within such spikes are taken to migrate by radiation enhanced diffusion which is governed by the locally transient temperatures and defect concentrations. The atomic mixing associated with such motions is examined, on the basis of the model, for a variety of ion-target systems. The dependences of spike mixing on diffusion mechanism, irradiation ion and energy, and sample temperature are discussed.

Design of cyclic fixed‐bed adsorption processes. Part I: Phenol adsorption on polymeric adsorbents

Abstract: A model for the adsorption of phenol in a fixed bed of a polymeric adsorbent is developed. Model parameters (equilibrium parameters, capacity factor, axial dispersion, film mass transfer coefficient, and intraparticle effective diffusivity) are experimentally determined from independent experiments. Numerical solution of the model equations uses the method of lines with double orthogonal collocation in finite elements. The model is used for the prediction of breakthrough curves and is part of a package for the design of cyclic processes.

Effect of laser radiation on tissue during laser angioplasty.

Abstract: The thermal properties of adipose and ceramic atherosclerotic plaque deposits and normal arterial vessel wall were measured in the temperature range of 25-95 degrees C. In general, the data indicate that fatty plaques exhibit the lowest thermal conductivity and thermal diffusivity of the three types, whereas calcified plaques seem to have the highest values. By using a video scanning thermograph, temperature rise was recorded in normal vessel wall and plaque during ablation of tissue. Theoretical analysis suggested that realistic modeling of laser angioplasty should account for scattering of light, water content, and ablation. This paper is a preliminary report of these results.

Unsteady heat transfer during laminar flame quenching

Abstract: Measurements were made of the unsteady heat transfer to a wall during the quenching of premixed, methane-air flames. One dimensional laminar flames were produced in a constant volume chamber and the heat transfer into the quenching surface was measured by means of a platinum thin film resistance thermometer. The experiments were performed at pressures near atmospheric over a range of equivalence ratios from 0.7 to 1.2. Predictions of the heat transfer were made with two numerical finite difference models, one with detailed kinetics and the other with single step kinetics. The main experimental results are: 1) the data are successfully correlated using the heat release rate of the flame prior to quenching; 2) the maximum heat flux is related to the quenching distance and thus it may be possible to use measurements of the quenching distance to predict the maximum heat flux. A comparison of the experimental results and the numerical calculations revealed that: 1) a single step reaction model predicts the heat transfer as well as a detailed kinetics model, to within 15% of the experimental results; 2) thermal diffusion and the chemical reaction rate of combustion are the dominant processes which determine the heat flux during quenching.

A Model for Multicomponent Droplet Vaporization at High Ambient Pressures

Abstract: An analysis of multicomponent fuel droplet vaporization under elevated pressures and temperatures is made, with particular emphasis on the liquid phase transfer and high pressure phenomena. A mathematical model is proposed, which consists of a gas phase with variable properties, liquid phase with an effective diffusivity and phase equilibrium at the gas-liquid boundary. Some calculation results are given for pentane-octane mixtures. It is shown that differences between the relative evaporation rates of different species are smaller when ambient pressure is increased. It is also shown that the potential for this particular miscible multicomponent droplet to undergo micro-explosions decreases as the pressure increases.

An analysis of the thermal response of power chip packages

Abstract: Since power densities in integrated circuits and power semiconductor devices are continuously increasing due to miniaturization of circuitry, the design of optimum heat spreaders and heat sinks for these applications requires rather sophisticated calculational methods. The chips and spreaders are usually rectangular in shape and although the problem is three-dimensional in nature, it is usually approximated by two-dimensional configurations. Steady-state and transient analytic solutions are presented for the axisymmetric, two-dimensional, and three-dimensional spreader geometries, which can be used to calculate the thermal resistance of the base alone. To determine the thermal resistance of the chip-base combination, the one-dimensional chip thermal resistance should be added to that of the base. These analytic solutions provide calculational means which are easier than the numerical methods. The exact analytic steady-state and transient solutions developed for the axisymmetric, two-dimensional, and three-dimensional configurations are in excellent agreement with the numerical calculations. The parametric calculations provide information on the important guidelines that a packaging engineer should bear in mind while designing and optimizing heat spreaders for power semiconductor applications. These points can be summarized as follows: 1) for a given chip area there exists an optimal base area, 2) increasing the base thickness initially decreases the thermal resistance and beyond a certain limit the latter increases with base thickness, and 3) the convective heat transfer coefficient strongly affects the thermal resistance and the usual assumption of an isothermal base is not always appropriate.

Longitudinal and lateral thermal dispersion in packed beds. Part I: Theory

Abstract: A new model is developed for the transient thermal response of a packed bed, using the method of spatial averaging. Equations for the average temperature of the fluid and the solid phase are derived from the point equations for thermal energy in each phase. The new model exhibits some unusual convective and dispersive coupling between the equations for the average fluid and solid temperatures. The response of the model equations to a pulse disturbance is analyzed. It is found that after a sufficiently long time has elapsed, the temperature pulses for the fluid and solid phases will be separated by a constant distance and will spread or disperse about their centroids at an equal rate. The pulse separation predicted by the new model equations is larger than that predicted using more conventional analyses of heat transfer in packed beds. Effective thermal conductivities measured under steady state conditions can differ significantly from those observed in transient experiments due to the spread in temperature pulses caused by heat exchange between phases. Estimates are made of the magnitude of the more important terms affecting longitudinal and lateral effective thermal conductivities under flow conditions, in order to make possible a direct comparison between theory and experiment in a companion paper.

The diffusivity of potassium chloride and sodium chloride in concentrated, saturated, and supersaturated aqueous solutions

Abstract: The diffusion coefficients of potassium chloride and sodium chloride were measured in concentrated, saturated, and supersaturated solutions at 25/sup 0/C employing Gouy interferometry. The results indicate a maximum in the diffusivity vs. concentration curve near saturation followed by a rapid decline in diffusivity toward zero with increasing concentration in the supersaturated region. This behavior supports the idea that the diffusion coefficient approaches zero at the spinodal concentration. The data were successfully correlated by modifying an empirical activity coefficient equation (Robinson and Stokes, 1955) to account for molecular cluster effects and employing the calculated activity coefficients along with a predictive equation for diffusivity in electrolytes (Robinson and Stokes, 1955).

Measurement of silicon interstitial diffusivity

Abstract: A conceptually simple experiment to measure silicon interstitial diffusivity is described. The structure uses a silicon wafer with buried layers deep in the bulk. Oxidation of the wafer surface generates interstitials that diffuse into the wafer and enhance the buried layer diffusion. The results show that the interstitial profiles are flat out to 40 μm for the times and temperatures investigated. We can thus conclude that the interstitials move significantly faster than previously thought.

Photoinduced diffusion of Ag in GexSe1−x glass

Abstract: Diffusion of Ag in GexSe1−x (x∼0.1) under UV light irradiation is studied using Rutherford backscattering spectrometry and microlithography techniques. The diffusion coefficient at 21 °C and 2 mW/cm2 is determined to be 2.7 nm2/s. The temperature dependence of the diffusivity follows an Arrhenius‐type equation with an activation energy of 5.32 kcal/mole (0.23 eV) and a pre‐exponent factor of 2.5×104 nm2/s. The reciprocity of irradiation intensity and exposure time with respect to the diffusion distance is confirmed. Specifically, the diffusivity is found to be directly proportional to the irradiation intensity.

Outdiffusion and diffusion mechanism of oxygen in silicon

Abstract: The outdiffusion profiles of oxygen in Czochralski Si(111) within the temperature range 700–1160 °C and for three processing conditions (nitrogen atmosphere, steam oxidation, and phosphorus indiffusion) were measured by secondary ion mass spectrometry. The diffusivity and solubility of oxygen in Si were determined by fitting these profiles to a simple diffusion model. Oxygen diffusivity shows little or no dependence on processing conditions and can be expressed as D=0.14 exp(−2.53 eV/kT) cm2 s−1 for the temperature range studied. Our observations show that point defects in Si have little effect on oxygen diffusion and demonstrate that oxygen diffuses primarily via an interstitial mechanism. Oxygen solubility was the largest during steam oxidation.

Effect of intraparticle mass transfer resistance on reactivity of immobilized yeast cells

Abstract: Effect of diffusion resistance on reaction by using an immobilized yeast entrapped by Ca-alginate gel was studied. Intraparticle effective diffusivity of substrate, De, depends upon cell density, cc, i.e. De/Do = k2(1 - k1cc)2. Here, D0 is a reference diffusivity, e.g. diffusivity in water; k1 and k2 are constants. Overall reaction rates of ethanol production by immobilized resting-yeast were measured. Experimental rates coincide well with calculated results using the effective diffusivity and reaction rate of free cells. Diffusion seemed to be restricted by cells. Thus large cell density does hot necessarily mean high reactivity. Finally, the curvature of the Lineweaver-Burk plot is pointed out.

Thermal diffusivity of chemically vapour deposited silicon carbide reinforced with silicon carbide or carbon fibres

Abstract: The thermal diffusivity of chemically vapour deposited silicon carbide reinforced with either Nicalon SiC yarn or PAN-precursor carbon fibres was measured by the laser-flash method during various time-temperature treatments. The diffusivity was found to depend on the degree of densification, the direction of heat flow with respect to the fibre orientation, and the thermal history. Structural modifications, confirmed by X-ray diffraction, produced large permanent changes in the thermal properties of the SiC-SiC composites when heated above 1200° C, while only minor changes were seen in C-SiC composites heated above 1500° C.