Showing papers on "Thermal diffusivity published in 1979"

Transient hot-strip method for simultaneously measuring thermal conductivity and thermal diffusivity of solids and fluids

Abstract: A transient hot-strip method has been developed for use with solids and fluids with low electrical conductivity. The hot strip (thin metal foil) is used both as a constant plane heat source and a sensor of the temperature increase. The accuracy of the method is so good that it might even be used for the measurement of the specific heat especially under difficult experimental conditions when the standard methods cannot be used or would be very inconvenient. This method has been tested in measurements on fused quartz, glycerine and Araldite at room temperature. The experimental conditions that cause deviations from the mathematical solution of the thermal conductivity equation are discussed and estimates for their maximum influence on the measured quantities are given.

Preparation and Thermal Properties of Dense Polycrystalline Oxyhydroxyapatite

Abstract: Solution-grown crystals of hydroxyapatite were sintered into polycrystalline oxyhydroxyapatite bodies, using the range 1050 to 1450°C. The heat capacity, thermal diffusivity, and thermal conductivity of the sintered bodies were measured by the laser flash method at 130–1000 K. The sintered bodies were 94.4 to 99.4% of theoretical density and 0.8 to 12 μm in grain size. Sintering is accompanied by grain growth and by vacancy formation and cell contraction due to thermal dehydration. Typical values of the heat capacity, thermal diffusivity, and thermal conductivity at room temperature are 0.73 J/g K, 0.0057 cm2/s and 0.013 J/s cm K, respectively. Low-temperature thermal conductivity increased with increasing temperature, similarly to that of amorphous solids. This odd behavior is discussed in terms of phonon mean free path.

On heating a stable salinity gradient from below

Abstract: When heat is applied at the bottom of a stable salinity gradient a series of layers with uniform temperature and salinity is formed. The evolution of this system is investigated in the laboratory and a numerical model of the process is developed. New layers are formed sequentially at the top of a growing convection region while lower down adjacent layers merge. For given fluid properties the convection depends upon one parameter Q, which is proportional to the (suitably non-dimensionalized) ratio of the salinity gradient to the heat flux. We find that the depth of the top of the convecting region and the number of layers present increase like the square root of time over the range of Q examined. This permits the definition of an effective conductivity, KT, for the total series of layers which is directly proportional to κT, the molecular thermal diffusivity, and inversely proportional to Q. The vertical growth of the layers is thus retarded by increasing Q. The average thickness of the layers decreases with increasing salinity gradient and appears to be independent of the applied heat flux.

Analysis of water and heat flow in unsaturated-saturated porous media

Abstract: This work investigates the theoretical and practical aspects of modeling water and heat flow in an unsaturated-saturated flow domain. Field experiments were designed and complementary laboratory analyses were employed to measure the relevant physical quantities that would enable the significance of non-isothermal effects to be determined. The Philip and de Vries non-isothermal flow model was adapted to the more general pressure (or matric) head-based approach and a new expression for the thermal liquid water diffusivity DTl is proposed. A general and versatile computer simulation program for modeling coupled non-isothermal transport is developed. The influence of coupling on diurnal subsurface moisture and heat transfer is evaluated by comparing the isothermal and non-isothermal transient numerical solutions to the heat and water transport problem. The results confirmed that coupling does not noticeably influence the temperature field, but does affect the evaporation and subsurface moisture fluxes. The non-isothermal theory is applied to calculate evaporation from dry land surfaces.

Turbulent thermal convection in the presence of rotation and a magnetic field: A heuristic theory

Abstract: The growth of linear, Boussinesq convective modes for a superadiabatic fluid in a planar geometry with negligible thermal diffusion or molecular viscosity is analysed. Small and large magnetic diffusivity limits are both considered. A finite amplitude theory is constructed by assuming that non-linearities (e.g. shear instabilities) limit the flow amplitude, and the dominant modes are assumed to be those which transport most heat. This leads to a unique prescription for the average velocity, superadiabaticity and horizontal lengthscale as a function of the imposed heat flux, rotation rate, large scale magnetic field and vertical lengthscale. Simple analytical results are provided (in terms of the relevant dimensionless numbers) which are as easy to apply as the conventional mixing length theory (MLT). The conclusions are: (i) For no rotation or magnetic field, the model reproduces MLT except that it predicts about an order of magnitude lower heat flux. (ii) Rotation alone or magnetic field alone inhibits the convection. For a given heat flux, the convective velocity and horizontal wavelength are reduced, and the temperature gradient increases. (iii) If R_0 ≾ 0.1, where R_0 is the nominal Rossby number, then the combined effect of rotation and magnetic field enhances the convection, and the maximum heat flux occurs at non-zero field. (iv) The rotational inhibition of convection in rapidly rotating stars does not substantially modify their static structure. (v) Convective velocities of around 0.02 cm/sec are predicted for the Earth's core, consistent with geomagnetic secular variation timescales, provided the toroidal field is less than about three times the poloidal field. (vi) In both the Earth and Jupiter, the actual magnetic field is within an order of magnitude of the field which minimizes the temperature gradient for a given heat flux. Application of these results to stellar and planetary dynamos is briefly discussed and critically assessed.

Analysis of thermal effects in adsorption rate measurements

Abstract: The simultaneous differential heat and mass balance equations describing sorption under non-isothermal conditions are solved, subject to certain simplifying assumptions. The solution provides a theoretical model which can be used to determine the significance of thermal effects in a transient sorption rate measurement and to analyse the uptake curves obtained when diffusion is too fast for the isothermal approximation to be valid. Experimental uptake curves for selected systems are analysed. The rapid uptake of butane in small commercial Linde 13X crystals is essentially controlled by heat transfer whereas in the A zeolite thermal effects are of only minor significance. The diffusion of 2,2,4-trimethylpentane in large (24–39 µm) crystals of 13X is an intermediate case in which both heat transfer and intracrystalline diffusion control the rate. The extent to which the intrusion of thermal effects can explain the anomalous dependence of apparent diffusivity on crystal size and the discrepancy between sorption and n.m.r. diffusivities is briefly considered.

Thermal and magnetic instabilities in a rapidly rotating fluid sphere

Abstract: A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r 0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number Rc The critical temperature gradient is smallest (Rc reaches a minimum) when the magnetic field strength parameter Λ ≃ 1 [Rc and Λ are defined in (23)] The instability takes the form of a very

Thermal, mechanical, and physical properties of selected bituminous coals and cokes

Abstract: Thermal, mechanical, and physical properties of virgin and heat-treated Pittsburgh seam coal were determined as part of a comprehensive study of combustion of monolithic coal block The information was sought to help characterize pyrolysis and combustion processes in underground coal mine fires, but should also prove useful in the study of in situ and surface coal gasifiers Measured properties include thermal conductivity, specific heat, thermal expansion, density, compressive and tensile strength, porosity, and permeability The transport property data were obtained (when feasible) in 2 mutually perpendicular directions of the anisotropic virgin coal material, and coal samples carbonized for 5 hr at temperatures of 350 C, 475 C, 500 C, 650 CC, and 850 C Other coals (Pocahontas No 3, Sewell, and Illinois No 6 seams) were investigated for porosity and relative permeability 49 references

Buoyancy-Affected Flows In Ventilated Rooms

Abstract: Calculations of velocity and temperature distributions in rooms with ventilation arrangements are reported. The method involves the solution, in finite-difference form, of two-dimensional equations for the conservation of mass, momentum, energy, turbulence energy, and dissipation rate, with algebraic expressions for the turbulent viscosity and heat diffusivity. The results are shown to be in reasonable agreement with available experimental data and the method is then applied to provide additional information useful for design purposes.

The influence of a third diffusing component upon the onset of convection

Abstract: The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

Some simplified expressions for the thermal conductivity in an external field

Abstract: For a polyatomic gas simple expressions have been derived for the thermal conductivity as well as for the variation of the thermal conductivity as a function of an external field. This has been achieved by using the total heat transport as a trial function in the kinetic theory instead of the usual approach in which translational and rotational heat transport are treated separately. For a number of gases a numerical comparison is made between both methods.

Depth Profile Measurement by Secondary Ion Mass Spectrometry for Determining the Tracer Diffusivity of Oxygen in Rutile

Abstract: Secondary ion mass spectrumetry has been applied for measuring the tracer diffusivity of oxygen in the c direction of single-crystal rutile for a temperature range of 1150 to 1450 K at 6000 Pa pressure of oxygen gas. Specimens diffusion-annealed in oxygen gas containing 18O were subsequently continuously sputtered and analyzed for 16O and 18O. The tracer diffusivity was determined from the depth profile of 18O, taking into account a surface exchange reaction of oxygen. The tracer diffusivity in Cr2O3-doped rutile was 3 to 8 times larger than that in pure rutile. For pure rutile, the diffusivity is expressed by D(m2/s)=3.4×10−7, exp [-251(kJ/mol)/RT], and for 0.08 mol% Cr2O3-doped rutile, by D(m2/s)= 2.0×10−8 exp[-204(KJ/mol)/RT]. The Cr2O3 doping had a catalytic effect on the rate constant of the surface exchange reaction on the c surface. The rate constant is represented, for pure rutile, by K(m/s)= 2.4×10−1 exp[-246(KJ/mol)/RT], and for 0.08 mol% Cr2O3-doped rutile, k(m/s)= 3.5×10−5 exp[-131(KJ/mol)/RT].

Diffusion of gases through polyurethane block polymers

Abstract: The diffusivities of simple gases through a series of polyurethane block copolymers of differing aromatic urethane content and type of soft segment were measured using a quadrapole mass spectrometer as a detecting device. Although an Arrhenius expression generally described the temperature dependence of diffusion in this system, a discontinuity was observed in the Arrhenius plots for some materials, and the discontinuity was found to be related to the onset of the glass transition in the hard domains. Increasing the hard segment content of the materials decreased the diffusivity due to the increase in the activation energy of diffusion. Increasing the soft segment length brought about a decrease in the activation energy with an increase in diffusivity. Polyster urethanes had lower activation energies for diffusion than polyether urethanes of similar hard segment composition. Finally, as the penetrant diameter was increased, a decrease in the diffusivity and an increase in the activation energy was noted.

Heat capacity measurements by means of thermal relaxation method in medium temperature range

Abstract: The thermal relaxation method is used to measure heat capacities of small samples in the temperature range around room temperature. The calorimeter is designed to measure under heat exchange gas and a steplike excess heat is applied to the sample by irradiation from a lamp.

Diffusion and heat flow equations with allowance for large temperature differences between interacting species

Abstract: For application to planetary ionospheres we have derived diffusion and heat flow equations for a fully ionized three-component plasma and for a partially ionized three-component plasma using a formulation that is valid for arbitrarily large temperature differences between the interacting species. These equations can be applied to ionospheric situations where steady state, collision-dominated conditions prevail and where the species drift velocities are much less than the species thermal speeds (low Mach numbers). The application of the diffusion and heat flow equations to the F region and topside terrestrial ionosphere indicates that the various transport coefficients can exhibit significant variation with the different species temperature ratios.

Universal Constants for Scaling the Exponential Soil Water Diffusivity

Abstract: The exponential form of the soil water diffusivity can be scaled either with the wetting front parameter Φf = xf/t½ or with the sorptivity A0 = F/t½; these variables, which arise in the problem of sorption in a dry soil, are xf the distance to the wetting front, t the time, and F the infiltrated water volume. It is shown that the three constants used in this scaling are not independent and that only one constant is needed.

Double-beam optical method and apparatus for measuring thermal diffusivity and other molecular dynamic processes in utilizing the transient thermal lens effect

Abstract: A method and apparatus for measuring thermal diffusivity and molecular relaxation processes in a sample material utilizing two light beams, one being a pulsed laser light beam for forming a thermal lens in the sample material, and the other being a relatively low power probe light beam for measuring changes in the refractive index of the sample material during formation and dissipation of the thermal lens More specifically, a sample material is irradiated by relatively high power, short pulses from a dye laser Energy from the pulses is absorbed by the sample material, thereby forming a thermal lens in the area of absorption The pulse repetition rate is chosen so that the thermal lens is substantially dissipated by the time the next pulse reaches the sample material A probe light beam, which in a specific embodiment is a relatively low power, continuous wave (cw) laser beam, irradiates the thermal lens formed in the sample material The intensity characteristics of the probe light beam subsequent to irradiation of the thermal lens is related to changes in the refractive index of the sample material as the thermal lens is formed and dissipated A plot of the changes in refractive index as a function of time during formation of the thermal lens as reflected by changes in intensity of the probe beam, provides a curve related to molecular relaxation characteristics of the material, and a plot during dissipation of the thermal lens provides a curve related to the thermal diffusivity of the sample material

Generalization of K Theory for Turbulent Diffusion. Part I: Spectral Turbulent Diffusivity Concept

Abstract: The gradient transfer theory for turbulent diffusion is reformulated in order to obtain an improved method for applied dispersion studies. The basic innovation is that diffusivity of single Fourier components of the concentration field is treated separately, i.e., spectral turbulent diffusivity coefficients are introduced. The value of the diffusivity decreases with increasing wave vector k of the concentration spectrum. The rate of growth of an expanding cloud of material thus becomes dependent on the stage of growth. This is in qualitative agreement with the statistical dispersion theory. It is shown that the assumption of k-dependent diffusivity leads to a nonlocal flux-gradient relation. A new function, the turbulent diffusivity transfer function, is introduced. The turbulent diffusive flux depends on concentration gradients at all points in the space. The diffusion equation is written in terms of the turbulent diffusivity transfer function. The width of the turbulent diffusivity transfer fun...

A new method for determining the apparent thermal diffusivity of thermally conductive food

Abstract: Two empirical parameters, j and f, have been used to determine the thermal diffusivity values of food by several researchers. Since there are considerable variations in j values, a new procedure was developed for the experimental determination of thermal diffusivity of foods without using this parametric value. A sample was filled into a cylindrical cell whose diameter and length were approximately 10 and 130 mm, respectively. The temperatures of the sample were monitored at the mid-point of the central axis and on the inside surface of the cell. These temperatures were used to estimate thermal diffusivity values together with an analytical formula for heat conduction in an infinite cylinder. The method was utilized to determine the thermal diffusivity, Biot number, and surface heat conductance values of water, 60% sucrose solution, glycerine, cherry tomato pulp, and apple pulp. There was close agreement between thermal diffusivity values determined experimentally and such values available in published literature. Mathematical procedures are presented for estimating errors in the thermophysical property values determined experimentally, where there are errors in locating temperature sensors in a sample, errors in the shape of the diffusivity cell, and errors in the temperature sensing device.

Tracer diffusivity of Ca 45 and electrical conductivity in CaO-SiO 2 melts

Abstract: The tracer diffusivity of Ca45 has been measured in CaO-SiO2 melts in the temperature range 1500 to 1700°C. In addition the electrical conductivity has been determined. Both properties decrease with increasing silica content. The activation energies (~30 kcal g-atom−1) are of the same order of magnitude. The electrical conductivity as computed from the diffusivity on the assumption that the total current is transported exclusively by divalent calcium ions and that the usual Nernst-Einstein relationship is valid, is somewhat lower than the measured electrical conductivity with the difference increasing with increasing silica content.

Effects of Thermal Spiking on Graphite-Epoxy Composites

Abstract: Tests were performed evaluating the effects of thermal spikes on the moisture absorption characteristics, the ultimate tensile strength, and the buckling modulus of Thornel 300/Fiberite 1034 composites. Measurements were made on unidirectional and π/4 laminates, using different types of thermal spikes. A survey was also made of the existing data. This survey, together with the present data indicate how thermal spikes affect the mois ture absorption and the mechanical properties of different graphite-epoxy composites.

Heat diffusion in a solid sphere and Fourier theory: An elementary practical example

Abstract: A method to determine the thermal diffusivity of a polymer, which is suitable for the undergraduate laboratory, is described. It serves as a practical demonstration of classical Fourier theory. In particular, techniques of realizing near‐to‐perfect boundary conditions are described.

The effect of strain‐induced band‐gap narrowing on high concentration phosphorus diffusion in silicon

Abstract: A strain effect has been found to explain the anomalous reduction in P diffusivity at surface concentrations greater than ∼4×1020 cm−3. It is shown that at diffusion temperatures, misfit‐induced strain causes a reduction in the effective Si band gap up to ∼−130 meV at the solubility limit of P. This band‐gap narrowing results in reduced P diffusivity through a relative reduction of P+V= pairs in the surface region. This complex is the dominant species for P transport at high P concentrations. The diffusion of P in the tail region is dominated by V− vacancies liberated during P+V= pair dissociation events. Thus, the tail diffusivity will likewise be reduced by band‐gap narrowing in the surface region. These reductions in diffusivity can be by as much as a factor of 6 depending upon temperature and P doping.