Mean Thermal Conductivity Research Articles

Combined Conductive and Radiative Heat Transfer through Open-Cellular Porous Plates.

The ability of the cubic lattice model for the thermal and radiative properties of open-cellular porous materials in predicting the combined effect of conduction and radiation in plane-parallel, open-cellular porous plates was investigated in comparison with available experimental data. The validities of the P1 approximation to radiative transfer and the simple adding method for the total heat flux were also addressed. It is concluded that the cubic lattice model can be utilized accurately to evaluate the temperature porfiles and heat transfer characteristics in open-cellular porous plates and that the simple adding method gives the fairly accurate total heat flux across the media. In addition, it is found that there exists only a little discrepancy between the results for the temperature profiles and mean total effective thermal conductivities obtained by the P1 approximation and those obtained by the exact numerical method.

Boiling on a straight pin fin with variable thermal conductivity

This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=ksat(1+b(T−Tsat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed.

Thermal properties of granulite facies rocks in the Precambrian basement of Finland and Estonia

We present results of heat production, thermal conductivity and P-wave velocity measurements of 252 rock samples from five granulite facies areas in Finland and Estonia. These compositionally mainly intermediate Archaean and Palaeoproterozoic metamorphic rocks have relatively high heat production values. Mean values averaged by areas range from 0.57 to 2.24 μW m −3. The lowest values are in the Varpaisjärvi area, which is the oldest and most mafic and where the highest metamorphic pressure occurred (8–11 kbar), whereas the highest heat production is found in the Turku granulite belt where the metamorphic pressure was 4–6 kbar. The heat production decreases with the increase of the metamorphic pressure. However, a general numerical relationship cannot be presented because of considerable variations in heat production data. There is no significant difference in the metamorphic temperatures of the studied granulites and therefore no dependence on temperature is found. Further, our data suggest no relationship between heat production and P-wave velocity. The mean thermal conductivity of granulites varies from 3.0 to 3.5 W m −1 K −1. Slightly elevated thermal conductivity values in the Varpaisjärvi and Lapland granulite areas can be attributed to higher sillimanite and quartz contents, respectively.

Terrestrial heat flow in the Paraná Basin, southern Brazil

We present 56 new heat flow values from the intracratonic Paraná Basin in southern Brazil. This large basin is filled with up to 5 km of Paleozoic and Mesozoic sedimentary rocks. In the Late Jurassic‐Early Cretaceous a great igneous event capped most of the basin surface with flood basalts up to 1700 m thick. Geothermal gradients computed from 79 deep exploration boreholes range from 20 K km−1 to 30 K km−1 with the lower gradients generally located in the central part of the basin. Thermal conductivities were determined on 247 core samples. The harmonic mean thermal conductivity of the section encountered by the boreholes decreases from 3.0 W m−1 K−1 at the eastern basin margin to 2.0 W m−1 K−1 in the basin center; this variation is related to the thickening of the basalt cap toward the basin center. Surface heat flow values for the 56 sites range from 40 mW m−2 to 75 mW m−2, with larger and more variable values (50–70 mW m−2) occurring along the eastern margin of the basin in the region without basalt cover. The heat flow in the central part of the basin (40–50 mW m−2) is less than that on the basin margin by about 15 mW m−2 and is more uniform. We discount advective effects as an explanation of the heat flow pattern because if a topographically driven flow system existed, it would diminish heat flow in the elevated recharge area along the basin margin and augment heat flow in the discharge area along the basin axis, opposite to what is observed. Wholly conductive models show that larger‐scale thermal conductivity contrasts produced by the flood basalts do not refract significant heat into the surrounding higher‐conductivity sedimentary section on the periphery of the basalts. Other model calculations show that the heat flow at the surface reflects the heat input from the basement with only minor, if any, redistribution within the basin. We conclude that the thermal data indicate a dominantly conductive thermal regime within the basin and that the observed heat flow pattern is not likely to result from intrabasinal causes. The observed pattern likely reflects the larger‐scale thermal structure of the lithosphere of this region, developed at the time the flood basalts were generated and extruded.

Contact conductance of selected metal-matrix composites

Thermal contact conductance data are reported for metal-matrix composite materials at various temperatures. The surfaces were ground using a diamond wheel; therefore, the surface characterization parameters were anisotropic. The measurements were for 2124 aluminum with silicon carbide particulate (SiCp) volumetric loading fractions of 25 and 30%, and 6061 aluminum with SiCp loading fractions of 40 and 55%. The results were nondimensionalized and compared with a recent contact conductance theory that accounts for surface slope anisotropy of conforming rough surfaces. All data were consistently overpredicted by the theory, which does not include composite material effects. In fact, the sample surfaces did not show the bivariate normal surface slope distribution fundamentally assumed by the theory. It was concluded that a new theory may be needed to account for composite particle effects, surface slope distributions other than bivariate normal, or both of these effects. P V Nomenclature contact microhardness contact conductance harmonic mean thermal conductivity surface height variance minimum profile slope variance maximum profile slope variance apparent contact pressure ratio of minimum to maximum rms profile slopes

Thermal conductivity of IR-opacified silica aerogel powders between 10 K and 275 K

The thermal conductivity of evacuated pure and opacified silica aerogel powders was measured in a guarded hot plate apparatus for temperatures from 10 K up to 275 K and external loads from 1.5*104 Pa to 105 Pa. Infrared optical measurements of the extinction give the possibility to separate contributions from solid thermal conduction and radiative thermal transport. Measured thermal conductivities range from 29 to 80*10-6 W m-1 K-1 at a temperature of 15 K and from 0.9 to 3.1*10-3 W m-1 K-1 at a temperature of 250 K. The solid thermal conductivities lambda powder of the powders were compared with those of the monolithic silica aerogel ( lambda monolith) the powder grains consist of. The ratio g'= lambda monolith/ lambda powder was found to be temperature independent in the investigated temperature range. Thus g' can be interpreted as a geometrically induced reduction factor. The mean thermal conductivities averaged over the application temperatures range from 0.7 to 2.2*10-3 W m-1 K-1 for boundary temperatures of 77.6 and 290 K and from 0.5 to 1.8*10-3 W m-1 K-1 for boundary temperatures of 20.4 and 290 K. The investigated silica aerogel powders show a large improvement potential for cryogenic thermal powder insulations. They are well suited to substitute expanded Perlite as cryo insulation.

The thermal blanketing effect of sediments on the rate and amount of subsidence in sedimentary basins formed by extension

The thermal blanketing effect of sediments with finite thermal conductivity on the rate and amount of subsidence in rift basins is presented, in contrast with Mckenzie's (1978) model, which assumed infinite thermal conductivity of the sedimentary covers. The post-rift cooling of the lithosphere is shown to be very slow owing to the blanketing effect. Even 200 m.y. after extension ceases, there is still an enormous amount of residual heat in the lithosphere. With moderate thermal conductivity of the sediments ( k s = 2.0 W/mK), the maximum discrepancy in subsidence predicted by the two models (i.e. the present model and that of Mckenzie) are 2 km, 2.6 km and 3.2 km for thinning factors of 1.5, 2 and 3 respectively. Subsidence is moderately sensitive to k s when k s is greater than 2.0 W/mK, becoming more sensitive to k s when k s is less than 2.0 W/mK. The presence of mudstone would further slow down the cooling. The thermal conductivity of the sediment is shown to govern the temperature gradient of rift basins, although it has little influence on heat flow. The heat production of the upper crust and sediment comprises an important component of heat flow. Unless heat absorption in rift basins is unusually high, subsidence is insensitive to the heat production of sediments. When the thinning factor is less than 2, the mean temperature gradient of rift basins is shown to decrease quickly over a few million years, and as a result such basins are not favourable as regards hydrocarbon maturity. The Central Graben of the North Sea is chosen to test the model. The model satisfactorily predicts the subsidence history and thermal evolution, with the base Zechstein as the basement and the Cenozoic subsidence as the thermal subsidence. The best-fit value of the mean thermal conductivity of the sediments in the graben is 1.67 W/mK, and the thinning factor is about 2.

Heat flow from a scientific research well at Cajon Pass, California

The long‐standing “stress/heat flow paradox” was the primary scientific motivation for the Cajon Pass borehole. For nearly two decades, the absence of a fault‐centered heat flow anomaly from measurements to relatively shallow (∼200 m) depths had indicated low average shear stresses (≤20 MPa) on the San Andreas fault, while laboratory data on rock strength and in situ stress determinations to about a kilometer had indicated high stress (∼100 MPa). Initial results from an unsuccessful 1.7‐km‐deep oil well at the site gave a high heat flow (∼90 mW m−2) consistent with a strong San Andreas fault; however, the late Cenozoic geologic history of the Cajon Pass area suggested that the anomalous heat flow was the transient effect of rapid erosion. Theoretical studies predicted that the ∼30% surface anomaly would be substantially reduced at depths of 3–5 km. The research borehole reached a total depth of 3.5 km. Below a superficial covering of Tertiary sedimentary rocks, it penetrated gneissic rocks with composition ranging from gabbroic to granodioritic. Core recovery amounted to only about 3% of the total depth, necessitating the use of drill cuttings to characterize thermal conductivity. This, in turn, resulted in much higher uncertainties in average conductivity (±10–15%) than would have occurred with a continuously cored hole (±3–5%). From a time series of temperature logs, equilibrium temperature gradients were established over selected intervals of 250–500 m to within 95% confidence limits of 2%. These gradients were combined with harmonic mean thermal conductivities having larger uncertainties to give interval heat flows, which vary systematically from 100 ± 5 mW m−2 in the uppermost 400 m to 75 ± 3 mW m−2 in the lowermost 300 m. Thus, at the Cajon Pass site, heat flow is decreasing with depth at a mean rate of more than 7 mW m−2 per kilometer, consistent with a frictionless fault and with theoretical predictions based on local erosional history.

Stabilization of CuNi/Nb-Ti superconductors by MgO powder

The CuNi/NbTi superconductor of a persistent current switch (PCS) with high normal state resistance is very susceptible to external disturbances. To stabilize the PCS, it is necessary to improve its mean thermal conductivity. A MgO powder coating was used on the surface of the conductors as a stabilizer. The thermal conductivity of MgO is two orders of magnitude larger than that of CuNi at < 10 K. Since the MgO is an insulator, it can be used at any place in the PCS. The values of minimum quench energy (MQE) for the Cu-Ni/Nb-Ti single wire and a formed strand conductor with a rectangular shape were measured using a pulse heating technique. The results obtained show that the MQE values for the stabilized single wire and the strand conductor with MgO powder were three times larger than those of the non-stabilized single wire and strand conductor. From these results it is expected that a PCS can be stabilized by a surface coating of MgO.

Calculation of the Mean Thermal Conductivity of Heterogenious Solid Mixture with the Voronoi-Polyhedron Element Method.

A method of discretizing a three-dimensional closed space into the Voronoi-polyhedron elements was applied to the numerical analysis of heat-conduction problems in heterogeneous solid mixtures. The computation was done for various mixtures of two randomly distributed components. Thermal conductivity of the two-component mixture is more strongly affected by the arrangement of components with respect to the mean heat flow direction than by the shape of components. The statistical mean of thermal conductivity can be roughly approximated by the geometrical average. Empirical formulae were obtained from the results. In order to accurately predict the thermal conductivity of a mixture of three or more components, the numerical calculating method divised in this study can be employed successfully.

Effects of Correlated Scattering on Coupled Heat Transfers by Conduction and Radiation through a Packed Layer of Glass Beads

The effects of correlated scattering on the combined conductive and radiative heat transfer through a packed layer of glass beads are theoretically examined. The energy equation and the spherical harmonic equations of the first order for radiative transfer are numerically solved utilizing the correlated or uncorrelated radiative properties for packed glass spheres. The correlated scattering calculations for temperature profiles and mean total effective thermal conductivities are compared with the uncorrelated scattering calculations and our previous experimental results

Relative contact pressure - Dependence on surface roughness and Vickers microhardness

An explicit expression for the contact hardness and the relative contact pressure is developed. This expression is simple and clearly shows the dependence of the contact hardness and the relative contact pressure upon the Vickers microhardness correlation coefficients and the surface roughness parameters. Parametric studies of the contact conductance are performed, and it is shown that theoretical predictions and experimental data are in good agreement. Nomenclature = mean contact radius, m = apparent contact area, m2 = constant for Vickers microhardness correlation ah = dimensionless conductance, C = - = Vickers indentation diagonal, m = conductance, W/mZ.K = bulk hardness, MPa = contact microhardness, MPa = Vickers microhardness, MPa = thermal conductivity, W/m.K = harmonic mean thermal conductivity, W/m.K = mean absolute asperity slope = constants in Eqs. (20) and (21) mks

The effects of plastic bending strain on the thermoelectric properties of bismuth telluride

In an effort to increase the thermoelectric figure of merit of bismuth telluride by reducting the phonon mean free path length and thermal conductivity, single crystals of the material were subjected to a series of plastic bending strains. The maximum strain that was applied is consistent with a separation between dislocations of the order of 2 μm. It was found that there is no observable change in the Seebeck coefficient, the electrical resistivity or the thermal conductivity, even when samples are bent to an inside radius of curvature of about 5 mm.

Low Rayleigh number flow in a heat generating porous media

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid, since conduction was the expected mode of heat transfer at low heat generation rates for a lead sphere air porous media system. The solution of the non-dimensionalized momentum and energy equations resulted in small Rayleigh numbers (2×10 −6 to 0.2) indicating the heat transfer is by conduction. Solutions for the stream lines and isotherms were obtained using a transient explicit finite-difference approximation using a mean bed thermal conductivity.

The integral mean diffusivity for particle-gas mass transfer calculations under thermal plasma conditions

A new integral mean diffusivity is proposed for the calculation of the mass transfer rate around a small particle immersed in a thermal plasma gas. Analogous to the integral mean thermal conductivity widely used for the corresponding heat transfer calculations, the integral mean diffusivity greatly facilitates the use of the convenient isothermal correlation, Sh=2.0, for the gas-particle mass transfer calculations. The calculation method accounts for both ordinary molecular diffusion and thermal diffusion. The latter has been found to play a significant role under thermal plasma conditions. The use of the integral mean diffusivity is illustrated with an example calculation on an Ar-He plasma system.

Thermal diffusivity of upper chalk from Hampshire, England

The thermal diffusivity of Upper Chalk from the Micraster coranguinum zone had been calculated from 8 year temperature data obtained from depths between 30 cm and 21.34 m at Harestock, near Winchester, Hampshire. Amplitudes and phase lags were calculated from these data using Fourier analysis. Values of thermal diffusivity were calculated from the variation of amplitude with depth and phase lag with depth for the first harmonic using the Fourier heat flow equation. Agreement between the two methods was very good between 30 cm and 914 cm depth. An overall mean value is 0.004489 ± 0.00052cm −2s −1. Using appropriate values of porosity (47%) and density the mean thermal conductivity is 1.519W m −1°C −1± 0.326, for the water saturated state.

Transient heat conduction under plasma conditions

A theoretical analysis was made of the different phenomena encountered and the assumptions involved in the calculation of the heat transfer rate to a single sphere under plasma conditions. In the presence of steep temperature gradients it is shown that if the integral mean thermal conductivity of the plasma is used in the evaluation of the heat transfer coefficient, the Nusselt number for the conduction heat transfer between the plasma and the particle is equal to 2.0. The results also show that the relaxation time of the thermal boundary layer around the particle is negligible compared to its transient heating-up time. Computations were carried for particles of different diameters (20–100 μn) and materials (Al 2O 3, W, Si, Cu…) immersed in plasmas of argon, nitrogen and hydrogen over the temperature range 4000–10000 K. These show that for Biot numbers greater than 0.02, temperature differences as high as 1000 K can develop between the surface and the center of the particle even for a particle as small as 20 μm in diameter. In a few cases where the heat flux is particularly high (hydrogen plasma at 10 000 K) the surface temperature of a 100 μm alumina particle can reach the boiling point of alumina (4000 K) while its center is still in the solid state. The results of a relatively simple analysis show that, except for a particle with a surface temperature above 2000 K immersed in an argon or a nitrogen plasma below 4000 K, radiation heat losses from the particle to the surroundings are negligible compared to the conductive heat flux from the plasma to the particle.

Calculation of Thermal Conductivity from Lithology and Laboratory Measurements on Oil Well Cores: ABSTRACT

The harmonic mean thermal conductivity of the whole rock column traversed by a well is calculated from the thicknesses of the different kinds of rock in the section and their respective thermal conductivities. Lithologic logs provide the thicknesses; laboratory measurements on cores, the conductivities. Heat flow can be then calculated by multiplying the mean conductivity by the temperature gradient obtained from corrected bottom-hole temperatures. In the sedimentary basins of Sumatra and Brazil the conductivities range from 4.1 to 6.5 mCal/cm°C sec but the average for all the basins is close to 5. The mean conductivity of a well depends on the sand-shale ratio and can probably be calculated without loss of precision without recourse to more measurements on samples. onductivity determinations and heat flow in three Tertiary basins in Sumatra and in two Cretaceous basins in Brazil involving over 2,000 wells are reviewed. It is suggested that calculations of mean conductivity and heat flow be added to the existing AAPG compilation of temperature gradients in North America. End_of_Article - Last_Page 1364------------

Thermal properties and coal rank in rocks and coal seams of the southern Sydney Basin, new South Wales: A palaeogeothermal explanation of coalification

Measurements of thermal conductivity on 106 disc specimens of rocks from 275 m of the Permian to Triassic section of the Southern Coalfield of the southern Sydney Basin have been carried out in an effort to explain a high rank gradient in the Permian coals. The samples came from six diamond drill holes north and west of Wollongong, although one hole only provided specimens of a syenitic sill (n = 17, mean thermal conductivity = 2.36 W/m°K, s.d. 0.03). When combined with previously published data on chip specimens, with which there is good agreement, from a further four drill holes the mean thermal conductivity for the late Permian and early Triassic sandstones and shales is 3.20 W/m°K. Heat generation by Permian volcanic rocks below the coal measures (from about 1 to 3 μW/m 3), and by basement granitic rocks, appears to be consistent with previously reported heat flow for the southern Sydney Basin (about 80 mW/m 2). This heat flow is a relatively high value for the east coast of Australia. Younger (Mesozoic and Tertiary) intrusive and extrusive igneous rocks produce local coal-rank anomalies, but do not appear to have any regional effect. The rank of coals above the Permian volcanic rocks appears to be little affected by the presence of the igneous rocks and the coal-rank decreases towards the major area of vulcanicity. Organic matter in sedimentary rocks interbedded with the volcanic rocks is of relatively high rank but it appears that these thermal effects do not extend more than about 100 m above the base of the coal measures. The area of high rank north and northwest of Wollongong seems likely to be a regional effect associated with a combination of high heat generation in basement and the Permian rocks, and high heat flow from the basement. Greater cover on the coal measures, together with an increase in the proportion of rocks of relatively low thermal conductivity in the cover, may also influence the rank in the Permian coal.

Computation of acoustic‐gravity waves, Kelvin‐Helmholtz instabilities,and wave‐induced eddy transport in realistic atmospheric models

A variety of motions associated with gravity waves and Kelvin‐Helmholtz instabilities have recently been detected by high‐power VHF and UHF radars at tropospheric, stratospheric, and mesospheric heights. The simultaneously observed mean temperature and wind profiles differ considerably from those used particularly in theoretical studies of wave‐mean flow interactions. Therefore a linear operational model has been developed describing acoustic‐gravity waves and Kelvin‐Helmholtz instabilities in compressible atmospheres with arbitrary vertical profiles of the mean temperature, wind, and viscosity coefficient. The linearized hydrodynamic equations are solved by the nonstandard multilayer method and a Gauss‐Seidel group iteration. Results from test computations of wave‐critical layer interactions and a Kelvin‐Helmholtz instability show good quantitative agreement with known theoretical results from simple incompressible models. Wave‐induced instabilities are parameterized by mean eddy viscosity and thermal conductivity, assuming that the wave‐perturbed gradient Richardson number is nowhere smaller than some critical value. A new iterative method is used to obtain the height profiles of the eddy transport coefficients. At mesospheric heights, wave‐induced dissipation limits the amplitudes of internal gravity waves so that no significant nonlinearities are introduced in the hydrodynamic equations.