Rosseland Mean Extinction Coefficients Research Articles

Design and optimization of core/shell structures as highly efficient opacifiers for silica aerogels as high-temperature thermal insulation

Opacifiers are usually doped in the silica aerogels to reduce the radiative heat transfer at high temperature. However, the doped opacifiers will enhance the heat conduction in the solid phase and increase the density of silica aerogels dramatically. For developing lightweight and efficient opacifiers, in this paper, different types of core/shell opacifiers are designed, and their extinction performance is investigated, theoretically. Then the optimal temperature-dependent particle size and doping amount of these opacifiers are obtained by maximizing the Rosseland mean extinction coefficient and minimizing the total thermal conductivity of silica aerogel composite. The results show that the hollow carbon black opacifiers might greatly reduce the densities of the opacifier-doped silica aerogels without deteriorating appreciably their insulating capability, and the carbon/SiC, carbon/TiO2 and carbon/Al2O3 core/shell opacifiers exhibit excellent extinction performance and would be strong candidates for high temperature due to their high extinction performance, low density and high-temperature stability. Finally, a core/shell opacifier-gradient-doped silica aerogel based on the optimal opacifier types and doping amount is designed, which significantly improves the insulating performance and reduces the density of silica aerogel composite. The results of this paper present important references for the process design and improvement of comprehensive performance of opacifier-doped silica aerogels.

Measuring radiative properties of silica aerogel composite from FTIR transmittance test using KBr as diluents

Radiative properties such as spectral extinction coefficient, Rosseland mean extinction coefficient and radiative thermal conductivity are the key features of porous insulation materials. For silica aerogel composites with fiber and opacifier, it is difficult to determine the spectral extinction coefficient and radiative thermal conductivity via experiment accurately. The spectral extinction coefficient of such composites is usually determined by a transmittance test using KBr as a diluent. The traditional model has several assumptions on determining the extinction coefficient from the transmittance measurement: the diluents are assumed as a pure transparent medium, the pressed pellet has no reflection, and the composite powder is in series with the KBr when calculating the effective thickness of the composite. Thus, the extinction coefficient determined from the traditional model with these assumptions will result in some uncertainty on predicting the radiative thermal conductivity. To overcome the drawbacks, improved models are proposed by considering the absorption of KBr diluents, sample reflection and random distribution of sample powder in the diluents. KBr diluted silica aerogel composite pellets with the same constituents and concentrations but different thicknesses are prepared using the pressed pellets method. The transmittances of the pressed pellets are measured by Fourier transform infrared spectroscopy (FTIR). The spectral extinction coefficients are calculated from the measured transmittances with proposed models. The radiative thermal conductivity of silica aerogel composite is calculated with the measured Rosseland mean extinction coefficient determined from different models. This study found that the developed models could eliminate the assumptions of the traditional model.

A theoretical model for the effective thermal conductivity of silica aerogel composites

In the present paper, a complete engineering calculation procedure for fast evaluations of the effective thermal conductivity of the silica aerogel composites is developed as follows. First, the spherical hollow model is adopted to calculate the conductive thermal conductivity of pure silica aerogels. Then, a mixing model is used to consider the conduction enhancement effects of doped opacifiers and fibers. Next, the Mie theory is adopted to calculate the temperature-dependent Rosseland mean extinction coefficient of the aerogel composites, and the radiative thermal conductivity is obtained according to the Rosseland equation. Finally, the superposition of the conductive thermal conductivity and radiative thermal conductivity gives the total effective thermal conductivity of aerogel composites. To validate the accuracy of the present model, some corresponding experimental measurements are conducted based on the Hot Disk thermal constant analyzer, and the experiment data agree well with the theoretical calculation values. The maximum deviation is about ±10%. The influences of the temperature, pressure and the structure parameters on the prediction of the effective thermal conductivity are then investigated. To determine the dominant factor of the effective thermal conductivity, the contributions of gas, solid and radiation to the total effective thermal conductivity are investigated individually and some significant results are obtained.

Measurement of the contribution of radiation to the apparent thermal conductivity of fiber reinforced cement composites exposed to elevated temperatures

The contribution of radiation to the apparent thermal conductivity of fiber reinforced cement composites exposed to a thermal pre-treatment up to 1000 °C is investigated using Fourier transform infrared (FTIR) spectrometry. The transmittance spectra are measured in the wavelength range of 2.5–16 μm. The radiative thermal conductivity is then calculated using the spectral extinction and Rosseland mean extinction coefficients. Experimental results show that for the analyzed materials radiation can represent up to 4.54% of the apparent thermal conductivity. The expanded uncertainty of the measurement is found within the range of 12.4–15.9%, being affected by the accuracy of the FTIR spectrometer in the most significant way.

Thermal Properties of Silica Aerogel Formula

The thermal conductivity of silica aerogel developed in this research program was measured using the transient hot-wire technique. The thermal conductivity of monolithic samples drops significantly from 9.3 mW/m · K to 3.2 mW/m · K with modest pressure reduction from 1 atm to 0.1 atm. The same aerogel in granular form has a thermal conductivity of 15.0 mW/m · K at ambient gas pressure with a modest compression applied to compact the granules and reduce the air void sizes. Radiation heat transfer in the hot-wire test may not be representative of its contribution in large scale applications. Measurements of the monochromatic extinction coefficient over the wavelengths of interest resulted in a Rosseland mean extinction coefficient of 2400 m−1 at 300 K. The small thermal penetration distance during the hot-wire measurements suggest that in actual use radiation could contribute approximately 2.5 mW/m · K with a possible upper limit of 3.0 mW/m · K to the effective thermal conductivity over that measured using the transient hot-wire method.

Cold protective clothing with reflective nano-fibrous interlayers for improved comfort

Purpose – The purpose of this paper is to develop multilayer clothing assemblies consisting of fibrous battings and reflective nano-fibrous thin layers for cold protective clothing for improved thermal insulation. Design/methodology/approach – Thermal insulation values of totally 20 assemblies made of varying layers of a thick polyester batting and four different types of thin interlayers were measured using a guarded hot-plate to investigate the effect of the properties of thin interlayers and construction of multilayer assemblies on thermal insulation. Cold protective jackets filled with polyester battings sandwiched with or without interlayers were also made and tested on the sweating fabric manikin-Walter. Findings – Results show that the Rosseland mean extinction coefficients of the thin interlayer and the associated radiative thermal conductivity of the interlayers have significant influence on thermal insulation of the assembly when more than one reflective nano-fibrous interlayers are sandwiched in the assembly. The cold protective jacket filled with multilayer polyester battings and reflective nano-fibrous interlayers have better thermal insulation and moisture permeability index (im) than those filled with the same multilayer polyester battings, but with non-reflective nonwoven interlayers or without interlayers. Originality/value – This paper clearly demonstrates the advantages of reflective nano-fibrous thin material for interlayers in the cold projective jacket.

Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation

An inverse model based on the shooting method, Mie theory and the improved Kramers–Kronig (KK) relation was combined with FTIR and Abbe refractometer measurements to calculate the complex refractive indices of various infrared opacifiers. The effects of opacifier sizes, types and shapes were then analyzed based on the Rosseland mean extinction coefficient using Mie theory and anomalous diffraction theory (ADT). This model provides theoretical guidelines for designing materials with optimized parameters, such as size, type and shape of opacifiers, to improve the aerogel thermal insulation at high temperatures. The results show that the optimum diameter of SiC particles to minimize the radiation is 4 μm for T < 400 K and 3 μm for T > 400 K. Carbon black is the optimum opacifier for T < 600 K while SiC is the optimum opacifier to minimize the radiative heat transfer for T > 600 K among the investigated opacifiers of SiC, TiO2, ZrO2, amorphous SiO2 and carbon black. The infrared extinction ability for various shapes is largest for oblate spheroids and decreases for spheres, cubes, cylinders with small length-to-diameter ratios, and then long, thin cylinders.

Radiative heat transfer study on silica aerogel and its composite insulation materials

This paper studies the thermal radiative transfer in silica aerogel and silica aerogel composite insulation materials (a xonotlite–aerogel composite and a ceramic fiber–aerogel composite). The spectral transmittances of silica aerogel, xonotlite-type calcium silicate, and ceramic fiber insulation materials–all considered semi-transparent mediums capable of absorbing, emitting, and scattering thermal radiation–are measured with a Fourier transform infrared spectrometer (FTIR) at different infrared wavelengths ranging from 2.5 to 25μm. The spectral transmittances are used to determine the specific spectral extinction coefficient and the specific Rosseland mean extinction coefficient of each sample. The radiative conductivity of each sample, deduced from the overall thermal conductivity measured using the transient hot-strip (THS) method, is compared against diffusion approximation predictions by using the measured spectral extinction coefficient. The results show that the spectral extinction coefficients of the samples are strongly dependent on the wavelength, particularly in the short wavelength regime (<10μm). The total Rosseland mean extinction coefficients of the samples all decrease with increasing temperature. The radiative conductivities are almost proportional to the cube of temperature, decreasing as sample densities increase.

Thermal conductivity of polyacrylonitrile nanofibre web in various nanofibre diameters and surface densities

The effects of variation in average nanofibre diameter and nanofibre web surface density on thermal conductivity of polyacrylonitrile nanofibre web was investigated in this study. The results demonstrate using thinner nanofibres results in a lower limit of thermal conductivity, better thermal insulation performance and a higher amount of Rosseland mean extinction coefficient that means lower radiative conductivity. It can be related to higher specific surface of thinner nanofibres that means more surface area for radiative scatter and absorption leading to lower conductivity. With the increase in the surface density of nanofibre web, thermal conductivity reduced and water vapour transmission rate and thermal insulation ability improved. Higher porosity percentage and smaller pore size in the web with higher surface density could result in lower thermal conductivity.

Temperature and pressure dependent effective thermal conductivity of fibrous insulation

In present paper, a numerical model combined radiation and conduction heat transfer was developed to predict the effective thermal conductivity of fibrous insulation at various temperatures and pressures. Effective thermal conductivities of the fibrous insulation were measured over a wide range of temperature (300–973 K) and pressure ( 10 −2 – 10 5 Pa ) using a developed apparatus. The transmittance spectra in the wavelength range of 2.5–25 μm were also measured at temperatures up to 973 K using a Fourier Transform Infrared Spectrometer. From transmittance data, the spectral extinction coefficients and Rosseland mean extinction coefficients were obtained at various temperatures to investigate the radiative heat transfer in fibrous insulation. The numerical and experimental data were compared. It was found that the calculated values corresponded with the experimental values within an average of 14.7 percent. Numerical results were consistent with experimental results throughout the investigated environmental conditions.

Experimental and theoretical studies on high-temperature thermal properties of fibrous insulation

In the present paper, an experimental apparatus has been developed to measure heat transfer through high-alumina fibrous insulation for thermal protection system. Effective thermal conductivities of the fibrous insulation were measured over a wide range of temperature (300–973 K) and pressure (10 −2–10 5 Pa) using the developed apparatus. The specific heat and the transmittance spectra in the wavelength range of 2.5–25 μm were also measured. The spectral extinction coefficients and Rosseland mean extinction coefficients were obtained from transmittance data at various temperatures to investigate the radiative heat transfer in fibrous insulation. A one-dimensional finite volume numerical model combined radiation and conduction heat transfer was developed to predict the behavior of the effective thermal conductivity of the fibrous insulation at various temperatures and pressures. The two-flux approximation was used to model the radiation heat transfer through the insulation. The experimentally measured specific heat and Rosseland mean extinction coefficients were used in the numerical heat transfer model to calculate the effective thermal conductivity. The average deviation between the numerical results for different values of albedo of scattering and the experimental results was investigated. The numerical results for ω=1 and experimental data were compared. It was found that the calculated values corresponded with the experimental values within an average of 13.5 percent. Numerical results were consistent with experimental results through the environmental conditions under examination.

Measurement of radiative thermal properties of thin polymer films by FTIR

Although a number of test methods have been reported for the characterization of radiative thermal properties of semi-transparent materials and textile fabrics, the need for specialized equipment limited the application of these test methods. This paper reports on the use of a conventional instrument, viz. Fourier transform infrared (FTIR) spectroscopy, for the characterization of radiative thermal properties of thin polymer films for application within an intermediate temperature range. Experimental measurements on spectral transmission with FTIR were performed on four types of thin films with high mass fraction, viz. one made of polyethylene (PE), two made of polyamide (NB and NW) and one made of aluminium foil (AF). From the measurements, extinction coefficients were calculated by using Beer's Law, and then the Rosseland mean extinction coefficients and radiative thermal conductivities were determined. The results showed that the thin AF film was the best at blocking radiation, whereas the thin PE film was the weakest. The two polyamide films (NB and NW), made of the same polymer but different in colour, had similar intermediate capability in blocking radiation, indicating colour has little effect on radiative thermal properties of polymeric materials.

Thermal properties of phenolic foam insulation

This paper presents experimental results concerning thermal properties of phenolic foams, with or without activated carbon. Effective thermal conductivity (keff ) of various samples is measured using heat flow thermal conductivity testers that comply with ASTM C518. Transmittance spectra are taken using FTIR for samples of various densities. Extinction coefficient spectra are obtained by applying Beer's law. The Rosseland mean extinction coefficients and radiative thermal conductivities are then obtained for various temperatures. Results show that keff increases with temperature. Furthermore, it takes only approximately 2 hours for the sample to become saturated with moisture. The keff of saturated samples is about 20 % higher than that of the dry samples. Addition of activated carbon shows no appreciable effect on keff . The extinction coefficient increases with sample density. Radiation accounts for approximately 15% of the total heat transfer for phenolic foams at near room temperatures.

A MONTE CARLO (MC) METHOD APPLIED TO THE MEDIUM WITH NONGRAY ABSORBING-EMITTING-ANISOTROPIC SCATTERING PARTICLES AND GRAY APPROXIMATION

A Monte Carlo (MC) method is applied to calculate radiative transfer in a nongray medium using spectral radiative exchange factor RD ij u . The creditability of the present MC model has been validated by comparing it with the results using other research methods. Meanwhile, the radiative transfer in an isothermal and nonisothermal medium with nongray absorbing-emitting-anisotropic ash particles is calculated by a nongray model and several gray approximation methods. A simplification from a nongray problem to a gray one by Rosseland's mean extinction coefficient, mean albedo y bar 2 , and Planck mean phase function is suggested.

Thermal radiative properties of phenolic foam insulation

Thermal insulation has long been an important subject in engineering. Foam insulations have become the most widely used insulations due to their low cost and ease of procesing. In recent years, phenolic foams find increasing applications because of their fire retardation. This paper presents experimental results of thermal radiative properties of phenolic foams, with or without activated carbon. Transmittance spectra were first taken using FTIR for samples of various densities. Extinction coefficient spectra were then obtained by applying Beer's law. Finally, by using the diffusion approximation, the Rosseland mean extinction coefficients and radiative thermal conductivities were obtained for various temperatures. Results show that the extinction coefficient increases with sample density. The addition of activated carbon increases the extinction coefficient slightly.