Total Band Absorptance Research Articles

On the application of the exponential wide band model to the calculation of radiative heat transfer in one- and two-dimensional enclosures

Various implementations of the exponential wide band model (EWBM) are used to model radiative heat transfer in one- and two-dimensional enclosures containing CO 2 and H 2O. These are, first, the original banded approach using the four-region approximation for the total band absorption, second, a numerical integration of the spectral transmittance, and third, the wide band correlated k-distribution method (CKM). A correlated and a non-correlated formulation are used to solve the radiative transfer equation. In two-dimensional enclosures, these formulations are implemented using a ray tracing method (RTM) and the discrete ordinates method (DOM), respectively. The wide band CKM is found to be the best choice concerning accuracy and computational effort.

Incorporation of the thermal radiative effect of CH4, N2O, CF2Cl2, and CFCl3 into the National Center for Atmospheric Research community climate model

This paper documents the incorporation of the radiative effect of trace gases CH4, N2O, CF2Cl2, and CFCl3 into the National Center for Atmospheric Research community climate model (CCMl) longwave scheme, which presently includes the radiative effect of H2O, CO2, and O3. This development is intended for using the CCMl to study the combined greenhouse effect of increasing atmospheric CO2, CH4, CF2Cl2, CFCl3, and N2O. The radiative effect of the trace gases in a homogeneous layer is parameterized based on Wang and Shi's (1988) analytical expression for the total band absorptance. For an inhomogeneous path, a scaling approximation is used to calculate the effective total band model parameters. The same treatment of the overlapping gaseous absorption bands used in the present CCMl scheme is adopted for the new trace gases.

Universal functions for estimating total vibration-rotation band absorptance—IV. Extension of the method and its applicability to the doppler line shape

We improved the accuracy of the method of universal functions (MUF) 1,2 for estimating total band absorptances and their derivatives for nonoverlapping Lorentz-profile lines of vibration-rotation bands for linear molecules and symmetric tops. The MUF accuracy is estimated for the CO 2 v 2- and v 3- fundamental bands and the Doppler line shape. The MUF has been further developed for the CH 4 v 3- and v 4- fundamental bands.

Total band absorptance and k-distribution function for atmospheric gases

Analytical expressions for the total band absorptance and absorption-coefficient distribution function for radiatively-important, atmospheric gases are derived from the Malkmus narrow-band model and the wide-band approximation of Edwards and Menard. For individual absorption bands, the expressions are functions of the band width, the mean line-half-width to spacing ratio and two parameters describing the spectral variation of the mean line intensity. Procedures to calculate these absorption band parameters directly from the AFGL absorption line data are presented. The accuracy of the formulation is demonstrated by good agreement in the 15-μm CO 2 band, the H 2O rotational band and the 9.6-μm O 3 band for the absorptances calculated from analytical expressions, line-by-line calculations and available measurements. This formulation thus provides a useful approach to calculate the coupled radiative processes of absorption and multiple scattering due to atmospheric gases and particles.

Azide binding to cytochrome c oxidase : Effects on the oxidation-reduction and spectral properties of cytochromes a and a3

The azide dependence of the properties of the hemes of cytochrome c oxidase has been evaluated in preparations of submitochondrial particles from pigeon breast muscle. Anaerobic suspensions were subjected to potentiometric titrations in the presence and absence of azide. When azide was present, the contribution of the high potential heme increased from 50% to 87% of the total absorption change at 603–624 nm with little change ( <1 nm) in the absorption maximum. The low potential heme decreased in total alpha band absorption and its absorption maximum shifted from 606 nm to 610 nm. The two hemes made approximately equal contributions to the Soret absorption peak and this changed only slightly when azide was added. In the presence of a constant azide concentration of 20 m M, the high potential heme had an essentially unchanged half-reduction potential at pH 7.0 ( U 1/2,7.0) but became less pH dependent at more alkaline pH values (30–50 mV/pH unit versus 60 mV/pH unit), while the low potential component became pH independent. The possible identification of the hemes observed in the presence of azide with cytochromes a and a 3 is discussed.

A wide-band absorption coefficient integration kernel

The concept of a wide-band absorption coefficient integration kernel is introduced and developed for use in problems involving the radiant heat transfer of real absorbing/emitting gases. For each of the non-transparent, absorption/emission bands of a gas, the kernel transforms the detailed wavenumber integrations to more convenient integrations over the absorption coefficient. A simple expression for the integration kernel is developed from the Tien and Lowder expression for the total band absorptance. The use of the kernel is then illustrated and compared with an exact solution through the example of an isothermal gas between two infinite, parallel plates.

Infrared radiation properties of methane at elevated temperatures

The spectral absorptivity of the v 3 and v 4 fundamental and the v 1 + v 4 combination bands of methane have been measured at low resolution for temperatures between 290 and 850 K. Spectral mean (narrow-band) parameters for the fundamental bands have been correlated from the Elsasser model, while total band absorptance data for all three bands have been correlated using the Edwards exponential wide band model. A total emissivity chart has been developed, based on the wide band absorption models.

Universal functions for estimating total vibration-rotation band absorptance—I. Linear molecules and spherical tops

We estimate total band absorptances and their derivatives for nonoverlapping lines of vibration-rotation bands for linear molecules and spherical tops. We use universal functions obtained by replacing the sums of line contributions by integrals over the rotational quantum numbers. An optical path is introduced for the total band. Only general information is utilized on vibrational transitions and line shapes. Power and asymptotic series have been obtained for Doppler and Lorentz line shapes. For a linear molecule and the Lorentz shape, approximate formulae have been derived for the universal functions.

Radiative heat transfer in a cylindrical mixture of non-gray particulates and molecular gases

The interaction between particulate clouds and molecular gases with respect to radiative heat transfer in a one-dimensional cylindrical medium with black walls is investigated. The particulates are assumed to have a non-gray absorption coefficient with a power-law dependence on wavenumber. The absorption coefficient of the molecular gases is described by the exponential wide-band model. Heat transfer rates are found through the evaluation of internal and external total hemispherical emissivities of the particulate cloud and through evaluation of total band absorptances for the molecular gases, modified to account for the interaction with the particles. Simple, closed-form expressions for the total hemispherical emissivities and total band absorptance are also presented, resulting in good accuracy.

Total band absorptance, emissivity, and absorptivity of the pure rotational band of water vapor

Based upon the exponential wide band model, an analytical expression is derived for the total band absorptance of the pure rotational band of water vapor. It is shown that the usual band absorptance expressions, which are based on this model, are inaccurate for this band. The use of the total band absorptance in computing the emissivity and absorptivity is also considered. Representations of these functions is achieved within a simple analytical framework.

An analytical expression for the total band absorptance of infrared-radiating gases

It is shown that an exact closed form expression for the total band absorptance of infrared-radiating gases can be obtained by employing the Malkmus narrow band model and the Edwards and Menard wide band approximation. Comparisons with other approximate analytical expressions are presented.

The optical path length approach to radiation heat transfer with isotropic scattering and gaseous absorption

The hemispherical total reflectance and transmittance for banded gaseous absorption and isotropic scattering are determined by the optical path length approach. The optical path length approach decouples the scattering and absorption so that any absorption can be evaluated once the path length distributions have been evaluated. The path length distributions are determined by numerical inversion of the Laplace transform and the exponential wide band model is employed to evaluate the absorption. The effects of scattering total optical depth, scattering albedo, pressure broadening parameter and gaseous optical depth on the scattering total band absorption properties are presented and discussed.

Comparison of an analytical model with approximate models for total band absorptions and their derivatives

The introduction of the total band absorption concept has greatly reduced the mathematical complexity of integrating the spectral function in determining the i.r. radiation by nongrey molecular gases due to vibration-rotation bands. A number of simple but approximate equations for total band absorption have been developed for the investigations of i.r. radiation by nongrey gases. Most of these equations are, however, limited to completely overlapped lines and are not applicable to the strong-line cases. Others, which account for the line effects, have been developed empirically and are not directly related to the spectral narrow-band models. Analytical equations for total band absorption and its derivative were derived directly from a spectral narrow-band model and they are universally applicable to all line strengths. Presented in this paper is the comparison of the analytical model with the approximate wide-band models. Also presented is the comparison of the foregoing models with a spectral function integrated to give total band absorption.

An approximate band model for radiative transfer in semitransparent solids

A simplified model for the spectral refractive index and absorption coefficient of semitransparent solids is developed from solid state lattice vibrational theory. This model accurately predicts the total band absorptance and total internal emittance for long pathlengths and selected solids. Total band absorptance is shown to be proportional to the square root of the pathlength when the pathlength is large. Comparison to exact results for α-quartz and lithium fluoride demonstrates that the total radiative transfer properties are accurately predicted by the model when the pathlength exceeds one millimeter.

Multi-Dimensional Radiative Transfer in Nongray Gases—General Formulation and the Bulk Radiative Exchange Approximation

The present paper presents a general formulation of the radiative heat flux and its divergence for multi-dimensional radiative problems involving nongray absorbing-emitting gases. The expressions obtained are in terms of total band absorptance rather than the spectral absorption coefficient. Thus the frequency integration is eliminated, and the expressions are more compact. They avoid the necessity of detailed spectral absorption coefficient data for radiative transfer computations. Also presented is the bulk radiative exchange approximation together with its refinement. It is proposed to circumvent the mathematical complexity inherently imbedded in nongray multidimensional problems. The approximation, which is valid in the optically thin and thick limits, is found to be general and useful, not only because of its simplicity, but also because of its accuracy in all optical conditions.

Accurate Spectral Modeling for Infrared Radiation

Direct line-by-line integration and quasi-random band model techniques are employed to calculate the spectral transmittance and total band absorptance of the 4.7 μ CO, 4.3μ CO2, 15μ CO2, and 5.35μ NO bands. Results are obtained for different pressure and path lengths. These are compared with available theoretical and experimental investigations. Total band absorptance values are available in the literature for certain pressure and path length conditions for these gases. Total absorptances have been calculated for the same physical conditions, employing line-by-line and quasi-random band models and the continuous correlations of Tien and Lowder, Cess and Tiwari, and Felske and Tien. In almost all cases, the line-by-line results are found to be in excellent agreement with the experimental values. The range of validity of other models are discussed.

On the Absorption, Reflection and Transmission of Solar Radiation in Cloudy Atmospheres

Abstract Band-by-band calculations have been carried out to evaluate the reflection, absorption and transmission of solar radiation by cloud layer and model cloudy atmospheres in the entire solar spectrum. The radiation transfer program is based on the discrete-ordinate method with applications to inhomogencous atmospheres. The gaseous absorption in scattering atmospheres is taken into account by means of exponential fits to the total band absorption based on laboratory measurements. Thick clouds such as nimbostratus. and cumulonimbus reflect 80–90% and absorb 10–20% of the solar radiation incident upon them. The reflection and absorption of a fair weather cumulus with a thickness of 0.45 km are about 68–85% and 4–9%7p, respectively. A thin stratus, whose thickness is 0.1 km, reflects about 45–72% and absorbs about 1–6% of the solar flux incident on the cloud top. The reflection of a 0.6 km thick altostratus is about 57–77%, with a larger absorption of 8–15%. A number of aircraft observations reveal that ...

Wide Band Characterization of the Total Band Absorptance of Overlapping Infrared Gas Bands

Abstract The exponential wide band model is used to establish a simple analytical basis for determining the total band absorptance of two overlapped infrared gas wide bands. Solutions are first developed for homogeneous mixtures. These results are then extended to the nonhomogeneous case by using an existing scaling prescription for the wide band parameters. Comparisons are made with available experimental data for the important case of overlapping carbon dioxide and water vapor bands near 2.7 microns. The agreement is good for the homogeneous cases and is excellent for the nonhomogeneous cases for a wide range of mixture compositions and temperature distributions.

Laminar convection with an absorbing and emitting gas

The heat transfer and fluid flow are determined for fully developed laminar flow in a vertical channel. The effects of natural and forced convection and thermal radiation are included in the analysis. The spectral variation of the radiation properties are included through the use of the total band absorptance. The analysis is general and specific numerical results have been obtained for the 15 micron band of carbon dioxide. A simplified approach for large path is also presented which is in excellent agreement with the more exact results.

A laboratory atlas of the 5 ν1 NH 3 absorption band at 6475 Å with applications to Jupiter and Saturn

The 5 ν 1 absorption band of NH 3 is displayed from 6418 to 6550 Å. The total band intensity has been measured: S B = 0.66 cm −1m −1amagat −1. Line intensities and self-broadening coefficients have been measured for some of the prominent lines. Our line intensities are in good agreement with those of Rank et al. (1966) , but are about 2 times greater than those of Mason (1970). The spectrum displayed was obtained photoelectrically at a pressure of 0.061 atm, and shows many more lines than the spectrum obtained by McBride and Nicholls (1972a) at a pressure of 0.39 atm. Therefore, our new measurements can provide the basis for making a more complete rotational analysis than those of McBride and Nicholls (1972a). Since the total band absorption has previously been measured by others on moderate resolution photoelectric scans of the spectra of Jupiter and Saturn, we can use the band intensity to derive the NH 3 abundance in the atmospheres of these two planets. The NH 3 abundances in a single vertical path obtained by this method are about 10m amagat for Jupiter and 2m amagat for Saturn. These results are in agreement with previous results obtained from higher resolution photographic spectra.