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

1978 ◽  
Vol 100 (3) ◽  
pp. 486-491 ◽  
Author(s):  
S. S. Tsai ◽  
S. H. Chan
Keyword(s):  
Heat Flux ◽  
Radiative Transfer ◽  
Absorption Coefficient ◽  
Radiative Heat ◽  
Spectral Absorption ◽  
Spectral Absorption Coefficient ◽  
Multidimensional Problems ◽  
All Optical ◽  
Exchange Approximation ◽  
Radiative Exchange

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.

Effects of Radiative Transfer Modeling on Transient Temperature Distribution in Semitransparent Glass Rod

2003 ◽  
Vol 125 (4) ◽  
pp. 635-643 ◽  
Author(s):  
Zhiyong Wei ◽  
Kok-Meng Lee ◽  
Serge W. Tchikanda ◽  
Zhi Zhou ◽  
Siu-Ping Hong
Keyword(s):  
Heat Flux ◽  
Radiative Transfer ◽  
Absorption Coefficient ◽  
Radiative Energy ◽  
Transient Temperature ◽  
Band Model ◽  
Two Dimensional ◽  
Spectral Absorption ◽  
Short Wavelength Band ◽  
Spectral Absorption Coefficient

This paper presents a method of modeling the radiative energy transfer that takes place during the transient of joining two concentric, semitransparent glass cylinders. Specifically, we predict the two-dimensional transient temperature and heat flux distributions to a ramp input which advances the cylinders into a furnace at high temperature. In this paper, we discretize the fully conservative form of two-dimensional Radiative Transfer Equation (RTE) in both curvilinear and cylindrical coordinate systems so that it can be used for arbitrary axisymmetric cylindrical geometry. We compute the transient temperature field using both the Discrete Ordinate Method (DOM) and the widely used Rosseland’s approximation. The comparison shows that Rosseland’s approximation fails badly near the gap inside the glass media and when the radiative heat flux is dominant at short wavelengths where the spectral absorption coefficient is relatively small. Most prior studies of optical fiber drawing processes at the melting point (generally used Myers’ two-step band model at room temperature) neglect the effects of the spectral absorption coefficient at short wavelengths λ<3μm. In this study, we suggest a modified band model that includes the glass absorption coefficient in the short-wavelength band. Our results show that although the spectral absorption coefficient at short wavelengths is relatively small, its effects on the temperature and heat flux are considerable.

scholarly journals Spectral Absorption Coefficient of Additive Manufacturing Materials

2021 ◽  
Vol 13 (4) ◽  
Author(s):  
Nicholas J. Wallace ◽  
Matthew R. Jones ◽  
Nathan B. Crane
Keyword(s):  
Additive Manufacturing ◽  
Absorption Coefficient ◽  
Radiative Heat ◽  
Manufacturing Processes ◽  
Spectral Absorption ◽  
Spectral Absorption Coefficient ◽  
Polyamide 12 ◽  
Active Thermography ◽  
Uncertainty Estimates ◽  
Properties Of Materials

Abstract Active thermography techniques are of interest for quality assurance of additive manufacturing processes. However, accurate measurements of thermophysical properties of materials are required to successfully implement active thermography. In particular, the spectral absorption coefficient of materials commonly used in additive manufacturing must be known to accurately predict the spatial distribution of thermal energy generated from absorption of power emitted by a laser or pulsed flash lamp. Accurate measurements of these optical properties are also needed to develop greater understanding of additive manufacturing processes that rely on radiative heat transfer to fuse powders. This paper presents spectral absorption coefficient measurements and uncertainty estimates of fully and partially dense ABS, PLA, and Polyamide 12 samples.

A Method of Measuring the Temperature Profile of a Thermal Barrier Coating Using Inverse Radiative Heat Transfer Methods

2011 ◽  
Author(s):  
Travis J. Moore ◽  
Matthew R. Jones
Keyword(s):  
Heat Transfer ◽  
Measurement Error ◽  
Absorption Coefficient ◽  
Temperature Profile ◽  
Radiative Heat ◽  
Thermal Barrier ◽  
Spectral Absorption ◽  
Spectral Absorption Coefficient ◽  
Barrier Coating ◽  
Spectral Emittance

Ceramic thermal barrier coatings (TBCs) are used in power generation and aerospace turbines to protect superalloy components from large and extended heat loads. These coatings allow for increased inlet temperatures, thereby increasing efficiency and reducing air cooling requirements. Knowledge of the temperature profile in a thermal barrier coating is critical for evaluating the TBC performance and monitoring its health, as well as for accurate simulation and modeling. Non-contact, non-destructive techniques for finding these temperature profiles are highly desirable. Current techniques are limited in that they cannot measure the entire temperature profile of the TBC along with its radiative properties. An inverse radiative heat transfer method capable of determining the temperature profile, as well as the spectral absorption coefficient and spectral emittance at various wavenumbers, of a TBC using non-contact techniques was developed. A model of the measurements of the intensity exiting the TBC, which account for the emission from the substrate as well as the emission and absorption of the TBC itself, was developed. The TBC was approximated as a one-dimensional, plane-parallel, non-scattering medium. Optimization methods were used to determine the desired parameters by minimizing the error between actual intensity measurements and those calculated from the model. This method was tested for a number of simulated measurements with and without measurement error. Even with 10% measurement error introduced, the base temperature of the TBC was determined with only 0.45% error while the error in the TBC surface temperature measurement was 3.36% and that in the spectral emittance of the bondcoat was 12%. The error in the spectral absorption coefficient was significant.

Optical Constants of Soot and Their Application to Heat-Flux Calculations

1969 ◽  
Vol 91 (1) ◽  
pp. 100-104 ◽  
Author(s):  
W. H. Dalzell ◽  
A. F. Sarofim
Keyword(s):  
Heat Flux ◽  
Light Scattering ◽  
Absorption Coefficient ◽  
Room Temperature ◽  
Optical Constants ◽  
Soot Concentration ◽  
Spectral Absorption ◽  
Spectral Absorption Coefficient

Data on the room temperature optical constants of soot are presented for the wavelength regions 0.4–0.8μ and 2.5–10.0/μ. Dispersion formulas are developed for interpolating the data between 0.8 and 2.5μ. The results are used to calculate the spectral absorption coefficient and the total emissivities of soot suspensions. It is shown that the correct values of the optical constants are needed in the use of light-scattering techniques for the measurement of the soot concentration but that uncertainties introduced in flux calculations by use of approximate values of the optical constants are not greater than those introduced by the present uncertainties in the values of the soot concentration.

Spectral Absorption Coefficient of Molten Aluminum Oxide from.0.385 to 0.780 mum

1995 ◽  
Vol 78 (3) ◽  
pp. 583-587 ◽  
Author(s):  
J. K. Richard Weber ◽  
Shankar Krishnan ◽  
Collin D. Anderson ◽  
Paul C. Nordine
Keyword(s):  
Absorption Coefficient ◽  
Aluminum Oxide ◽  
Molten Aluminum ◽  
Spectral Absorption ◽  
Spectral Absorption Coefficient
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