Statistics of the Thermal Radiation Field

1965 ◽  
Vol 139 (1B) ◽  
pp. B202-B211 ◽  
Author(s):  
Evelyn Fox Keller
Keyword(s):  
Thermal Radiation ◽  
Radiation Field ◽  
Thermal Radiation Field

Kinetic and thermodynamic treatments of a neutral binary gas mixture affected by a nonlinear thermal radiation field

2012 ◽  
Vol 90 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Aly Maher Abourabia ◽  
Taha Zakaraia Abdel Wahid
Keyword(s):  
Thermal Radiation ◽  
Radiation Field ◽  
Molar Fraction ◽  
Distribution Functions ◽  
Mixture Component ◽  
Gas Mixture ◽  
Nonlinear Thermal Radiation ◽  
Binary Gas Mixture ◽  
Kinetic Coefficients ◽  
Thermal Radiation Field

In the present study, the kinetic and the irreversible thermodynamic properties of a binary gas mixture, under the influence of a thermal radiation field, are presented from the molecular viewpoint. In a frame comoving with the fluid, the Bhatnagar–Gross–Krook model of the kinetic equation is analytically applied, using the Liu–Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the binary gas mixture, such as the temperature and the concentration. The distinction and comparisons between the perturbed and equilibrium distribution functions are illustrated for each gas mixture component. From the viewpoint of the linear theory of irreversible thermodynamics we obtain the entropy, entropy flux, entropy production, thermodynamic forces, and kinetic coefficients. We verify the second law of thermodynamics and celebrated Onsager’s reciprocity relation for the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are estimated via Gibbs’ formula. The results are applied to the argon–neon binary gas mixture, for various values of both the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.

Effect of Block Valve and Crack Arrestor Spacing on Thermal Radiation Hazards Associated With Ignited Rupture Incidents for Natural Gas Pipelines

2016 ◽  
Author(s):  
Brian Rothwell ◽  
Thomas Dessein ◽  
Andy Collard
Keyword(s):  
Natural Gas ◽  
Thermal Radiation ◽  
Radiation Field ◽  
Radiation Intensity ◽  
Radiant Energy ◽  
Valve Closure ◽  
Damage Potential ◽  
Class 1 ◽  
Thermal Radiation Field ◽  
Over Time

A study was undertaken to evaluate crack arrestor and mainline block valve (MLBV) spacing distances beyond the limits defined in the 49 CFR Part 192 for Class 1 locations for the design of a 42-inch (1,067-mm) OD arctic pipeline. The study assessed whether an MLBV spacing longer than that required by 49 CFR Part 192 for Class 1 locations can provide a level of safety equivalent to that afforded by the spacing recommended in the code. This was accomplished by comparing the hazards in terms of the volume of natural gas released over time, the potential for damage to surrounding structures, and the life safety risk to personnel and the public. The analysis was performed using the software tool PIPESAFE (version 2.20.0), which was developed for a group of pipeline operators by Advantica Technology (now DNV-GL). A full transient analysis of the flow inside the pipeline and through the rupture opening was carried out with automatic shut-off valve (ASV) closures simulated as boundary condition changes at the locations of the valves triggered by the local transient pressure. Gas outflow rates were fed to a structured flame model that calculates the temperature distribution within the flame and the radiant energy emitted and uses the latter to determine the incident thermal radiation field in the area surrounding the rupture, the associated hazard areas and the accumulated thermal radiation dosage over time. These results were compiled into contour plots of thermal radiation intensity for different times; plots of the total area within specific contours of thermal radiation intensity for different times; and plots of the total area within specific contours of accumulated dosage. The dosage-area curves facilitate a direct comparison of the various MLBV and crack arrestor spacing options considered within this study by providing a simple means to establish if the change in spacing causes a substantial change to the affected areas for dosages up to the limits associated with specific levels of lethality to humans and for piloted ignition of wooden structures. It was found that valve spacing has a strong effect on the time at which closure begins to affect the outflow rate. The decline in flow rate after valve closure had significant influence on the thermal radiation field, but these effects only occurred at a relatively late stage. Increasing fracture length led to considerable changes in the shape of the thermal radiation field, but the total footprint within which casualties might be expected in the event of an ignited rupture release and the severity of injuries within the footprint are unaffected by valve closure under the assumed conditions. Similarly, the damage potential to surrounding buildings was unaffected by valve spacing, indicating that increased valve spacing could be implemented in remote, low population density areas without affecting safety.

The thermal radiation field

1974 ◽  
Vol 9 (4) ◽  
pp. 247-262 ◽  
Author(s):  
D.A. McIntyre
Keyword(s):  
Thermal Radiation ◽  
Radiation Field ◽  
Thermal Radiation Field

Influence of Thermal Radiation on Electrons in a High Temperature Plasma

1967 ◽  
Vol 22 (2) ◽  
pp. 145-147
Author(s):  
D. Biskamp ◽  
D. Pfirsch
Keyword(s):  
Diffusion Coefficient ◽  
High Temperature ◽  
Thermal Radiation ◽  
Radiation Field ◽  
Velocity Space ◽  
Temperature Plasma ◽  
Coulomb Collisions ◽  
High Temperature Plasma ◽  
Thermal Radiation Field ◽  
Fokker Planck

The velocity space diffusion coefficient of electrons in a thermal radiation field is derived “classically” and compared with the corresponding FOKKER-PLANCK coefficient arising from COULOMB collisions in a plasma. The HAMILTON-JACOBI theory is used which is especially suited to this problem.

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