Radiation transfer in inhomogeneous exponential media
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C. Tezcan
Abstract
The angular distribution of the radiation intensity and the related constants C and D∗ are calculated for a new choice of c(x) having the form of the Morse potential in quantum mechanics c(x) = 1 – a – be−2αx + de−αx. We use the modified Eddington method. The radiation intensity in this method is given in terms of the unknown even and odd functions of the space variable × and the direction cosine. The coefficients of these functions depend only on the space variables and satisfy second order differential equations. We solve the resulting second order differential equation using the Nikiforov-Uvarov method. The method provides exact analytical expressions and is not previously used to solve radiation problems. The numerical results are listed in a table for both the constants C and D∗ and the albedo and in the limiting cases are compared with the homogeneous values.
Kurzfassung
Die Winkelverteilung der Strahlungsintensität und der entsprechenden Konstanten C und D∗ wurde für eine neue Auswahl von c(x) Werten in Form des Morse-Potentials in der Quantenmechanik berechnet: c(x) = 1– a – be−2αx + de−αx. Dazu wurde die modifizierte Eddington-Methode verwendet. Bei dieser Methode ist die Strahlungsintensität gegeben in Form von unbekannten geradzahligen und ungeradzahligen Funktionen der Raumvariablen × und des Richtungskosinus. Die Koeffizienten dieser Funktionen hängen nur ab von den Raumvariablen und befriedigen Differentialgleichungen zweiter Ordnung. Die sich ergebende Differentialgleichung zweiter Ordnung wurde mit Hilfe der Nikiforov-Uvarov Methode gelöst. Die Methode liefert exakte analytische Ausdrücke und wurde bisher noch nicht zur Lösung von Strahlungsproblemen verwendet. Die numerischen Ergebnisse werden in einer Tabelle für die Konstanten C und D∗ und die Albedo dargestellt und in den Grenzfällen verglichen mit den homogenen Werten.
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© 2006, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Minor actinide burning in a CANDU thorium reactor
- Modeling of the TOSQAN test facility with the lumped parameter code COCOSYS
- Thermal-hydraulic modeling of the onset of flow instability in MTR reactors
- 10.3139/124.100302
- 10.3139/124.100304
- Radiation transfer in inhomogeneous exponential media
- Neutron transport problems for extremely anisotropic scattering
- Milne problem for isotropic and linearly anisotropic scattering for specular and diffuse reflecting boundary conditions solved with the HN method
- ICDE-results on complete common cause failures in the light of results obtained with the POS model
- Modelling of the cumulative behaviour of Caesium and Strontium activities in nuclear fuel
- Analytical study of the closure flow inside the ETRR-2 core chimney
- Minimizing radiation exposure for the reactor staff during the dismantling of a TRIGA research reactor
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Minor actinide burning in a CANDU thorium reactor
- Modeling of the TOSQAN test facility with the lumped parameter code COCOSYS
- Thermal-hydraulic modeling of the onset of flow instability in MTR reactors
- 10.3139/124.100302
- 10.3139/124.100304
- Radiation transfer in inhomogeneous exponential media
- Neutron transport problems for extremely anisotropic scattering
- Milne problem for isotropic and linearly anisotropic scattering for specular and diffuse reflecting boundary conditions solved with the HN method
- ICDE-results on complete common cause failures in the light of results obtained with the POS model
- Modelling of the cumulative behaviour of Caesium and Strontium activities in nuclear fuel
- Analytical study of the closure flow inside the ETRR-2 core chimney
- Minimizing radiation exposure for the reactor staff during the dismantling of a TRIGA research reactor
