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.
References
1Horak, H. G.: Astrophysics J116 (1952) 47710.1086/145639Search in Google Scholar
2Horak, H. G.: Astrophysics J119 (1954) 4210.1086/145794Search in Google Scholar
3Chandrasekhar, S.: Radiation Transfer, New York, Dover Publication1960Search in Google Scholar
4Pomraning, G. C. J.: Quant Spectrosc Radiat Transfer9 (1969) 101Search in Google Scholar
5Pomraning, G. C.; Larsen, E. W.: J Math Phys21 (1980) 160310.1063/1.524645Search in Google Scholar
6Pomraning, G. C.; Larsen, E. W., Badhan, V. C.: J Math Phys23 (1980) 815Search in Google Scholar
7Pomraning, G. C.: J Math Phys22 (1981) 162310.1063/1.525091Search in Google Scholar
8Pomraning, G. C.: J Quant Spectrosc Radiat Transfer27 (1982) 51710.1016/0022-4073(82)90104-2Search in Google Scholar
9Sobolev, V. V.: Light Scattering in Planetary Atmospheres. London: Pergamon Press, 1975Search in Google Scholar
10Mullikin, T. W.; Siewert, C. E.: Ann Nucl Energy7 (1980) 20510.1016/0306-4549(80)90066-3Search in Google Scholar
12Larsen, E. W.; Pomranning, G. C.; Badham, V. C.: J Math Phys21 (1981) 244810.1063/1.524681Search in Google Scholar
13Larsen, E. W.; Mullikin, T. W.: J Math Phys22 (1981) 85610.1063/1.524951Search in Google Scholar
14Larsen, E. W.: J Math Phys22 (1981) 146310.1063/1.525085Search in Google Scholar
15Garcia, D. M.; Siewert, C. E.: J Quant Spectrosc Radiat Transfer25 (1981) 27710.1016/0022-4073(81)90096-0Search in Google Scholar
16Saad, G. A.; Hendi, A. A.; El-Wakil, S. A.: Astrophys Space Sci100 (1984) 38110.1007/BF00651613Search in Google Scholar
17Saad, E. A.; Hendi, A. A.; El-Wakil, A.: J Quant Spectrosc Radiat Transfer34 (1985) 6510.1016/0022-4073(85)90172-4Search in Google Scholar
18El-Wakil, S. A.; Atia, M. T.; Haggag, M. H.; Saad, E. A.: J Quant Specrtrosc Radiat Transfer29 (1983) 1451Search in Google Scholar
19El-Wakil, S. A.; Haggag, M. H.; Machali, H. M.; Saad, E. A.: J Quant Spectrosc Radiat Transfer32 (1984) 17110.1016/0022-4073(84)90081-5Search in Google Scholar
20Mullikin, T. W.; Siewert, C. E.: Ann Nucl Energy7 (1980) 20510.1016/0306-4549(80)90066-3Search in Google Scholar
21Tezcan, C.; Kaskas, A.; Guleçyuz, M. C.: J Quant Spetrosc Radiat Transfer76 (2003) 10710.1016/S0022-4073(01)00243-6Search in Google Scholar
22Erdogan, F.; Tezcan, C.: J Quant Spectrosv Radiat Transfer72 (2002) 8910.1016/S0022-4073(01)00015-2Search in Google Scholar
23Nikiforov, A. F.; Uvarov, V. B.: Special Functions of Mathematical Physics Birkhauser, Basel 198810.1007/978-1-4757-1595-8Search in Google Scholar
24Yesíltaş, O.; Šimsek, M.; Tezcan.C.: Physica Scripta67 (2003) 472Search in Google Scholar
25Aktaş, M.; Sever, R.: J Mol Struct710 (2004) 223Search in Google Scholar
26Eğrifies, H.; Demirhan, D.; Büyükkılıc|, F.: Physica Scripta59 (1999) 90Search in Google Scholar
© 2006, Carl Hanser Verlag, München
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Articles in the same Issue
- 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
