Application of the HN method to radiative heat transfer for a non-conservative slab
-
S. Bulut
and M. Ç. Güleçyüz
Abstract
The HN method is used to calculate the partial fluxes relevant to radiative transfer in a plane parallel medium for linearly anisotropic scattering with specularly and diffusely reflecting boundaries. The solutions are obtained for the non-conservative case. The numerical values of the heat flux functions at the boundaries of the medium are calculated for the two source functions. The numerical results and the convergence of the HN method are compared with earlier results.
Kurzfassung
Die HN Methode wird angewendet zur Berechnung der Teilströme, die relevant sind für die Übertragung von Strahlungswärme in einem planparallelen Medium für linear anisotrope Streuung mit spiegelnden und diffusen Reflektorrandbedingungen. Man erhält Lösungen für den nicht-konservativer Fall. Die numerischen Werte der Wärmestromfunktionen an den Rändern des Mediums werden berechnet für die Zwei-Quellen-Funktionen. Die numerischen Ergebnisse und die Konvergenz der HN Methode werden verglichen mit früheren Ergebnissen.
References
1 Chandrasekhar, S.: Radiative transfer. London: Oxford University Press; 1950Search in Google Scholar
2 Case, K. M.; Zweifel, P. F.: Linear Transport Theory, 1st Ed.; Addison-Wesly Publishing Company Inc.: Reading Massachusetts; 1967Search in Google Scholar
3 Özisik, M. N.: Radiative transfer and interactions with conduction and convection; New York: Wiley1973Search in Google Scholar
4 Tezcan, C.; Kaskas, A.; Güleçyüz, M. Ç.: The HN Method for Solving Linear Transport Equation: Theory And Applications. J. Quant. Spectrosc. Radiat. Transfer78 (2003) 243–254Search in Google Scholar
5 Tezcan, C.; Kaskas, A.; Güleçyüz, M. Ç.: The singular eigenfunction method: the Milne problem for isotropic an extremely anisotropic scattering. J. Quant. Spectrosc. Radiat. Transfer62 (1999) 49–5710.1016/S0022-4073(98)00040-5Search in Google Scholar
6 Bulut, S.; Güleçyüz, M. Ç.: The HN method for slab albedo problem for linearly anisotropic scattering. KERNTECHNIK70 (2005) 301–308Search in Google Scholar
7 Bulut, S.; Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: Th effect of different expansion of the exit distribution on the extrapolation length for linearly anisotropic scattering. KERNTECHNIK72 (2007) 77–85Search in Google Scholar
8 Özisik, M. N.; Siewert, C. E.: On the normal mode expansion technique for radiative transfer in a scattering, absorbing and emitting slab with specularly reflecting boundaries. Heat Mass Transfer 12 (1969) 611–620Search in Google Scholar
9 Özisik, M. N.; Siewert, C. E.: Several Particular Solution of the One-Speed Transport Equation. Nuclear Science and Engineering40 (1970) 491–494Search in Google Scholar
10 Beach, H. L.; Özisik, M. N.; Siewert, C. E.: Radiativ transfer in linearly anisotropic scattering conservative and non-conservativ slab with reflective boundaries. In. Heat. Mass Transfer14 (1971) 1551–1565Search in Google Scholar
11 Siewert, C. E.; McCormick, N. J.: On an exact solution in the theory of line formation in stellar atmospheres. The Astrophysical Journal149 (1967) 649–653Search in Google Scholar
12 Atalay, M. A.: PN solutions of radiative heat transfer in a slab with reflective boundaries. J. Quant. Spectrosc. Radiat. Transfer101 (2006) 100–108Search in Google Scholar
© 2008, Carl Hanser Verlag, München
Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Application of the HN method to radiative heat transfer for a non-conservative slab
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Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Application of the HN method to radiative heat transfer for a non-conservative slab
- Application of the spectral Green's function method for numerically solving discrete ordinates problems in cylindrical geometry
- Chebyshev polynomial (TN) approximation to neutron transport theory and application to the critical slab problem
- Spherical albedo problem for isotropic scattering
- The slab albedo and criticality problem for the quadratic scattering kernel with the HN method
- An analytical solution for the time-dependent SN transport equation in a slab
- Deterministic calculation of grey Dancoff factors in cluster cells with cylindrical outer boundaries
- New calculations of excitation functions of some positron emitting and single photon emitting radioisotopes
- Prediction of the time-dependent failure rate for normally operating components taking into account the operational history
- Assessment of FEMAXI and TESPA-ROD codes for modelling of BDBA in RBMK-1500
- A study on the neutronic performance of the ARIES-RS fusion reactor with various coolants bearing nuclear fuel