Research Article

The Slab Critical Thickness Problem with Reflecting Boundary Condition for the Anlı-Güngör Scattering Function

Volume: 44 Number: 4 December 28, 2023
EN

The Slab Critical Thickness Problem with Reflecting Boundary Condition for the Anlı-Güngör Scattering Function

Abstract

The criticality equation, which defines the relation between the secondary neutron number and the thickness of the slab, and the numerical solutions of this equation are investigated with reflecting boundary condition for the recently studied the Anlı-Güngör (AG) scattering function. The analytical calculations are performed by HN method. The numerical results are calculated with Wolfram Mathematica software for the varying secondary neutron number, the varying scattering parameter, and the varying reflection coefficient. The critical slab thickness values decrease for increasing reflection coefficient as expected.

Keywords

References

  1. [1] Anli F., Güngör S., Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry, Applied Mathematical Modelling, 31 (2007) 727-733.
  2. [2] Mitsis G.J., Transport Solutions to the One-Dimensional Critical Problem, Nuclear Science and Engineering, 17 (1963) 55-64.
  3. [3] Case K.M., Elementary Solutions of the Transport Equation and Their Applications, Annals of Physics, 9 (1960) 1-23.
  4. [4] Case K.M., Zweifel P.F., Linear Transport Theory, Massachusetts, (1967).
  5. [5] Carlvik I., Monoenergetic Critical Parameters and Decay Constants for Small Homogeneous Spheres and Thin Homogeneous Slabs, Nuclear Science and Engineering, 31 (1968) 295-303.
  6. [6] Sahni D.C., Sjöstrand N.G., Criticality and Time Eigenvalues for One-Speed Neutron Transport, Progress in Nuclear Energy, 23 (1990) 241-289.
  7. [7] Sahni D.C., Some New Results Pertaining to Criticality and Time Eigenvalues of One-Speed Neutron Transport Equation, Progress in Nuclear Energy, 30 (1996) 305-320.
  8. [8] Sahni D.C., Sjöstrand N.G., Non-monotonic variation of the criticality factor with the degree of anisotropy in one-speed neutron transport, Transport Theory and Statistical Physics, 20 (1991) 339-349.

Details

Primary Language

English

Subjects

Classical Physics (Other)

Journal Section

Research Article

Publication Date

December 28, 2023

Submission Date

January 20, 2023

Acceptance Date

October 9, 2023

Published in Issue

Year 1970 Volume: 44 Number: 4

APA
Gülderen, D., & Türeci, R. G. (2023). The Slab Critical Thickness Problem with Reflecting Boundary Condition for the Anlı-Güngör Scattering Function. Cumhuriyet Science Journal, 44(4), 775-784. https://doi.org/10.17776/csj.1240161

Cited By

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