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Title: Criticality conditions for a finite homogenized natural-uranium fueled reactor with prescribed thermal neutron flux (English)
Author: Zezula, Rostislav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 15
Issue: 5
Year: 1970
Pages: 328-338
Summary lang: English
Summary lang: Czech
Category: math
Summary: In the paper the following problem of the nuclear reactor theory is mathematically formulated (in the two-group diffusion approximation and for multidimensional geometries): For a prescribed flux $\Phi$ of thermal neutrons in the core $\Omega$ of the finite homogenized reactor the distribution $M(x)$ of the fuel concentration in $\Omega$ which induces this given flux $\Phi$ in the reactor core $\Omega$ is to be determined. The conditions (in particular on the form of the boundary $\Omega$ of the core $\Omega$ as well as of the boundary $\Lambda$ of its reflector $\Lambda$) are given which are sufficient for the existence of a unique solution of this problem and, especially, also for the existence of a unique solution in the special case of flattened thermal neutron flux $\Phi = \Phi_0 = const$ in the reactor core $\Omega$ which is of practical significance for it yields the minimum of the critical mass. ()
MSC: 35J60
MSC: 35Q40
MSC: 82D75
idZBL: Zbl 0228.35076
idMR: MR0273905
DOI: 10.21136/AM.1970.103304
Date available: 2008-05-20T17:48:44Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] V. Bartošek R. Zezula: Flat Flux in a Slab reactor with Natural Uranium.Report ÚJV ČSAV 1310 (1965).
Reference: [2] R. Zezula: A sufficient condition for the flattening of thermal neutron flux and some related problems.(in onedimensional geometries). Apl. Mat. 14 (1969), 134-145.
Reference: [3] A. Miasnikov R. Zezula: Radial flux flattening in a cylindrical reactor with natural uranium.(In Czech - Internal Report OTRF, ÚJV ČSAV).
Reference: [4] V. Bartošek R. Zezula: Flat flux in a slab reactor with natural uranium.Journal of Nuclear Energy Parts A/B, 1966, vol. 20, pp. 129-139. 10.1016/0368-3230(66)90023-1
Reference: [5] M. Hron V. Lelek: Flux flattening by means of a nonuniform fuel distribution in a slab reactor with finite reflector.Report ÚJV ČSAV 1660 (1966).
Reference: [6] V. Bartošek R. Zezula: Stability of flat thermal flux in a slab reactor.Apl. Mat. 13 (1968), 367-375. MR 0243795
Reference: [7] Ladyzhenskaya O. A., Uraľceva N. N.: Linear and quasilinear equations of elliptic type.Nauka, Moscow 1964 (in russian). MR 0509265


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