Geodesic
Criticality conditions for a finite homogenized natural-uranium fueled reactor with prescribed thermal neutron flux
Applications of Mathematics, Tome 15 (1970) no. 5, pp. 328-338 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.1970.103304
Classification : 35J60, 35Q40, 82D75 
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Zezula, Rostislav. Criticality conditions for a finite homogenized natural-uranium fueled reactor with prescribed thermal neutron flux. Applications of Mathematics, Tome 15 (1970) no. 5, pp. 328-338. doi: 10.21136/AM.1970.103304

[1] V. Bartošek R. Zezula: Flat Flux in a Slab reactor with Natural Uranium. Report ÚJV ČSAV 1310 (1965).

[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.

[3] A. Miasnikov R. Zezula: Radial flux flattening in a cylindrical reactor with natural uranium. (In Czech - Internal Report OTRF, ÚJV ČSAV).

[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. | DOI

[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).

[6] V. Bartošek R. Zezula: Stability of flat thermal flux in a slab reactor. Apl. Mat. 13 (1968), 367-375. | MR

[7] Ladyzhenskaya O. A., Uraľceva N. N.: Linear and quasilinear equations of elliptic type. Nauka, Moscow 1964 (in russian). | MR

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