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Critical Calculations of the Slab Reactors

Nuclear Science and Engineering, 1966
The problem of critical dimensions of an infinite-slab multi-layer multiplying system can be solved by a general procedure due to K. M. Case.
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Criticality of a Slab Reactor with Finite Reflectors

Nuclear Science and Engineering, 1979
The Case method is applied to the critical problem of a slab reactor with finite reflectors. The solution of the albedo problem is used to simplify the analysis of such a two-media problem.
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Exact Solution of a Critical Problem for a Slab

Journal of Mathematical Physics, 1961
By using the Case method of expansion of the angular neutron distribution into series with respect to eigenfunctions of the plane Boltzmann equation, the critical problem of a slab has been formulated. By means of symmetry considerations, the problem of boundary condition has been reduced to one singular integral equation, which has been treated by ...
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The critical slab with the backward-forward-isotropic scattering model

Annals of Nuclear Energy, 1985
Abstract The variation of the critical slab thickness from backward to forward scattering is studied for specified isotropic scattering. Numerical results are obtained from the zeroth and first-order approximate analytical expressions, derived using the method of elementary solutions.
C. Tezcan, R. Sever
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Critical temperature shifts for finite slabs in the ε-expansion

Journal of Physics A: Mathematical and General, 1978
The critical temperature Tc(b) of a d-dimensional system with finite thickness b in one of its dimensions approaches its bulk limit as b to infinity according to Tc( infinity )-Tc(b) varies as b- lambda . To first order in epsilon =4-d the shift exponent lambda is found to be given by lambda =2-((n+2)/(n+8)) epsilon +O( epsilon 2), and thus satisfies ...
A J Bray, M A Moore
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Fourier mode analysis of reflected slab and sphere criticality

Progress in Nuclear Energy, 2004
Abstract The criticality solution to one-speed neutron transport equation using Fourier mode analysis is described for reflected slab and spheres. The variation of critical distances under different specular reflection conditions is investigated considering linearly anisotropic media.
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The Critical Conditions in a Reactive Slab with Slowly Varying Surface Temperature

IMA Journal of Applied Mathematics, 1985
Summary: Liouville's nonlinear partial differential equation is considered for an infinite rectangular strip domain with a slowly varying boundary condition. The equation describes a layer of chemically reactive material under conditions where the resistance to surface heat transfer is negligible and the ambient temperature varies slowly along the ...
Adler, J., Nhamburo, P. T.
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TN approximation to reflected slab and computation of the critical half thicknesses

Journal of Quantitative Spectroscopy and Radiative Transfer, 2006
Abstract The criticality solution to one-speed neutron transport equation using the TN approximation is described for reflected slab. In the solution, Marshak type boundary condition is used. The critical half thicknesses are computed for different values of c and reflection coefficients.
Anli, F.   +3 more
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Critical problem for finite slabs with sinusoidally space-dependent scattering ratio

Transport Theory and Statistical Physics, 1985
Abstract The critical problem for a finite slab with sinusoidally space-dependent scattering ratio is discussed. Numerical results for the corresponding critical parameter are reported and commented.
BOFFI V. C   +3 more
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Critical Problems for Bare and Reflected Slabs and Spheres

Nuclear Science and Engineering, 1984
High-order PN calculations of critical radii are carried out for both bare and reflected spheres in the one-speed model and also of critical half-thicknesses for slabs.
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