The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory

Atalay, M.A.

doi:10.1016/0306-4549(95)00024-7

Cited by 18 publications

(4 citation statements)

References 9 publications

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“…This value is easy to estimate numerically using the spectral radius of the matrix W 0 . In Tables 2.3-2.6 we compare our results with those [NaLo08] and [At96].…”

Section: Numerical Resultsmentioning

confidence: 97%

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Integral Methods in Science and Engineering

2013

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“…This value is easy to estimate numerically using the spectral radius of the matrix W 0 . In Tables 2.3-2.6 we compare our results with those [NaLo08] and [At96].…”

Section: Numerical Resultsmentioning

confidence: 97%

“…Comparison between the values calculated for the critical value of σ /λ and the solution published by Atalay[At96] and Naz and Loyalka[NaLo08] when…”

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confidence: 94%

Integral Methods in Science and Engineering

2013

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“…Kritiklik probleminde amaç, ikincil nötron sayısı ile reaktörün kalınlığı arasında matematiksel bir bağıntı elde etmektir. Problem birçok araştırmacının üzerinde çalıştığı sayısal çözümleme açısından zor bir problemdir [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Kritiklik Problemiunclassified

Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri

Türeci

2019

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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Özet:Tek-hızlı nötron transport teoride son zamanlarda çalışılan lineer-kuadratik anizotropik saçılma fonksiyonu belirli kritik levha kalınlıkları için yansıtıcı öz değerlerini çözmek amacıyla kullanılır. Lineer-kuadratik anizotropik saçılma özelliği gösteren nükleer materyale sahip bir düzlem reaktör göz önüne alınmıştır ve problem yansıtıcı sınır koşullarını içermektedir. Amaç belirli ikincil nötron sayılarına ve belirli reaktör kalınlıklarına göre yansıtıcı katsayılarını bulmaktır. Sayısal sonuçlar Modified FN yöntemi kullanılarak bulunmuştur. Abstract:The recently studied Linear-Quadratic anisotropic scattering function in one-speed neutron transport theory is used to solve the reflection eigenvalues for the certain critical slab thicknesses. A slab reactor including the nuclear material is taken into account for the linearquadratic anisotropic scattering with the reflection boundary condition. The aim is to find the reflection coefficients according to the secondary neutron numbers and the reactor thickness. The numerical results are obtained by using the Modified FN method.

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“…The critical slab problem was investigated by Mitsis [2] with the Case method [3,4], Carlvik [5], Sahni and Sjöstrand [6][7][8], Sahni [9], Dahl and Sjöstrand [10]. It was investigated for the reflecting boundary conditions by Garis [11], Garis and Sjöstrand [12], Atalay [13], Türeci et al [14]. The problem was investigated with different methods such as the Case method, CN Method [15], FN method [16] and HN method [17].…”

Section: Introductionmentioning

confidence: 99%

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

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Türeci

2023

Cumhuriyet Science Journal

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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.

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The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory

Cited by 18 publications

References 9 publications

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering

Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri

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

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