* Meysam Mohammadnia Department of Nuclear Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran *Author for Correspondence

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1 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic CQUISITION N NLYSIS OF FLUX N CURRENT COEFFICIENTS IN THE CORE OF FISSION NUCLER RECTOR WITH HEXGONL GEOMETRY BY FLUX EXPNSION NOL METHO * Mysa Mohaadnia patnt o Nuca Engining, East Than Banch, Isaic zad Univsity, Than, Ian *utho o Cospondnc BSTRCT Nodaization, considing th spatia htognitis o th acto co, is cucia o th accuacy o nutonic cacuations. In this pap, Fu Epansion Noda Mthod FENM which is suitab o nodaization cts in th nod cons is odiid to sov th inta-noda u anayticay. Nw coations a intoducd in this pap o gaa actos which a unctions o bucing od and pitch usd o dtining inta-noda u. Thy vad syty in inta-noda u coicints which wi duc cacuations ug this thod. W hav ound ipotant suts about th ation btwn u and cunt coicints with bucing od. In two paa nod suacs u and cunt coicints in μ = λ <&λ > a sytic and B u and cunt coicints a qua but in μ = this is vs. Kywods: Nodaization, Fu Epansion Noda Mthod FENM, Hagona Goty, Nuton Fu istibution INTROUCTION Noda thods chaactiz th goba nuton u distibution in ts o a sa nub o paats in ach o sva ag gions, o nods, into which th acto co is subdividd o this pupos. Such thods gnay qui dtaid htognous inta-noda u distibutions to constuct hoognizd paats o ach o th any nods into which a acto co ay b dividd and to cacuat couping paats that in th avag u soution in adjacnt nods. Th goba avag noda us ust thn b cobind with th inta-noda htognous u soution i a htognous u distibution is quid Stacy, 7. In FENM poposd by th inta-noda us w pandd into a st o anaytic basis unctions o ach goup. Thy ipovd th noda couping ations and a nw typ o noda bounday conditions was poposd, which quid th continuity o both th zo- and ist-od onts o patia cunts acoss th noda suacs Xia and Xi, 6. In this pap w hav usd th FENM with intoducing voutic avag u Φ tota. Considing tna bounday conditions and th continuity o patia cunts in th vicinity o noda suacs, w hav cacuatd u coicints o ach nod. By substituting th u coicints in th voutic avag u coation, avag nuton u o ach goup and nod is achivd in od to b usd o th cacuation o K o Pow-Mthod Mohaadnia t a.,. MTERILS N METHOS Th ist stp in diving noda quations is th taction o nuton baanc quation ug th Botzann tanspot quation by intgating ova oving nuton dictions, ngy goups and vou o a nod. Mati o o two-goup diusion quation in th-dinsiona hagona goty is Mohaadnia t a., ; owna, : Copyight Cnt o Ino Bio Tchnoogy CIBTch 7

2 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic Copyight Cnt o Ino Bio Tchnoogy CIBTch 8 t t Th Eign vau quation coud b wittn as oows: In Eq., and a cad undanta bucing and ist haonic bucing spctivy. Fo th two Eign vaus o, Eign ati a dind as oows Mohaadnia t a., ; owna, : /, / Th auiiay u coud b dind as a poynoia. B Figu : Coodinat syst o th hagona nod Mohaadnia t a., Eight intac patia cunts and ist-od onts o th intac patia cunts as th bounday conditions that constain th inta-noda u distibutions in hagona nod a shown in Figu. Wh abitay unit vctos a: y cos 6,,,,5, z 7 z cos 8 y z cos 5 I and having cosh h, h cosh I i i and nowing that i i cos, i i cos. Fo quations and o th two goups o nuton ngy in two ods, th oowing oua is obtaind Mohaadnia t a., ; owna, :

3 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic / SN BCS + SN BCS / SN B CS 6 SN B CS Th soution o quation 6 ads to ou sts o two quations in which ou quations ust b zo: [, ], B B, B B 7 Th answs o quations 7 a as oows: B S, B R 8 B B Th ation btwn auiiay u and inta noda u is SN K B CS K H X, Y, Z R S H X, Y, Z SN K B CS K RESULTS N ISCUSSION In quation th t sid is inta-noda u and th scond ati in th ight sid o th quation is auiiay u. Eightn unnown coicints o, B, in two ods =, = and two ngy goups a obtaind o anaytica intgation o quation. Th boundais o th suac intgas a intoducd in Figu Mohaadnia t a.,. Copyight Cnt o Ino Bio Tchnoogy CIBTch

4 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic Figu : Intga boundais o a hagona nod Mohaadnia t a., Tab : Fu coicints o ist sid = Coicints whn cosh cosh cosh cosh Coicints whn cos cos cos cos h / h / / / 5 6 cosh cosh cos cos cosh cosh cosh cosh h / h / / / 7 8 h h h / B h h B h h B B h h B5 h h B6 B7 h h B8 h h cosh B hh h / cosh / h / cos / / cosh / h / h h / cos / / h Copyight Cnt o Ino Bio Tchnoogy CIBTch h cos / hh / ccoding to th intga boundais, quation o th suac nub and o th od bcos quation. Fo th concisnss coations o suacs -6 a not bought h. H h g, h H h H H dz R SN K B CS K S SN K B CS K dy

5 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic Coicints o and B o th abov quations a dind by ug nw paats nad gaa actos. Ths gaa actos a intoducd in od to a th bnit o th syty o hagona nod. Thy a unctions o K bucing od and H Pitch. H cos H cos H, H cos h h, Th aontiond and B coicints a bought in Tab o od. Fo cacuating φ g whn λ > λ < w hav to add th suts o utipication o th ist coun by th scond thid coun o ach ow. This is th cas o oth tabs. vag suac cunt o od and o suac can b wittn as q.. H h,, g g y z g, H h H h H J dz dy Tab shows cunt coicints o and B. Tab : Cunt coicints o ist sid = cos / h h cos / h h cos / cosh / h / / h h 5 / h h 6 7 cos / cosh / h /, 8 h h cosh / B cos / cosh cosh B cos / cosh cosh B cos / h / h / B / cosh cosh B5 / cosh cosh B6 cos / h / h / B, B 7 B8 h h h / cos / cos / cos / cos / / / / cos / cos / / h cos / cos / cos cos cos / cos cos cos / / / / cos cos / cos cos cos / / / h / By anaytica soution o th intgas o u and cunt on th suac o th hagona nod with spct to th Figu, Figu by ug th syty o hagona nod and considing Eq., w hav ound ipotant suts about th ation btwn u and cunt coicints with bucing od. Copyight Cnt o Ino Bio Tchnoogy CIBTch

6 Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at Vo. S, pp. 7-/Mysa Rsach tic In two paa nod suacs u and cunt coicints in µ=, λ> and λ< a sytic and B u and cunt coicints a qua but in µ=this is vs. Thy vad syty in intanoda u coicints which wi duc cacuations ug this thod. CKNOWLEGMENT Th autho gatuy acnowdgs suppot povidd by patnt o Nuca Engining, East Than Banch, Isaic zad Univsity o Ian, Ghiaasht. REFERENCES owna T, L, Xu Y and Kozowsi T. Thoy Manua o th PRCS Nutonic Co Siuato, PRCS, U.S. NRC,.6. Mohaadnia M, Paziandh and Sdighi M. vopnt o a coput cod o nutonic cacuations o a hagona attic o nuca acto ug th u pansion noda thod. Nuca Tchnoogy and Radiation Potction Stacy WM 7. Nuca Racto Physics John Wiy & Sons Inc Nw Yo 5-5. Xia B and Xi Z 6. Fu pansion noda thod o soving uti-goup nuton diusion quations in hagonagoty. nnas o Nuca Engy Copyight Cnt o Ino Bio Tchnoogy CIBTch