7 - NRE 4214 HW Set 7 — Single Phase Heat Transfer 1....

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Unformatted text preview: NRE 4214 HW Set 7 — Single Phase Heat Transfer 1. Problem 104 of Tom-easand Kazimi, Vol. I, pp. 459.- 2. Problem 10-4 ofTOdteas and Kazimi, Vol. I, no.4”. 3. WaterentersaPWRoomehmnelatZDOOpeiund‘BO’Fwiflinveiocityofls fps. The fuelrodsare 12 ft long and contain U02 pellets 0.5" in diameter surrounded by a helium gap 0.003“ thick and ZircaJoy cladding 0.03" thick. The rods ate W in a square lattice 0.?" between oentm. Heat is genmwd sinusoidaily in the node. The total power generated in an average rod is 4.3 x 105 bin/hr. Ignoring the extrapolation length and cross flow mm channels, (3) determine the fictional pressure drop in the eon: and coolant exit temperature. (b) determine the heat flux, heat transfer coefficient, mmpemure. cladding surface temperature, and maximum fuel temme at an elevation 3 it below the channel exit. (Use Rf, kg, kc = 1.15. 0.135, and 8.0 btulhr fl °F respectively). 4. It is desired to estimate the rate of heat loss from a meteomiogical installation using an experiment with a small geometrically similar model of 1/5 the linear dimensions. The desired surface temperatum of the installation and the expected air temperature and wind velocity and direction are known. Under these expected conditions, both free and famed convection am probably important, and it fiterefore appears teesonabie that the resume! veiooity disu'ibution will depend upon both the Reynolds and Grashof numbers. it is desired to use air in the model experiment and to maintain similarity between the model and hill-scale apparatus by varying air pressure and velocity. The temperature dependence of fluid properties may be ignored. it. What premre and relative air velocity should be used in the model experiment to maintain dynamic similarity? b. What wili be the relative heat flux from the model? NRE 4214 HW Set # 7 — Single Phase Heat Transfer Solutions :1. 1M af'i'odmesmd anlmiflal. 1,1115; 459. U ' Fraud Ethacm hm Parallel Fla)“; . figffmdzt wadi‘h and 5PM,th efimle‘; +0 "25* ASSwmpflmi : . Maguagm mam 44.99am ' . Ne? tax-17a! ("Sandbag *‘t'm Bayi3T+JUKH+M do _ EBTH 313‘s: #43 33 Uau+zaz} " x3+fin+fl§i + u- u w“ {A - 31w 3% wivfiwyé «1 AI. - ET. ELF J“ '3’! k (i) Asqmpfeh‘c Satm‘rfm ‘Far mfiw mu Luau-f 6L”; PM Mr x. ' ("h-To) 3 Ch}: 4- (2) WWW To 3% 'HM ‘mlcl- +cmA—‘scmfinu.. 1 A; : Ira 0* d” 8 OP K Cc: djl {3) w M): :: 2U- — C¢H5+M+ -_EQD1£'§‘5HAJLLCEJ ‘1? '- d é’ = ELP’U-Cn [4) d31- k Imee-aralnfi Ecb. L4) / but“ caxf .' CF: EEEUCG {31 + [SIB-1' C1 (g) 2}: Eat: LIL Add“ 1 amalifims. : 31 C13 aw : @ we 42%;... #1:” a 12 5%!“ — — ‘35? ca: “if <%US A +hllr0l bawnclarnl WU+rnn II‘S- Motto: +53 C-u*a.£.u:a:tt C2- , Eflcrfi‘j Emile WW HM. and {1.4.3 arbiira-FJ {omfl‘m x 344M, : EN” {My 25 OFETmix)-Tfl] = 23x W \erg 223:5 Nth-Tam m mam _ at " “1H1: thlIMLfiq s 6L? X 1 T (fl-Tu = —-—L—'—’“ 5 5—5 JCTJI‘E) :43 {in} M End; a? il’fx : L5 I x __1_ + Ca] End-5C1, z -5 +3 IL C 1 A h 1 D + C2 .3 fl CD x + E; 2}: ‘j 1 -5 +5 (I; ’1 a“ t 7/?“ y" + is jEC‘WCWl-flz] {7 55F? If .05 2.1.: ..—5. 9 15 +3 2 {a}; + 151 Scldj : m. EC‘P’UCa j :—Zk*fij3 j 2!: .r'S F5 ,5 : Emma-fibrin: p ‘5'?" Cf} Ci 5-; C; @ L5 : 5 T Tu} 3 1|wa E555 £2) gay-55} Lg:- cap-f; .'_ (Tm—Tc.) : ELIVMS X + Emlk TEMffith-M bi‘fibibmh‘m t 1/ Egan fluid}: Tmcx}_Ta= in” ‘ €fiUJ E205 L1") 1: [3) LaALtld .' (TM-m) = 5575 3k EDUI MW‘M - In E 1‘"! '1‘.m -Tw "'. 'Plf'm £301) 1n = :i F0 r m: 'Fl WA lira: qu “all 4* Flawqu be : hair'an ._ a: M “EMAPHMH 2 W I: 45 M)? a 31L 4'5 -| — ' -— = 2 IF- 5 k I AM if?) 715* 97 - - 15’ Cm: I! : Parnbalfc Usiagd'a Prfifilx. : TIM. Marc. p?”qu Cat-+1. I‘M W114 -Fmr a. PMaIgBHC uélvu-Ia Prfl'FJ-A Wm ‘Hu. Plait)“.r 5:- Had : Mi : U#,Mn: Ll" Ga) E39) rem”; +0 ‘. a3: ECT’UCW. ca {r—Gfi aw _ 53 MA :43 k a 4‘ x c? 7.. emc'Kéi-é‘ewcmczk “3) k ('5‘) (“/15 T141 “Haifa! bout/Lottery CmcliHr/M (vegbuzfla) {-5 OLeFeIr-m'me C2 l‘n CM be L217 fer—FM'VM;:17 (In cum/all energy [galqmcc on +141 sLPI-em be'bdeeva ‘H/q indel- Cx=o) cu”! OWL-j arbil‘vaxj local-[m X”. c2: - L3. 92 (I?) Will TeMPeV‘oLH-Mve ,’ (12) TEWLPEVQMWL’ D15 hkfi'l-‘L Visa/(«JET Mama/i. 5:31-5- :35? {IE} CM [:4 I'lnHa’ijtLd JFD la‘mld +5 EAS 2. PruhIBrn 134 of Todrm and Kazimi, Vol. I, pp. 459. Affiriu—M WEM Fray-rHES :dbuml ‘11::‘1’hcge @EDD-C VH1: _H:"'_ I 5‘50 : Snfi‘H- tum/5. W‘ 570:: #729; E (eh-BILL): RC = : 7217- if 54.34 Chflld't' : 7_,4.S‘] KID; )4 :12 m5" ‘4': PM #3 : w = 53.93.2- II‘ can-6%:- D}l'+lp4~.5_ BaeHer LarrefQHm : (E7) [Ct-'3‘”; G'FHu 'Hxi-) I“? a. Nu”: o-DE‘S Re Pr 3 cum: 4 C tau-7 (Pr {1&04014 j RE>ID fink; L/D: lie/0mm: -_-. tight; )0: __~,oK an? fl_3 :- Nam: flog-s3, 9¢(7.+s¢1xm‘) * (033$) = “29-1-7 ‘r z _ D =ILZQ-Bie-‘FL _: 3_?q?xm w/MK NW 7; *3- "‘ a I; 5. Q _ ganxtn : 1,43? nu: ‘w' _ 57m: ' __i___—- + Lam-fr.) fiTm‘W: Q harm") an RL 5 ___|________.__—-——- = l~43fixm {Eiquxmfl- [flifi.hIL‘fIE-J o + L. com/am) E -‘_________——-—-'--.—-- I 1T! {Elfin-K Hr when 5TH”: MM +gm+emm vii-Pfennig: Wm... “Ha-n .PruimL-r; fipale‘ fi-M-Jl ‘HM fi‘dnalilbvu «side Surénq L um” IMFJMTM % TP' :1? 2”" ENE/nan Engine-LL: ‘FW :1 dimumhu mu Mm Thflfi W Z A; E +332 I I 2+5? THL Wt” =2flp'c dd? .1 = "7'" Cr (Tm-1|I - 1;“ {HR} Tmlil - TERI. “ml—E ll] J“, LEM-W Tm {'1}: [cant ._l'__l— ILA V‘s/Phi Izhmrj bu”: 3. Water enters a P‘W’R core channel at zone pain and 4lltl°F with a eeleeity cf 15 fps. The fitel reds are 12 ft long and eentain U02 pellets 3.5" in diameter surrounded by a helium gap ELDEB" thick and Zirealcy cladding MB” thick. The rods are arranged in a square lattice ll?" between centers. Heat is generated sinuseidally in the reds. The total power generated in an average red is 4.3 x M5 hustle. Ignoring the extrapolatien length and cross flew between channels, {a} determine the frictional pressure drep in the cure and coolant exit temperature. {b} determine the heat flux, heat transfer coefficient, eenlant temperature. cladding surface temperature. and maximum fuel temperature at an elevation 3 ft belcw the channel exit. [Use kf, kg. k6 = 1.15, {Ll 35, and an htut'hr fl rJ‘F respectively). fell! 1? .rr 1 _ -3. 1 A‘Fm: P — ED ‘- Leila ate ft mew: 11D : a.|432 t—‘t «.1 DE : net-An.” -.; 4-_Ll-fifi ate fl- Pencil-ed I. zeteepeia w. = , . A 4%D'F time-M1 em U“ at.» _3 IF‘FP'I- = ‘50.;5‘? a it; a Lil-Smile .—. Lat-7'3 liners @bm -.-. tilt Ala = 4.3 are; Btu/Lt— , _ étnl- - 431'“: : elects 3m " M" ' T ‘ l-ZS‘E-eEEe'e ml“ low. ._ laF@ 4“? = 4;.44 Baht/flan. II' :-« “at; : Lhé-l‘hlfl Ss?-4‘ an Prawn” me Mata-«hot ml Hut W bulk +£me "'TE'J" Tp alc+trmréc TM @ %;‘i}r J Mal. 11:: ale+ch;-¢e +14 Tait. 9+ mmi' QAAifin-x Dun-2r Ha-e 47135+MAL¢ W in MA Ezfi’j we,“ Fey‘me M W balam over Hun 5w YEW. .. q” “I I; J, m D c- 4, L : EWL TTD ? ("C-'1:- il +CmD) : '5 6-7110; Brim/hr J' T kim'-L.; = m : mm = Emma :m‘uwm/rs... 5—H” w. I.2.§E’#3Ln Tc: fiE‘l'E'M‘im 'Huz laud? Laud Hmngr a} 2:51,, l.ch aim L444 H4 Weigm mwiah‘m (€13. [Dali-Nb)» [Tim 101mm Fwy“ iii-44 nu wnlwmhd (1+ HM; [5:ch bulk +Empamfi4w] @ anew-1‘}: —~> er: 44-74 rim/H3 C DEE-L {bra/Pflw = «3-333 Bin/hr H'F 1"; [-243- g‘“ HEWL'F : es” 'z 'F-+/$cr_‘ - |.I{ P/D-fim WP 1532;. P/D ~1‘a4ao :- Lzl’; [P/D:;.?n ck] ' Tcul'iz-Ji : 321;- 4- Twl “ 35-! + git-[Le Ezfi’ 13-4: A“; I; E : T _ T : ’Tl' R i I L—————-Rc:/R WEE F: in 2 F + 2-” '53 F +L L3 fiI-FK: = 1’. “Dan T‘FL: Fuel mx.uv-fl . .I- _ Tc : 3463.}: L a I ‘%s it is desired to estimate the rate of heat loss from a meteorological installation using an experiment with a small geometrically similar model of US the linear dimensions. The desired surface temperature of the installation and the espeeted air temperature and wind velocity and direction are knovm. Under these expected conditions, both free and forced convection are probany important, and it therefore appears reasonable that the reduced velocity distribution will depend upon both the Revnolds and Grashof numbers. it is desired to use air in the model experiment and to maintain similarity between the model and full-settle apparatus by varying air pressure and velocity. The temperature dependence of fluid properties may be ignored. a. What pressure and relative air veloeity should be used in the model experiment to maintain dynamic similarity? b. What will be the relative heat flux from the model? M“: N” (M’Rfl Cor) Pr, tewwngP [mew-tel; ‘FseMFflh‘l Gr : C31" REM = Rer 3, m rs. <‘~’%’>r(%'7”l "J 5 (6% MD?) _ (em) a) 24‘ m ' f” *5 ibriémi Q: E/RT G3 aria-d Sine! = (Plea)... = P D h % .3. e t (5) 5 og.o3so)3mw= II —--| Fun- J N ...
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This note was uploaded on 11/09/2009 for the course NRE 4214 taught by Professor Abdel-khalik during the Fall '09 term at Georgia Institute of Technology.

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7 - NRE 4214 HW Set 7 — Single Phase Heat Transfer 1....

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