Solution HW8 06 - 529M7an 79W flay/1mm? 3 530.334 Heat...

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Unformatted text preview: 529M7an 79W flay/1mm? 3 530.334 Heat Transfer ASSIGNMENT 8 Assignment due: Friday, May 5, 2695 by 4PM o Read chapters 7 and 8 in your textbook 0 Study solved problems in these chapter Problem 1. Ethyiene glycol flows at (L02 1ch 5 through a 4— mm diameter, thin—waned tube, The tube is coiled and submerged in a well—stirred water bath maintained at 25"C ,. If the fluid enters the tube at 85"C, what heat rate and tube length are required for the fluid to leave at 30"C '2 Neglect heat transfer enhancement associated with the coiling. Problem 2. To cool a summer home without using a vapormompression refrigeration cycle, air is routed through a piastic pipe (k = (1.15 W/mnK , D, #0.! m, D" =On13 m) that is submerged in an adjoining body of water: The water temperature is nominally at Tm MTG , and a convection coefficient of 11" wiSOO W/mz-K is maintained at the outer surface of the pipe. Ifair from the home enters the pipe at a temperature of TIN m 30?? and a volumetric flow rate of ‘v’,=0.025 1713/5 , What pipe length L is needed to provide a discharge temperature of 77W, m18°C ‘2 What is the fan power required to move the air through this iength of'pipe if its inner sulfaee is smooth? 60AM??? '. Problem 3. Water is to be heated from 15“C to 65 “C as it flows through a 3*(337 inner diameter 5—»: long tube» The tube is equipped with an electric resistance heater that provides uniform heating throughout the surface of the tube. The outer surface of the heater is well insulated, so that in steady operation all the heat generated in the heater is transferred to the water in the tube. If the system is to provide hot water at a rate of 0.01 1123 (min, determine the power rating of the resistance heater Also, estimate the inner surface temperature of the pipe at the exit. . gs = constant ;. 7:, at A '1? gig? in ‘ were”. .a Problem 4. The surface of a 35-111 long flat plate is maintained at 40”C, and water at a temperature of 4 “C and a velocity of 0.5 m/ s flows over the surface. (a) Using the film temperature T! for evaluation of the properties, calculate the heat transfer rate per unit width of the plate, (1' (W / m) . (1:) Calculate the error in {1' that would be incurred in part (a) if the thermophysical properties of the water were evaluated at the free stream temperature and the same empirical correlation were used. (c) In part (a), if a wire were placed near the leading edge of the plate to induce turbulence over its entire length, what would be the heat transfer rate? Problem 5. In an industrial facility, air is to be preheated before entering a furnace by geothermal water at 120°C flowing through the tubes of a tube bank located in a duct“ Air enters the duct at 20°C and 1 atm with a mean velocity of 4.5 m/ s, and flows over the tubes in normal direction, The outer diameter of the tubes is 1.5 cm , and the tubes are arranged in—line with longitudinal and transverse pitches of SL =5}- : S cm . There are 6 rows in the flow direction with 10 tubes in each row, as shown in the figure. Determine the rate of heat transfer per unit length of the tubes, and the pressure drop across the tube bank. Office hours: C. Herman, Latrobe 102 after class MW and by appointment PROBLEM 8.2.6 KNOWN: Ethylene glycol flowing through a coiled, thin walled tube submerged in a well—stirred water bath maintained at a constant temperature FIND: Heat rate and required tube length for prescribed conditions SCHEMATIC: 30 mfg? Tm: °c nga’td“ "" " ' engine 8‘ z ‘73,,=25°c ' ASSUMPTIONS: (i) Steady-state conditions, (.2) Tube well thermal resistance negligible, (3) Convection coefficient on water side infinite; cooling process approximates constant wall surface temperature distribution, (4) KB, PE and flow work changes negligible, (5) Constant properties, (6) Negligible heat transfer enhancement associated with the coiling B 1 Ba 5; «:0 gfiafk PROPERTIES: Table A-5, Ethylene glycol (Tm = (85 +E°Cl2 m 0°C m 333 K): cp m 2562 -7 . I/kgK, tt== 07522 X 10 u N 5/1112, lc F» 07260 W/mK, Pr = 51.3 ANALYSIS: From an overall energy balance on the tube, fl oz "3818- 2— 30 gem = ran up (Tm - itm) wmlcg/sx 2562 eagles," 85 )° C emu! (1) <- For the constant surface temperature condition, from the rate equation, As m cloonv I HATlini I m b (2) 39-0-5 ' EEG-2? {g . .22.! c AT - 25 AT 2 AT HAT [tin-Mimi: ~25 ° C-- 85—n25 °C:}/ (In =2?.9°C7 3 Em ( o I) ATE (35‘ ) i ) 85_25 () Find the Reynolds number: to determine flow conditions, 4th 4X0, 1 I RED 3 m m 03. cg s 2 2 1217 (4) 7r DH 2‘: x0301}, 1n><0 522 x10" N s/m Hence. the flow is laminar and, assuming the flow is hilly developed, the appropriate con‘elation is —« 2.3?» NuD “4 112=3..66, ii: Nu—IE‘: 3 66x0 260flm/0iooimmm7W/mz K (5) k D m K. From Eq (2), the required area, As, and tube length, L, are zat3~> 25747 2 324 0.936 2 AS 51%} WISH W/m Kine-WC = serene n1 2 42.55 L =AS fit D :0, 1448111 I71: (0.003m) mm" < COIMMENT S: Note that for fitlly developed laminar flow conditions, the requirement is satisfied: C12- 2 (LID) 1’ RED Pr = (15 3/0003) 1' (813 X 51.3)= (1122 > G ()5. Note also the sign of the heat rate qcmw when using Eqs. ( l) and (2) Pmlalm 2 : 6W khan/11.: 59215417524 511,944; GvrvoL OWSI’IZQ. filo {a Fwd: m pipe ézgmz a» MW, a dwarf, fawmfim of hwy; U r» 54. WWI” Arafat/flea! 22?» awe, 22C; a/D’Wui/L, £44. WPWS : @1- a A? [IV/n i: J firm 7r” 7m'1;7;"'”= 2&3 ‘ PL‘fl/Hfl/Cyflnr’» 45.: Mafia/ka A; xyy,¢xxaflzv%1 a?“ = 0‘0263‘W-we, Wr=07t>7 . . “1.1% L ‘ v I ‘ 540% ’1 \le 7b.; ~ I? o .q- many; I. . by , D 1,7531%, £595“? ml mas/Jo é; ain't 6v mic AKSUJ'Vyofia-h; m Walfinm wwwfi'afiv 1:: MW Aamf— M49.» 0%umf, {$2 754w 1‘4. flay/{ueébped 733m: . U.) 79%,» 7%w Vafpa'w 1/ mvlflg-w a Bah/5 we? WPV “u m‘W‘NMMJ rump] >> 23w vwvéwlbw 741w. A, {IJ¢.‘AK(0'7 m 555; mow/fog, ‘ Iowa-Mr .9“ 75/2,. S [50 WM; w». 9, 02,3 gag/5' y®fij P2}, 2. {0 00:; «£3— ? Io 42.2.0.1; ty 0 x“ 37> kw :: Q02$(42w07j 5/0297,” ":9 AIL : 19,9355 " 0.025(320126]; %/q7D7/a'$fl/ 12", {503’ W/«w‘fl; “J”? EL thaw of law} fiayum“ I I . ' 4*.” 123%: fi%‘ [95: $9,”): . r Ago, “L... .3." fl mm :4) Pufm 2 (Zflzfip'f 2K: P ‘f UML) Z M {/Ewluvh’m/Z/ , A5,»:- ‘it; 4&1? t5 q A 7A.” Ewan; Mum, gs.— m’ (,3, 57m, .. z”) a Pm. m;— Zw ) : ,th ‘ (kW/S x /n/é/</- x 0,, 023’ X/pb'ix C 39.7; g) =>. A = :‘x 56. 5’ 4 5.2? 17?, -.»- H6! y 9.1;? L J’fltfiw Wavy/V p; AP " 3 u a : 203.be ’5 L30 I } V?!» fixadzf 15/3 14/ _ /_., / panama/5 (2.2,, >,— 2x0“) ‘ x -/ WW (2m); 51: m” . 3 %=) agony-49km“ (I) ‘3th Flow (a) eurfme, Maci- J911.3% [‘5 anti-mm (2:) 5mm mm surth . T5 3 1% Egg-«5 ~.- 40°C. ;; f”‘l42.l kgfmb' k=0.65\ w/moc wam (Tb-#40’a) WA: o,&53x10""m"/s. Tibia W4. (1? “HM (IA:ch Pr= 4&1»- Crogs EMMA Arm: Ac. 321% D“ ” iflaowfi = 7.0% xww Heat Tramskr euri'nm arm‘. 3: ' L 3 “(I L -": _ :- w ' 2m ' .u A5 52 D nu) oamuem) 04mm ‘ Ewafizqug w: n we? IA 10" zxugsxouiy» ; Volume. How mire : “’0‘”; WL/mm #5 0-“ MVMM 15/0759 - ' «v ThvéLJh/‘f , 6 WWW -"-‘(‘l‘lfl-lkglmaflnfifiIW/mu) , a; Mums zq'qu‘J/M‘“ "9 meta-4 k ls ml (is = W”: x m 4—”— ' : 75423.A/n-5 Qt: Iii/LC? (TE'TL) fig to; méwluuém W == k ‘3 a __ a Wm55,_. ‘- ;: (mi/SIS)“me 63m ‘3 '5 ‘9 Mfls‘fiz’gwwfi/w 7"" , ' s q I l ‘ 1 ~ *- ‘ , . _/ Lw: Q "354.6 ‘9 POWE‘F G‘f' , ~>/n: fl,é‘3lr0A0,3 /(la-7;D) m...— (fi‘xfia :15 K g; {(1.57 I,” “124‘ an}; m c" 0" ~ Tsw'fl” a I T i'fg '3 RD“, E) 7.5: 1 7;“ ‘2: 2 rpm 2/11“;- %. W4, WV: Known: fLa’hu/C {Off/Darm 0% Ev 7am lama AM: in.) I M :59 L951)»; w {Jim Yehyequa, (b; h m’ DA»??? 7‘?“— Wm a) E/u. Muiflbn p/um 25L. 7%“, Is ert-u. from «94*. #3 E {th 45w?” [7" = V‘“ J pm/wvfn'aj" j 7 I .——> 7363 4°C {ta/(wuer 3’“; Vk : j rm 5 ._M_________._7,____._..__._.... “75‘ 3 4061, T . I ‘ " V1 5:» b Aha-j 914 at) Wm»? 71!}?! fE/IW 7%,: — a, 2 22 6 Era/YR. :9 [9: “HE/7AM» ,&£= ‘ffi’erWW/me Kama lax/wk ,Op M; 9: s’é/E/AJ/kjm ~ Mug «my: arms“ (QELU fl 3 W .zZJafxrof mixeyf fiat-W547 4'! w (mu/«m» m. ‘ ,6 < P 6&0, “ M ‘It ’ p - V ML 3 T ': (0..037fle4/ "ii/3 [Jr/5 5x”:< 3.22.: SI”? figs. = éxn’" .a. M" flfiflé - . l' “7 /: z ' m x£4027t2arorx~-‘2”— JWMé-éw/S 2 m7 me Ppywl‘tl-f'h é": [Airy I; J: Mir/mm [6) AW? "EL, {611, Sfizam film/)EV-LWQ 79c: ([56 3 277k. P:/aoc> ky/méb ’14.: {Séo Y/pué/t/kS/ml gé: 5.1‘77 W/h‘h/fi fir: H44, Cy; (LJUé/cjfl‘fij‘ (oi/flat: /avux0.fx’/.f 3' PM" A J W d-””*”"”° {fan {a}? {W emigfynu/L [ahrzfivfizm a: W MC; ’2‘ :mosmaf-H/Mrz ,tn 3— :; A 3 w Jig“? C d~5"3"”‘)wwi711(Wuu/kifl W/‘u/L :7 ‘1? —= [Mn—7m) r, 20.94/ch ’i’1 9,:’ k D @5534.— LZWDV : (7 cl Mil-’vzpemfirhu/fl [aiwl-Lubbh I. (l . A7" " 5/5 s “957%; Affli- 9"“ S w" "Jud-"b has}? CV 7 5 w WWW/15, ‘ - I I X rxff‘62)/$2 [’V/IIIMIL [4%- A, J :2 7M; k% [III-.1! nulllrnsulillnlll I unlll-ln¢l.l¥c._la .I an:- 6 I Ell H .33 33E “cams: Friction factor f and correction factor x for {ulna banks (Imm Zuknuskus. Ref 16. 1985) FIGURE 7-w27 iii?!" l m a C R wk- Illwannwusum I‘m“?! m r. m H c m . w n m. m d m m Nb u..... m. .m S W .\. dude 53th “We dln'a bank. 3 f heat trarisfer per y.- g'Air kw fififithérféémflér ii! #“Wfié ' 5 [law direction with ID tubes Erie the rate 0 thmngh thé tubes 65 a tpbe'b'anlv. luca'ie d th'e_ psassare drap miss the gube ; air is tq bé preheated henna efiteringa furna'ce by 3&0- duct A]! enters thg du‘ct at 20°cf'and 1 atm with is mean oajnc'uy cf 45 mls. _§he_tuba's hernia! diréclion. The b‘u’ger diam'éter'of thé 111ng Is and thé tubes are arranged til-line wlth lunglfiudlnal and transveme N Alf Is haated by geothermal water tn 3 tube bank“ The rate. of heat d e .m m e I. e d E b m m l 3 Wm h mD a 50% .m m4 m 8:7. .m n Wu .El.m B .fl‘, 5.. “Nu r: fa W. .Wu W 73.. D. .F._.l.... M. ...H..K.. H .m n.a F tummy". C ELI. mm.“ D. ..P,..B‘.. .‘ .fl. my .5 be .m . .. "WE =.Dw t 31 Thu d fium 85“ .H 7! .mr 9.- m L mm w Lam m E ma 0 WW.“ 0 n... dw Wpurmw U” D: .mqm DMSHH “e M I ECG I: "m :lChBl. HUS nn 6... 65th.“ lfl VA E H.“ n gm pr. Inmrhm 3.19m“. cull EEEEE‘ La wamm—rgeeegze’ ’.fifiififfl‘afigrfizew _u..~..- .... - a u—nflé ' -- HEATTRANSEEWW» -" V: 4 5 m 7;. 120%: m Assumpiions 1 Steady operating cenditiens exist 2 The surface temperature a; T] u: we Cf the tubes is equai to the temperaluje of geothermal water "‘" O O O O G Pmperfles The exit temperature of air, and thus [he mean temperature, is nut '. knowm We evaluate the air prepedies at the assumed mean temperature a: 59?? {wili be checked Eater) and 1 atm are Tabieafi: M. (3 (3 Q (3 Q g k '2 002893 Wlm -‘ K. p m 1&6 icgi'm3 ~— (3 G 0 0 (“.9 (3 gammy/eye. ‘Pr=07202 M G) o (a) O O G) p, new; X._1E_i‘5§cglea~s 1.1.3:,I=Pr437,= 07073 H" 0 G O 0 O O ' éiee, the density pfaire‘ttfie inlettemperatme of 20%] (for use in the massiiew W O (D {19 G (9 C3 [afie'eeiee‘iaijori atthe inlet) is pl 2" 102.01} kglma a a... .. a Q G {a a May's}; {it is given the; D "9: 9.0.15 m'. 5;. m Sr? 0 05 m, and “V = 4 5 :11]; Mags) 0 a O ‘ Then the maximuguieieciiy age! the Reyneififs number based on the maximum SL=ST=5cm Dm15cm :ST', . are». (4:5 W = 5-43 "1’s wmgp _; (3.06 kgfm=xe43 ml5)(0.015 m) u fl X"ig"§kglm-s 7 FIGURE 7—28 Schematic for Example 7?? = 5093. emigrated ageing praper reieiiee [mm Table 53 - - - = - N ' t 5:92." -.' - . ~le dew!er- “ I 292197.073?!” = 5312.4th I 3'- ;; "7'; "I . q 5 ' ' ‘ T032 137 {we Nueeeit aerate: is eppiieebie gq tube banks with N; > 18 in our case. the - nun:qu 'rdweis NL @715. egg the: corresponding coneciien faster from 'i'abie 3}? i: 0,945.:Then the aqegage‘Nusseit number arid heat transfer mam" f0 .éii met as in the'teige Eankrbeceme ..- :3I33'l-H . . m. -' ' Res. J: '49.3{u.ozaoswrm = 922. Win13 i°C length“: m}. the heaut treesifer s'ufietge area and the mass flow rate oi air ' (evaluateg ettneiniet} are 5 ‘ ' ‘ ~u '. - fine {oi—Lil! number ef'tuhee [SW = ML X N; = 6 x 10 = 50 For n ueii lube : A, ewe We: mm me) :—~ 2.827 m? §. ‘1.- : -‘- '.-. -'.:'::..-.: - .1 fir =.. rix: := ewes») . #05394, kgméites genomes mm m) = 2 709 kgls Theethe fluid exit termzxelraimeI the tag mean temperature difference, and 813 I reie pf heat transier beeeme ' HT“? (T—T}ex I: .r s I P may (2 709 kglsiiiflm mfg " um) w 29(1) C *- 120 -- (120 ~- 20)cxp(—- at, (fl-9ED _ tT,-— f.) w (I;- I.) m (320 -- 29.11) ~ (120 - 20) m a M“ " lam". -- Tana", - To] mitten «- as miner) - '20)} 954 C Q = MAT!" = (seawrm? “CW. 327 m3)l95 4°C) = 249 x 1&4 w The rate of heat transfer can atso be determined in a simpler way "Iran's Q = neon” 2 racprr, — r.) = (2 799 against)? iflrg “ones 1: ~ zone a 249 >< :04 w For this square Err-line tube bank, the irintion coefficient corresponding to HEg = 5088 and SLID =1 511 5 m 3.33 is, from Fig 7475. f = 0 16 Also, x =1 I for the square arrangements Then the pressure drop across the tube hank becomes d J3 d X vim . a «Pin 9-" APsNrix-ch 5K1? > ' sum {39% 1-H“ (I 06 trglrn3)(6.43 info)J ( m a S“) Hill!) 2 1):: 21 Pa lirg‘rnls Discussion The arithmetic mean fluid temperature is (7} + Talia = (20 + 1109)]? =1 65 4‘0, which is fairly close to the assumed value of STD There» tare, there Is no need to repeat calculations by reevaluatlng the pronertles at 65 riff} (It can be shatvrr that doing so would change the results by less than 1 percent. which is much less than the uncertainty in the equations and the charts used). ,,__m.m.__.W——H.W . “'"tfn‘winfittl'ugfigtfiv-TH- f. assassinate-viii - , em m...rmge.t:n‘.-:Jr if? omit? Thermal insulations are materials or combinations of matcn'aIs that are used primarily to provide resistance to heat flow (Fig. 7&9) You are prob» “my familiar with sovorai kinds of insulation available in the market Most insulations are heterogeneous materials made of low thermal conductivity materials, and they involve air packets This is not surprising since air has Gm: of the lowest thertnai conductivities and is readily ovoilainte The Sty- mfaam commoniy used as a packaging material for TVs. VCRs, oomput~ (its. and just about anything because of its tight weight is aiso an excelient Insulator , Ternpemtrrre difiismttce is the driving force for heat flow, and the greater “it: 1t‘vlrtporatorra difference. the larger the rate of heat transfer. We can slow "“two the heat flow between two mediums at different temperatures by smiling "barriers" on the path of heat flow Thelma] institutions serve as such barriers. and they piay a major role in the design and manufacture of “‘5 enorgy-effioien: devices or systems, and they are usually the cornerstone 0f energy conservation projects A 1993 Drexel University study of the a“""EiMntensive {LS industries revealed that insulation saves the U S W "(his section can be stunned without a loss in continuity L-g' FIGURE 7-29 Thermal insulation retards heat transfer by acting as a barrier in the path of heat flow ...
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Solution HW8 06 - 529M7an 79W flay/1mm? 3 530.334 Heat...

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