A = total heat-transfer area in the heat exchanger CHAPTER 3. Heat Exchanger Design

Transcription

1 CHAPE 3 Heat Excanger Desgn s capter ll prde te framerk n t desgn a Duble Ppe and Sell and ube type Heat Excanger. Detaled teretcal dscussn n te prncples f eat transfer as cnscusly left t readers t read standard textbk n eat transfer. A bref ree f eery tpc tat uld be needed n te understandng f eat excanger desgn as been prded t assure cntnuty and cmpreensn. A duble-ppe eat excanger s cnssts f t cncentrc ppes t ne flud flng trug te nner ppe le te ter flud flng trug te annular space.wle a sell-andtube eat excanger cnssts f tube bundles enclsed n a cylndrcal sell t ne flud flng trug te tubes and te ter flud flng utsde f te tube bundles enclsed n te sell. e tree fundamental mde f eat transfer are () cnductn, () cnectn and (3) radatn. Cnductn ccurs en te transfer f eat s trug mlecular actn. ere s a need f pyscal cntact but tut sgnfcant dsplacement r mement f mlecules. It culd take place tn a sld r nn-mng flud medum. On te ter and, cnectn requres te mement r mxng f fluds. It takes place beteen a sld surface and a cntactng mng flud tat are at dfferent temperatures. adatn s te transfer f eat n te frm f electrmagnetc aes. s mde f transfer des nt requre te presence f an nterenng materal r pyscal cntact. HEA EXCHAGE DESIG EQUAIOS ate f eat ransfer Smlar t ter transprt penmena, te rate f eat transfer s als expressed n terms f drng frce and resstance. e general rate expressn fr eat transfer s cnenently expressed n terms f erall eat-transfer ceffcent, U, c s defned n an analgus manner t etn s la fr cnecte eat transfer. Fr Duble Ppe eat excanger, te rate f eat transfer may be cmputed usng Equatn 3-. q UA ln eq 3- Heer, t crrect mxed fl n a sell and tube type f eat excangers, a gemetrc crrectn factr, Y, as t be added t accunt fr te fl deatn frm duble Ppe eat excangers. us, ere: q UAY ln eq 3- A = ttal eat-transfer area n te eat excanger, = temperature dfference beteen t and cld streams at eat excanger termnals ln = lgartmc mean temperature dfference (LMD)

2 HEA EXCHAGE DESIG ln eq 3-3 ln( / ) Y s crrelated t t dmensnless temperature rats namely te eat capacty Z, and te effecteness f te eat excanger X. Values f te gemetrc crrectn factr fr dfferent number f tube t sell passes may be dered frm Fgure 3- and 3-. Z and X A B B A A B B B eq 3-4 Fgure 3-. Crrectn factr fr mxed-fl ype Heat Excangers ne sell pass; t r mre tube passes. Adapted frm ASME as cted by Fust, 980. earrangng equatn---- and expressng n terms f resstance, q UAY ln eq 3-5

3 HEA EXCHAGE DESIG 3 us UA eq 3-6 Fgure 3-. Sell passes; fur tube passes. Adapted frm ASME as cted by Fust, 980. e Oerall eat transfer ceffcent maybe based n te nsde, U r based n te utsde, U. e cce f erall eat transfer ceffcent uld depend n c f te resstances uld be cntrllng r bgger. Wle erall eat transfer ceffcent s drectly prprtnal t cnecte eat transfer ceffcent, cnecte resstance s nersely prprtnal t te cnecte eat transfer ceffcent. us, te ler te cnecte eat transfer ceffcent te mre cntrllng ts resstance. If ten <<<, >>> tus q U A Y ln eq 3-7

4 HEA EXCHAGE DESIG 4 On te ter and, f <<< en us >>> q U A ln eq 3-8 In a steady-state transfer f eat frm a t flud stream utsde te tube t a cld flud stream nsde te tube, te fllng steps are nled: cnectn frm te t flud utsde te tube t a tube all surface, cnductn trug te tube all, and cnectn frm te surface t te cld flud flng nsde te tube. us, a 3- resstance erall eat transfer ceffcent s, U A U A A k x Am A If utsde flm resstance s cntrllng, Equatn 3-9 s reduced t, eq 3-9 U D D k x D Dm eq 3-0 Wereas f te nsde flm resstance s cntrllng, te rkng equatn uld be: U k x D Dm D D eq 3- Heer f fulng exts n bt sdes f te all, addtnal scale resstances ll be ncrprated, f, A f, and f, A f, eq 3- ere f, and f, are te fulng ceffcents f te nsde and utsde surfaces f te tube, respectely. us, te erall resstance, U, s: U A U A A A f, k x Am A A f, eq 3-3 A smlar smplfed equatn may be dered fr knn cntrllng flm resstance.

5 HEA EXCHAGE DESIG 5 able 3- ss typcal fulng factr fr dfferent lquds at dfferent flud elcty. able 3-. ypcal Fulng factr (Fust, 980). Fulng Factr, d = / d r F ft /Btu Water Velcty 3 ft/s r less 3 ft/s r mre Seaater (up t 5 F) Well ater Delaare and Leg rer aters Brne Fuel l Cnducte Heat ransfer Furer s La f Heat Cnductn states tat te eat flux, q/a, (te rate f eat transfer per unt tme per unt area) s prprtnal t te temperature gradent (- d ) and nersely all tckness: q A d k dx eq 3-4 ere: x ( x x) ( ) x (ka) ( ( x ) x ) k eq 3-5, tckness f te all, temperature drp acrss all, cnducte termal resstance f all Were te prprtnalty cnstant k s te termal cnductty tat ndcates gd te materal cnducts termal energy. In mst engneerng applcatns k may be cnsdered cnstant except n g temperature drps. In cases ere k ares t temperature a lnear relatnsp suc as n Equatn 3-6 may be used (McCabe, 00): k a b eq 3-6 Were a and b are emprcal cnstants and s te temperature f te medum. In case f radal cnductn f eat n a ll cylndrcal essels r ppes, te area perpendcular t te drectn f eat fl s nt cnstant but s prprtnal t te radus ( A rl ). us, fr ll cylndrcal cnfguratns t utsde radus r t nsde radus r, rat s greater tan.4 (Mc Cabe): q k( L)( ln( r / r ) ) ka L ( ( r r ) ) eq 3-7

6 HEA EXCHAGE DESIG 6 ere: ( r ka r ) L eq 3-8 A r ( r L (Lgartmc mean surface area) eq 3-9 L L ) ( r ln(r r / r ) L (Lgartmc mean radus) eq 3-0 ) In cases ere te utsde t nsde radus rat s less.4, lgartmc mean radus ll just be equal t aerage radus. Seres f esstances At steady-state, te rate f eat transfer trug a all cnsstng f a seres f layers f dfferent cnductng meda A, B, C tat are n excellent termal cntact ll be equal t te rate f eat transfer n eac layer, q q q q eq 3- A B e ttal temperature drp acrss te multlayer all s equal t te sum f te temperature drps acrss eac layer, C A B C eq 3- Wereas te ttal resstance f te multlayer all s equal t te sum f te nddual resstances, / q eq 3-3 A B C Were resstance fr eac layer s: q x ( k A) A A A A A eq 3-4 q x ( k A) B B B B B eq 3-5 q x ( k A) C C C C C eq 3-6

7 HEA EXCHAGE DESIG 7 Cnecte Heat ransfer etn s La fr Cnecte Heat ransfer states tat te cnecte eat flux s prprtnal t te dfference beteen te surface temperature,, and te temperature f te flud f alng te eat fl pat: q A ( f ) eq 3-7 = A eq 3-8 Were: = Cnecte resstance = Cnecte eat transfer ceffcent (lcal flm ceffcent) A = eat transfer area n-cntact t te flud Seeral emprcal equatns ere dered t estmate cnecte eat transfer applcable ceffcent fr dfferent types f eat excangers tat perates as eaters, cndensers, rebler and eapratrs. Heat ransfer tut Pase Cange s sectn cers te estmatn f cnecte eat transfer ceffcent f fluds nle n eatng and clng n Duble Ppe and Sell and tube type f eat Excangers. Duble Ppe Heat Excanger e Seder-ate equatn s applcable n te estmatn f te cnecte eat transfer ceffcent f fluds flng nsde te tube f a duble ppe eat excanger. It culd als be use t estmate te cnecte ceffcent f te annulus flud prded te annular dameter s reflected as equalent dameter, Deq.. Seder-ate equatn s applcable nly fr nn-metallc flud t Prandtl number beteen 0.5 t 00 and eynld s number f at least 0,000. Fr lng tubes (L/D) >50 ( Mc Cabe 00 ). e cnecte eat transfer ceffcent fr te tube flud s: D k e / 3 Pr 0.4 eq 3-9

8 HEA EXCHAGE DESIG 8 ere DV c p e, Pr eq 3-30 e cnecte eat transfer ceffcent fr te annular flud s: k ere D k eq e,o /3 Pr 0.4 eq 3-3 4S D e q P eq 3-3 D eq = equalent r ydraulc dameter S = crss sectnal area f te flud stream P = etted permeter and tus: S 4 D d and P D d eq D d D d 4 D eq eq 3-34 D d eq D D d eq 3-35 e eynld s umber f te annulus flud s ten equal t e,o D eq eq 3-36 Fr a srt tube t L/D < 50, (McCabe, 00): s D L 0.7 eq 3-37 Were: s = aerage eat transfer ceffcent er te srt tube lengt = eat transfer ceffcent fr fully deelped turbulent fl (lng tube)

9 HEA EXCHAGE DESIG 9 Lamnar Fl Frced Cnectn (Geankpls, 995) / u Gz eq 3-38 ere: = scsty at te mean bulk temperature f te flud =scsty f te flud ealuated at te tube all temperature mc / 3 p u, Gz, k D kl 0.4 Sell and ube ype Heat Excanger cmpute fr te utsde eat transfer ceffcent,, n a sell and tube eat excanger, Fgure 3-3 as been cmmnly used. e cce f ptc t dameter rat and tube ptc arrangement are used smultaneusly t te eynld s number t determne te j g max alue c ll n turn use t estmate te aerage ceffcent. Fgure 3-3. Heat ransfer Ceffcent fr Fl rmal t tube banks.adapted frm ASME as cted by Fust et.al., 980.

10 HEA EXCHAGE DESIG 0 cmpute fr te nsde eat transfer ceffcent,, n a sell and tube eat excanger requres tube lengt t dameter rat, L/D. Fgure 3-4 c s applcable fr bt lamnar and turbulent fls culd be used t estmate te cnecte ceffcent. L/D s grap aganst te eynld s number t determne te j g alue c ll n turn be use t estmate te aerage cnecte ceffcent. Fgure 3-4. Crrelatns fr Heat and Mass ransfer t Smt ubes. Adapted frm Brn et.al., 950. ere C p am Pr /3 0.4 D 3 j 3 g.86 eq 3-39 e L

11 HEA EXCHAGE DESIG Heat ransfer t Pase Cange Cndesatn Cndensatn f apr may be f Flmse r Drpse cndensatn. Flmse Cndensatn ccurs en apr f rganc substances cndense n cld metallc surfaces frmng a cntnuus flm. Wle Drpse cndensatn ccurs en apr cndenses n cld metallc surfaces and des nt frm cntnuus flm but rater drplets cndensates nly. Flm ype Cndensatn n Vertcal Surface As cted by Fust et al (980), usselt dered te basc rkng equatn fr te ealuatn f flm type cndensatn n te ertcal surface. e dered equatn requres seeral assumptns as presented by Fust:.) Pure apr s at ts saturatn temperature..) e cndensate flm fls n lamnar regme and eat s transferred trug te flm by cndensatn. 3.) e temperature gradent trug te flm s lnear. 4.) emperature f te cndensng surface s cnstant. 5.) e pyscal prpertes f te cndensate are cnstant and ealuated at a mean flm temperature. 6.) eglgble apr sear exsts at te nterface K 3 L l H g / 4 eq 3-40 ere ρ l, ρ = denstes f lqud and apr g = gratatnal acceleratn k e = lqud termal cnductty e = lqud scsty H = latent eat f aprzatn = apr saturatn temperature = surface temperature W = cndensate, #/r e abe equatn as been fund t be farly n agreement t expermental alues. Heer, assumptn as t deal t because te cndensate des nt fl strctly n te lamnar regme. Mst expermental alues are ger tan te predcted alues frm te abe equatn. An ncrease f 0 percent f te predcted alue as been recmmended, tus,.3 K 3 L l H g / 4 eq 3-4

12 HEA EXCHAGE DESIG Flm ype Cndensatn n Hrzntal Surface As cted by Fust et al, n te same assumptns, usselt dered te rkng equatn fr te cndensatn f apr n rzntal surface as: 0.75 K 3 D Hg l / 4 eq ). Fr e > 40, s multpled by. t accunt fr te effect f rpplng (McCabe, Heer, en te amunt f te cndensate s knn, Mc Adams ( 954 ) presented an alternate equatn, 0.95 K 3 W gl /3 eq 3-43 Were W s te amunt f cndensate n lb/r Banks f Hrzntal ubes e result n te sngle rzntal tube may be extended t estmate te aerage cnecte eat transfer ceffcent, f bank f tubes n ertcal rs (Brn,950), ere: 4 eq 3-44 / 4 3 / 4 3 / / 4 3 n 3 / 4 n eq 3-45 s number f tubes per r le subscrpts,, 3, 4 etc. are r numbers. Cmbnng te abe equatns, 0.75 K 3 D Hg l / 4 eq 3-46 Heer f splasng ccurs as te cndensate fls frm tube t tube Kern (950) as cted by Fust (980), prpsed a mdfcatn f te rkng equatn as flls;

13 HEA EXCHAGE DESIG K 3 D /3 Hg l / 4 eq 3-47 Fr turbulent cndensatn n ertcal surfaces, as cted by Fust (980), Krkbrde (934) and Clburn (933) prpsed a reasnable estmatn f te cnecte eat transfer ceffcent, c K 3 g /3 0.0 ec /3 4 Pr eq 3-48 Cndensate prpertes are ealuated at a mean flm temperature, f, ere: f s 3 4 s s eq 3-49 s V = saturatn temperature f cndensng apr s = temperature f sld surface Flm Blng n Submerged Hrzntal Cylnder r Spere 997) Blng eat transfer ceffcent may estmated usng Mcelly equatn (Perry and Green, 0.5 qc A P Pk 0.33 eq 3-50 Were Cpe ; BU = eat capacty # F X 970 BU = latent eat eapratn # K : BUft ft = termal cnductty e rf 4.97 x0 3 #f = surface tensn ft P Psa, Pressure f system = pressure f system Q = rate f eat flux A e, = densty f lqud and apr ese prpertes are ealuated at F r apr sde temperature

14 HEA EXCHAGE DESIG 4 Cengel, (003) prpsed an alternate equatn fr te estmatn f flm blng ceffcent applcable fr bt rzntal cylnder r a spere, q A C gk 3 ( l )[ D( s 0.4c sat p ) ( s sat )] / 4 ( s sat ) eq 3-5 ere: A = area f surface f cylnder r spere n cntact t flud C = 0.6 fr rzntal cylnder; C = 0.67 fr spere = eat f aprzatn g = gratatnal acceleratn V, L = densty f lqud and apr, respectely V, k V = scsty and termal cnductty f apr, respectely s = surface temperature f t cylnder r spere sat = blng temperature at te specfed pressure c p = specfc eat capacty f apr HEA EXCHAGE DESIG SPECIFICAIO Fgure 3-5. Sell-and-ube Heat Excanger. Layut and Ptc Arrangement ubes are usually arranged n a trangular r square ptc arrangement. Ptc s te center-t-center dstance beteen tubes. tated square ptc, a aratn f square ptc s te trd cmmnly used tube arrangement as presented n Fgure 3-6. Wle a trangular ptc arrangement ffers mre eat transfer area per unt lume f a eat excanger, te square ptc arrangement ffers ease n cleanng and mantenance peratns. A mnmum f.5 ptc t dameter rat and/ r a mnmum ebb tckness beteen tubes f apprxmately 3. mm culd ensure suffcent strengt fr tube rllng. Wereas a 6.4 mm clearance s suggested fr mecancal cleanng requrement (Hett, et. al., 994). In mst desgn, te ptc t dameter rat range frm.5 t.5 (Peters et. al, 004).

15 HEA EXCHAGE DESIG 5 Fgure 3-6. ube Layut Patterns: (a) Square Ptc; (b) rangular Ptc; (c) Square Ptc tated; (d) rangular Ptc t Cleanng Lanes. ube layut nrmally flls symmetrcal arrangement ang te largest number f tubes at te center. Wt an apprprate ptc t dameter rat and ptmum ppe dameter csen, knn ttal eat transfer area, uld lead t te sell dameter specfcatn. Mnmum sell dameter s calculated by: Were Sell Dameter Mn = c D + ( c + ) C eq 3-5 c = umber f tubes at te Center C = Clearance Clearance = Ptc Dameter eq 3-53 ere Ptc Ptc Da Dameter tal eat transfer Area (A ) s equal t te prduct f ttal number f tubes and eat transfer area per tube. A = πdl eq 3-54 ere d L = tal number f tubes = Eter nsde r utsde dameter = Lengt f tube

16 HEA EXCHAGE DESIG 6 At a set ppe dameter d, a cmprmse s csen beteen and L usng t 0 (Hett, et. al., 994). L rat f 5 D sell A cnsequence f csng ger rat uld result t lnger tube lengt and eentually smaller sell dameter. Wt smaller sell dameter, tube seets, sell dameter etc. uld be tnner, ence, ceaper. At a knn lumetrc fl rate, lnger tubes (less number f tubes) uld prde fr ger tube elcty, eer suc desgn mgt encunter dffculty n baffle supprt n te sell sde. Standard tube lengts n a sell and tube type eat excanger cme n 8, r 6 ft and are aalable n a arety f dfferent dameters and all tckness (Peters and mmeraus, 99). Heer 0 ft tube lengts are n te mst cmmnly used (Perry and Green, 997). able 3- ss te number f tubes n a cnentnal tube seet layut at dfferent sell dameter, ptc arrangement and number f passes fr ¾ and nc tube dameters. able 3. umber f ubes n Cnentnal ubeseet Layuts. Sell One-pass -pass Fur-pass ID, n. Square Ptc rangular Ptc Square Ptc rangular Ptc Square Ptc rangular Ptc ¾-n.-OD tubes n -n. ptc ¼ ¼ n.-od tubes n ¼-n. ptc ¼ ¼ Adapted frm able 7, p 608. Plant Desgn and Ecnmcs fr Cemcal Engneers 4 t ed. O.5.. Baffle and ube Seet. Baffles and ubeseet Fgure 3 7. Segmental Baffles.

17 HEA EXCHAGE DESIG 7 Baffles are used t supprt tubes mecancally aganst saggng and pssble bratn. ey als drect flud fl and cntrl elctes. Amng te dfferent types f baffle, te segmental types are te mst cmmnly used. Segmental baffle cut s nrmally 5% f te dsk dameter (maxmum f 45%) (Peters et. al, 004). e rat f baffle spacng t baffle cut s a majr desgn parameter fr te effecte cnersn f pressure drp t eat transfer (Hett, et. al., 994). Heer t accmmdate l pressure drp requrement, te dsk use f and dugnut baffle type reduces pressure drp by 50% - 60% (Hett, et. al., 994 and Peters et. al, 004). Cmmn baffle spacng fr Sell and ube ype eat excanger ranges frm 0% t 00% f te sell dameter (Peters and mmeraus, 99). EMA recmmends a mnmum spacng f 50 mm r 0% f sell dameter c eer s greater (Perry and Green, 997). Wen maxmum spacng s sugt, t suld nt exceed te alue ndcated n able 3 3 (Hett, et. al., 994). s as been set t antcpate effects f temperature n materals f cnstructn. It suld be nted tat at smaller baffle spacng, sell sde pressure drp s g. Fr unsupprted tube span, te maxmum unsupprted tube span suld equal t 74d 0.75 (d s utsde tube dameter). e unsupprted span s reduced by % fr alumnum, cpper and ter allys (Perry and Green, 997). able 3 3. Maxmum Unsupprted Stragt ube Lengt (all dmensns n mllmeters). Maxmum Unsupprted Span ube Materals and emperature Lmts ( C) ube OD Carbn and Hg Ally Steel (400) L Ally Steel (454) Alumnum & Alumnum Allys (apprx.) ckel-cpper (36) Cpper & Cpper Allys ckel (454) tanum & Zrcnum at Cde Max. ckel-crmum-irn (538) Allable emperature Adapted frm able 6. p 7. Prcess Heat ransfer. (Hett 994). EMA sets mnmum tckness fr baffle and supprt plate tckness as sn n able O 5. Fr tubeseet tckness calculatns, bendng and searng f tubeseet ae been cnsdered by EMA (Jaad and Farr, 988). e EMA equatn fr te requred tckness n bendng s

18 HEA EXCHAGE DESIG 8 ere G P S F GF P S = equred tckness f tubeseet = Dameter = Appled Pressure = ASME allable tensle stress =.5 Fr Smply supprted plate =.0 Fr Fxed plate eq 3-55 e requred tckness fr te searng stress at te uter tube permeter s: 0.3 D d p L P S eq 3-56 ere D = 4 A C A = Area f tubeseet tn uter tube permeter C = Permeter f uter tube d = Outsde dameter f tube p = Dstance beteen tubes e resultng tckness resultng frm equatns 3-55 and 3-56 are cmpared t te tckness as specfed by EMA (able 3-4). Wceer s tckner ll be specfed fr used. able 3 4. Baffle and Supprt Plate Mnmum ckness (EMA). DISACE BEWEE OMIAL SHELL ISIDE DIAMEE (Inces) ADJACE SEGMEAL PLAES, (Inces) >39 < ⅛ 3 6 ¼ ¼ ¼ 5 6 ⅜ 8 4 ¼ ⅜ ⅜ ½ 4 30 ⅜ ⅜ ½ ⅝ >30 ⅜ ½ ⅝ ⅝ Pressure Drp Acrss te Heat Excanger Cnecte eat transfer ceffcent ncreases t ncreasng flud elcty. Heer, ts large flm ceffcent can be cunter-balanced by te detrmental effects f ncreased pressure drp due t ncrease n flud elcty (Perry and Green, 997). Judgment n te cmprmsed elcty fr net benefcal effect culd nly be dne by ecnmc analyss cnsderng smaller equpment cst (smaller eat transfer area) ersus g pumpng cst (at ger pressure drp).

19 HEA EXCHAGE DESIG 9 Kern (950) prdes fr te estmatn f pressure drp n bt sell sde and tube sde. ese equatns presented by Backurst and Harker (973) are reprduced n te fllng paragrap: ube Sde On te tube sde, te pressure drp cnssts f t cmpnents, te frctn lsses n te tubes and te lss due t cange n drectn: t fg Ln 4n 6.4s lb t 0 DtS t g n eq 3-57 fg L Pt n s 0 K t n.6 6 DtS t m eq 3-58 ere G t = Mass elcty n te tubes a at ft m n m a t t lb ft r kg m s eq 3-59 eq 3-60 = tal number f tubes n = umber f tube sde passes a = Crss-sectnal area f fl per tube D t = ube dameter ft m = Flud elcty ft m s s ft n m m f = Frctn Factr ft m 0.33 ft f 0.05e r n eq 3-6 f 0.7 m m 0.33 e eq 3-6 Applcable fr e >000

20 HEA EXCHAGE DESIG 0 Sell sde s fg D L lb s s 9 DeS sb m eq 3-63 P S fg D L 0 K s s 6 DeS sb m eq 3-64 ere G s D s S = Mass elcty n te sell = Sell nner dameter [ft] [m] = Specfc graty f te flud lb ft r kg m s 0.4 s = eq 3-65 L B f f f = ube lengt [ft] [m] = Baffle spacng [ft] [m] = Frctn factr ft n 0. e m m 0. e ft n m m eq 3-67 eq 3-66 Applcable fr e >500 Peters and mmeraus, (99) prde an alternate equatn fr pressure drp acrss te tube and sell as reprduced n te fllng paragrap: Fr tube sde P B f G Ln p g D c ere subscrpt refers t nsde f tube at bulk temperature eq 3-68 f = Fannng frctn factr fr stermal fl based n cndtns at te artmetc-aerage temperature f te flud n p = umber f tube passes = Cnersn factr n etn s la f mtn, g c

21 HEA EXCHAGE DESIG g c ft lbm r lbf eq 3-69 Φ I = Crrectn factr fr nn-stermal fl. 0.5 eq 3-70 en D /μ s less tan 00 and eq 3-7 en D G B s greater tan 00; = Vscsty at artmetc aerage (bulk) temperature f flud = Vscsty f flud at aerage temperature f te nsde tube all surface = Crrectn factr t accunt fr frctn due t sudden cntractn, expansn and reersal f fl drectn B F F F fg L g D e e r c eq 3-7 Fr fl acrss tubes, te fllng equatn can be used t apprxmate pressure drp due t frctn: B f G g r s ere subscrpt refers t utsde f tube at bulk temperature f = Specal frctn fr sell-sde fl s f 0.5 c DG f b eq 3-74 b b X X 0. I 0.08X.08 L X L eq 3-75 eq 3-76 eq 3-73

22 HEA EXCHAGE DESIG ere X rat f ptc transerse t fl tube dameter eq 3-77 X L rat f ptc pallalel t fl tube dameter eq 3-78 r = umber f rs f tubes acrss c sell flud fls B = Crrectn factr t accunt fr frctn due t reersal n drectnal fl recrssng f tubes, and aratn n crss sectn B en te fl s acrss unbaffled tubes r B umber f tubes crsses as a rug apprxmatn Varatn f Kern metd and ter estmatns by Bell-Delaare metd and Wlls and Jnsn metd are dscussed n Prcess Heat ransfer (Hett, et. al., 994). Heat Excanger emperature Lmts e mst cmmn eat excanger medum used fr clng s ater. Asde frm ts abundance and cst, ater exbts relately g eat capacty. In te desgn f eat excanger, t s bus tat eter large quantty f clng ll be used r greater ater temperature cange suld be antcpated t cme up t smaller eat excanger. Large quantty f clng ater uld result t ger ater elcty. s g elcty ll reduce fulng but ncreases ater and pumpng csts. On te ter and, large ater temperature ncrease ll requre less ater and pumpng csts. Heer, at g temperatures, ater exerts cnsderable crrse actn n steel, partcularly f ater cntans dssled xygen (Peters et. al, 004). Furtermre at g ater temperature scalng tends t ncrease (Backurst and Harker, 973). mnmze scale frmatn, ater temperature suld nt be mre tan 0ºF (Backurst and Harker, 973; Peters et. al, 004). prtect aganst fulng and crrsn, ater temperature (utlet) suld nt be eated abe 58 F (Baasel, 974). Agan a gd cmprmse as t be set beteen large quantty f clng ater and greater ater temperature cange. Fr te clng ater, n an pen crculatn systems suc as clng ters and spray pnds, te temperature f te cled ater s 8-3ºF abe te et bulb temperature (Baasel, 974). Heer snce xygen s pcked-up n eery pass, treatment f ater s necessary f crrsn and grt f mcrrgansm s t be cntrlled (Peters et. al, 004). Wen usng clng ater t cl r cndense a prcess stream, assume a ater nlet temperature f 90 F (frm a clng ter) and a maxmum ater utlet temperature f 0 F (Seder et al, 004). As t te temperature dfference, te rule f tumb s tat te greatest temperature dfference n an excanger suld be at least 36 F and te mnmum temperature dfference suld be at least 0 F t (Lrd et. al., 970).