Heat Exchanger Design

Transcription

1 World Academy of Science, Engineering and Technology 008 Hea Exchanger Design Su The Mon Than, Khin Aung Lin, Mi Sandar Mon Absrac This paper is inended o assis anyone ih some general echnical experience, bu perhaps limied specific knoledge of hea ransfer equipmen. A characerisic of hea exchanger design is he procedure of specifying a design, hea ransfer area and pressure drops and checking heher he assumed design saisfies all requiremens or no. The purpose of his paper is ho o design he oil cooler (hea exchanger) especially for shell-and-ube hea exchanger hich is he majoriy ype of liquid-o-liquid hea exchanger. General design consideraions and design procedure are also illusraed in his paper and a flo diagram is provided as an aid of design procedure. In design calculaion, he MaLAB and AuoCAD sofare are used. Fundamenal hea ransfer conceps and complex relaionships involved in such exchanger are also presened in his paper. The primary aim of his design is o obain a high hea ransfer rae ihou exceeding he alloable pressure drop. This compuer program is highly useful o design he shell-and-ube ype hea exchanger and o modify exising deign. Keyords Shell-and-Tube Hea Exchanger, MaLAB and AuoCAD T I. ITRODUCTIO HE process of hea exchange beeen o fluids ha are a differen emperaures and separaed by a solid all occurs in many engineering applicaions. The device used o implemen his exchange is ermed a hea exchanger, and specific applicaions may be found in space heaing and aircondiioning, poer producion, ase hea recovery, and chemical processing. The problem of hea ransmission is encounered in many indusries and because of he diversiy in he fields of applicaion here exis counless difference in deail. Hoever, he calculaion principle underlying he problem o design a hea exchanger are everyhere he same, and i is he purpose of his paper o presen design calculaions raher han o deal ih he deails of individual problems and special cases [1]. A compuer program in MaLAB has been rien for shell and ube hea exchanger design. ormally, he hea exchanger design calculaions are seems o be complex and repeaed calculaions are required ih assumed and/or fixed daa. So, many hermodynamic and fluid dynamic parameers are encounered ino designs procedure and herefore his condiion ill saisfy and save he ime by using a compuer. Su The Mon Than is ih Deparmen of Mechanical Engineering, Pahein Technological Universiy, Myanmar, (corresponding auhor o provide Phone: ; Fax: ; Khin Aung Lin is ih Deparmen of Mechanical Engineering, Thanlyin Technological Universiy, Myanmar. Mi Sandar Mon is ih Deparmen of Mechanical Engineering, Yangon Technological Universiy, Myanmar. Wih he help of his compuer program, no only he shell and ube hea exchanger can be designed ihou knoing he deail design calculaion bu also plan engineer can modify he currenly used hea exchanger for some necessary changes, such as blocking he blon ou ubes ihou much effecs o operaion, changes in fluid flo rae according o oher process, ec. I is hoped ha his paper ill aid in classifying he many deails quesions ha arise during design calculaion and his ill suppor pracicing engineers o apply he formal backgrounds in fluid flo and hea ransfer o he pracical problems posed by he design, selecion, esing, or insallaion of he shell and ube hea exchanger. II. DESIG COSIDERATIO The designer mus consider several facors ha influence he shell-side hea ransfer coefficien ha, in urn, deermine he rae of hea ransfer in he shell-side. 1. When baffles are provided, he sysem direcs he shell-fluid from axial flo o op-o-boom flo or side-o-side flo ih he effec ha he hea ransfer coefficien is higher han for undisurbed flo along he axes of he ubes [].. Paerns of ube layou influence urbulence and hence hea ransfer coefficien e.g. riangular pich gives greaer urbulence han square pich. And under comparable condiions of flo and ube size he hea ransfer coefficien for riangular pich are roughly 5% greaer han for square pich [3]. 3. Closer he baffle spacing, greaer is he number of imes he shell-fluid is o change is direcion resuling in greaer urbulence [4]. 4. Shell-side coefficien is also affeced by ube size, clearance and fluid-flo characerisics [5] 5. Shell-side flo area varies across he bundle diameer ih he differen number of ube clearances in each longiudinal ro of ubes. Tha s hy here is no rue shell-side flo area by hich he mass velociy of he shell-fluid can be compued. The correlaion obained for fluids floing in ubes is obviously no applicable o fluids floing over he ube bundles puncuaed ih segmenal baffles [3]. 6. There are some erms used in hea exchanger specificaion problems and heir soluions, hich are ofen confused. These are raing, design and selecion. Raing defines as he compuaional process in hich he inle flo raes and emperaures, he fluid properies, and he hea exchanger parameers are aken as inpu and he oule emperaures and hermal duy (if he exchanger lengh is specified) or he required lengh of he hea exchanger are calculaed as oupu []. 604

2 World Academy of Science, Engineering and Technology 008 Design defines as he process of deermining all essenial consrucional dimensions of an exchanger ha mus perform a given hea duy and respec limiaions on shell-side and ube-side pressure drop. Selecion defines choosing a hea exchanger from among a number of unis already exising []. Mos designers employ empirical relaions ih a cu-andry approach ha depends on heir judgmen and experience for convergence on a ne design by exrapolaion from esed unis. Hoever, an analyical approach is easier o follo for he less experienced designer, since i shos he basic relaionships. Our primary concern in his paper shall be hermal analysis based on analyical approach developed by Wolverine. III. IITIAL CODITIOS AD REQUIREMETS In general, he design of mos hea exchangers involved iniial condiions in hich he folloing variables are knon and assumed daa: 1. flo rae of fluids. emperaure range of fluids 3. lengh/ube and arrangemen of ubes Wih his informaion, i mus prepare a design for he opimum exchanger ha ill mee he required process condiions. Ordinarily, he folloing resuls mus be deermined. 1. umber of ubes and shell diameer. Hea ransfer rae 3. Overall hea ransfer coefficien 4. Tube side and shell side pressure drop IV. DESIG PROCEDURE This compuer program as divided ino hree main seps. 1. Calculaion of oal number of ubes. Calculaion and Checking of hea load 3. Calculaion and Checking of pressure drop for ube and shell side A. Calculaions of Toal umber of Tubes The suiable ube size, ube diameer (D ) and ube maerial are chosen firs. The ube configuraion has o be decided. In our program he equilaeral riangular pich geomery is se since i is mosly used. o oher configuraion is available in our program. Toal number of ubes mus be calculaed by using folloing equaions. πds CTP (1) 4CLP ol πd CTP () 4CLP Fig.1 reproduced from Tabordk defines he principal hea exchanger dimensions. D ol is he ouer ube limi diameer and D cl is he cenerline ube limi diameer (D cl D ol - D ) here D is he ouside diameer of he ubes). The baffle cu heigh is shon as a heigh L bch ; he value of he baffle cu B c is (L bch /D s ) x100%. B c Ds Fig. 1 Baffle and Tube Bundle Geomery [6] The diameral clearance beeen he shell inernal diameer D s and ouer ube limi diameer D ol is L bb. One half of L bb is he idh of his bypass channel. A pass pariion lane is shon ih a idh of L p. The diameral clearance beeen he shell inernal diameer D s and he diameer of he baffle D b is L sb, here he gap is equal o L sb /. L sb L bch Bc.100 Ds Fig. Baffle Cu and Clearance [6] The dimensions D s, D ol, baffle cu (% of D s ), and L bb and L sb, shon in Fig., can be obained from a ube layou draing of he hea exchanger [6]. B. Calculaion and Checking of Hea Load for U-Tube Design procedures of hea load check ih calculaion of hea ransfer coefficien of shell and ube side are as shon in Fig Calculaion of Tube-side Hea Transfer Coefficien Because of oal number of ube and oal ube-side flo rae are knon, ube side mass flo rae (G 1 ) can be solved as oal flo rae divided by he ube-side flo passage area per pass. In our program, removable insers are insalled inside he ubes. Use of ube insers (ire mesh or ised ape ypes) is highly effecive in laminar flos inside ubes. Insallaion of insers on he ube-side of hea recovery unis o increase energy recovery via a larger overall hea ransfer coefficien and smaller emperaure approaches. To overcome he fac ha laminar flo hea ransfer coefficiens are almos independen of fluid velociy and performance is difficul o improve using plain ubes even resoring o large pressure drops, eiher insers or exernal lo fins may be he simple soluion. Properly designed unis ih ube insers normally are much 605

3 World Academy of Science, Engineering and Technology 008 smaller in size and have smaller or equal pressure drops as convenional plain ube unis [7]. Fig. 3 Flo Char for Hea Load Fig. 4 Tube ih Inser Plae According o he Fig. 4, use he folloing equaion for he ube-side flo passage area. a πd i /4 (3) For Laminar flo, 1/ 3 hd d Re.Pr φ (6) u k L For Transision flo, /3 hd /3 1/ d u 0.116(Re 15) Pr φ 1+ (7) k L For Turbulen flo, hd / u 0.03 Re.Pr φ (8) k The crierion of disinguishing beeen laminar and urbulen flo is he observed mixing acion. ussel number (u) is a funcion of Reynolds number (Re) and Prandl number (Pr). u of he flo inside ube can hen be calculaed by above Reynold number equaion. Tube-Side Hea Transfer Coefficien is also calculaed by above Reynold number equaion [7].. Calculaion of Shell-side Hea Transfer Coefficien The sream analysis shell-side hea ransfer coefficien for single-phase flo h as (α ss ) is used by folloing equaion. α ss (J C J L J B J R J S Jµ ) α 1 (9) In his expression, α 1 is he ideal ube bank hea ransfer coefficien calculaed for all he flo across he ube bundle and J C, J L, J B, J R and J S are he correcion facor. J C is calculaed by using (10). J C F C (10) F C 1-F W (11) In his equaion, he fracion of he cross-secional area occupied by he indo (F ) is calculaed from (1). θcl Sin θcl FW - (1) 360 π For a ell-designed uni, J C ypically ranges in value from 0.65 o The maximum value of Baffle leakage correcion J L is 1.0. To calculae J L, (13) is used. J L 0.44(1-r s )+[1-0.44(1-r s )]exp(-.r lm ) (13) From his equaion r s and r lm are calculaed from 14 and 15. Ssb r s (14) S + S sb Ssb + S rlm b Sm Afer ha, J L is calculaed. b (15) a f [ (l f n f ) + ( π d f x 3/ ) ] f (4) a n a -a f (5) Where, a is ube cross flo area, a f is ip area of plae fin, a n is he ne flo area for one ube. To calculae ube-side flo passage area for one pass, a n is muliplied by /one pass. And hen, calculae ube side mass flo rae G 1. Afer ha, Reynold number of he flo inside ube can hen be calculaed by he folloing equaions. Fig. 5 Single-segmenal Shell and Tube Hea Exchanger Shoing Baffle Spacing [8] 606

4 World Academy of Science, Engineering and Technology 008 Fig. 6 Tube Lengh Definiion for U-Tube [8] Fig. 5 depics a single-segmenal shell-and-ube bundle geomery ih fixed ube shees a boh heads in hich he shell-side flo makes one shell pass from one end of he ube bundle o he oher ih he flo direced across he ube bundle by he baffles. The inle, cenral and oule baffle spacing are shon and are idenifies as L bi, L bc and L bo, respecively. By changing b, baffle spacings L bi, L bc, L bo are change. L bi and L bo, are ofen equal in lengh o L bc, expec hen he firs and las baffle comparmens mus be enlarged o allo for he placemen of he respecive shell-side nozzles. The baffle layou is deermined from he inle, cenral, and oule baffle spacing and he effecive ube lengh. The effecive ube lengh L a is equal o he oal ube lengh less he combined hickness of he o ube shees. The number of baffles (an ineger) and baffle spacing can be deermined from hese values. The effecive lengh for deermining he baffle spacing for U-ube exchanger includes he sraigh lengh of he ube plus D s /, here D s is he shell inernal diameer. Thus he baffle spacing a he U-Bend, shon in Fig.6, should include he ube sraigh lengh in his comparmen plus (D s /) or 0.3 D ol [8]. By using he folloing Equaion, baffle spacing are calculaed. L bi {1.5/ b +1} (16) L bo L bi D ol (17) L bc {1.5-L bi }/{ b -1} (18) The maximum limi of Bundle by pass correcion facor J B is 1.0 a r ss ½. To calculae J B, use F sbp. J exp[-c F (1-3 r B bh sbp ss (19) The empirical facor C bh 1.35 for laminar flo (100 Re) and C bh 1.5 for ransiion and urbulen flos (Re>100). To evaluae his expression, one requires he raio of he bypass o he cross flo area F sbp, and he raio r ss of he number of sealing srips ss (number of pairs if any) passed by he flo o he number of ube ros crossed beeen baffle ips in one baffle secion cc. To calculae F sbp, use he folloing equaion. Sb F sbp (0) S m S b L bc [(D s -D ol )+L pl ] (1) In above expressions, S b is he bypass area; L pp represens he idh of he bypass lane beeen ubes. For siuaions ihou a pass pariion lane or for such a lane normal o he flo direcion, se L pl 0 hile for a pass pariion lane parallel )] o he flo direcion L pl is equal o ½ he acual dimension of he lane or can be assumed o be equal o a ube diameer D. ss r ss () cc Ds Bc cc 1 (3) Lpp 100 Where L pp 0.866L p for a 30 layou, L pp L p for a 90 layou and L pp 0.707L p for a 45 layou. This expression has a maximum limi of J B 1 a r ss 1/ [8]. The unequal baffle spacing correcion facor J S accouns for he adverse effec of an inle baffle spacing L bi and/or oule baffle spacing L bo larger han he cenral baffle spacing L bc. Some exchangers have larger baffle spacing in he inle and oule nozzle comparmens compared o he cenral baffle spacing, alloing placemen of he shell-side nozzles ihou inerference ih he body flanges and ihou overlapping he firs baffle. The flo velociy in hese comparmens is hus loered and has an adverse influence on hea ransfer. The correcion facor J S <1.0 for larger inle and oule spacing han he cenral baffle spacing. For inle and oule baffle spacing equal o he cenral baffle spacing, no correcion is required and J S 1.0. The value for J S is deermined direcly from he effec on he flo velociy and is given by he folloing expression. (b -1) + (Lbi/Lbc ) Js ( -1) + (L /L b bi bc + (Lbo/L ) + (L /L 1-n bo bc ) ) 1-n bc (4) Where n0.6 for urbulen flo and n1/3 for laminar flo. The number of baffle comparmens b is deermined from he effecive ube lengh and he baffle spacing [6]-[8]. In laminar flos, hea ransfer is reduced by he adverse emperaure gradien formed in he boundary layer as he flo hermally develops along he flo channel. The laminar flo correcion facor J R accouns for his effec. For laminar shellside flo J R <1.0 (i.e. for 100 Re) hile for Re>100, no correcion is needed and J R 1.0. J R (J R ) 0 10 c 0.18 (For0 Re) (5) c ( cc + c )( b +1) (6) Where c is he oal number of ube ros crossed by he flo in he enire hea exchanger and c is he number of ube ros crossed in he indo area. For Re>0 bu Re>100, he value is proraed in (7). The minimum value of J R in all cases is Re J R (J R ) 0 + [( J R) 1] (7) 0 80 For laminar shell-side flo J R <1.0 hile for Re>100, no correcion is needed. The correcion facor J µ is greaer han 1.0 for heaing he shell-side fluid and vice-versa for cooling he shell-side fluid. 607

5 World Academy of Science, Engineering and Technology 008 To calculae ideal ube bank hea ransfer coefficien h s (α 1 ), use he folloing equaion. α j 1 c p m Pr -/3 (8) j1 a1 Lp D a a Re a a Re (9) 3 (30) a 4 For hea load check, he overall hea ransfer coefficien, U, can be achieved from (31). 1 (31) Uo r o 1 1 r o r o 1 1 ln r i hi h + si k r i hso h o In his equaion, fouling resisance (facor) associaed ih fluid ouside ube R fo (1/h so ) and fouling resisance (facor) associaed ih fluid inside ube R fi (1/h si ). K is all hermal conduciviy. And hen, calculae overall hea ransfer coefficien. The hea ransfer area A is calculaed by he folloing equaion. πd f x3 A ( π dol1) + nlf + L1 (3) In his equaion, nex erm is represened for inser plae hea ransfer area. F T is he correcion facor. Log Mean Temperaure Difference is calculaed by folloing equaion [7]. T T1 T m T lm (33) T ln T1 Where, T T ho T co subscrip i inle T 1 T hi T ci subscripo oule The hea load is compued from (34) and comparing ih given hea load. q U A F T T lm (34) If he calculaed hea load is greaer han he given hea load, i can be said ha he design is saisfied. If no, by increasing T, he oal number of ubes, and he hole procedure may be repeaed ill he above condiion is saisfied. C. Calculaion and Checking of Pressure Drop Design procedures of Pressure Drop check for shell and ube side are as shon in Fig.7. The pressure drop for ube side is compued from he summaion of (35) and (36) and comparing ih alloable pressure drop. For he nozzle losses, i is usually sufficien o calculae he loss for each nozzle a abou hree imes he velociy head in he nozzle [1]. ρvnoz p noz 3 (35) gc Where, v noz is calculaed a he smalles cross-secion area for flo (i.e. highes velociy) in he nozzle. The combined header and ube enrance losses are esimaed in a similar ay, bu using he velociy inside he ube, V i. Fig. 7 Flo Char for Pressure Drop on Shell and Tube Side ρv i P en 3 (36) gc The pressure drop for shell-side flo is equal o he sum of he inle nozzle pressure drop, he bundle pressure drop and he oule pressure drop. The inle and oule nozzle pressure drops can be approximaed as being equal o o velociy heads each. The bundle pressure drop is equal o he sum of he crossflo pressure drops p c, he indo pressure drops p, and he o end zone pressure drops (firs and las baffle comparmens) p e as illusraed in Fig. 8 [6]-[8]. So, he bundle pressure drop for shell side is compued from using (37) and comparing ih alloable pressure drop. p oal p c + p + p e (37) p c p bl ( b -1) R B R L (38) 608

6 World Academy of Science, Engineering and Technology 008 p bl 0.00 f 1 cc m /ρ R µ (39) 1.33 b 1 b Re (40) 1 Lp/D f b n n L L R bc + bc (49) s L L bo bi p e is he pressure drop in he o end zones of he ube bundle and R s is he pressure drop correcion for unequal baffle spacing a he inle and/or oule ih respec o he cenral baffle spacing. For all baffle spacing of equal lengh, R s is.0. n is 1 for laminar flo and n is 0. for urbulen flo [6]-[8]. V. CASE STUDY A ransmission oil cooler is designed according o he MaLAB program discussed above. Fig. 8 Pressure Drop Regions in Shell-side Flo [8] b Re 3 b (41) b 4 R µ -m µ (4) µ R exp[-c F (1-3 r B bp sbp ss (43) p [ ] R (44) L exp -1.33(1+ rs )rlm P -0.15(1+r s ) (45) Where p bl is he ideal bundle pressure drop for one baffle comparmen of he b comparmens. f 1 is he fricion facor and he empirical consans. R µ is he viscosiy correcion facor and R B is he bypass correcion facor. The limi of R B is 1 for r ss 1/. Use C bp is 4.5 for laminar flo (100 Re) and C bh is 3.7 for ransiion and urbulen flos (Re>100). R L is he leakage correcion facor. S M mɺ (46) m S 0.001mɺ p b ( c) R LR (47) µ ρ Where M is he shell-side flo rae in kg/s and p and m are he pressure drop and mass velociy in all b indo zones for urbulen flo (Re>100). p p 1 + R R )] c e (48) bl B S cc TABLE I IPUT DATA FOR TRASMISSIO OIL COOLER FOR DIESEL HYDRAULIC LOCOMOTIVE Tube side Shell side Fluid Hydraulic aer oil Inle Temperaure ( C) Oule Temperaure ( C) Flo rae (m 3 /hr) Hea load 8 8 (kw) Pressure drop (bar) Max orking pressure (bar) 15 The folloing figures are obained by using he MaLAB Program. Reynolds umber in Tube umber of Tube Fig. 9 A fac of Reynolds umber on umber of Tubes 609

7 World Academy of Science, Engineering and Technology 008 Hea Transfer Coefficien in Tube (W/m K) umber of Tube Fig. 10 A fac of Hea Transfer Coefficien on umber of Tube I can be seen ha in Fig. 9 and Fig. 10 shos ha he Re and h o are gradually decreased corresponding o as high as. Because of mass flo rae are consan, velociy are increase and Re, h o are also decrease. Beeen oal number of ube 0 and 40, here are a sligh rise in hea ransfer coefficien because of changing from urbulen flo o ransiion flo. Reynolds umber in Shell b b3 b Tube Lengh (mm) Fig. 11 A fac of Reynolds umber on umber of Baffles and Lengh of Tube The decreasing paern of curves of Reynold umber and hea ransfer coefficien shon in Fig. 11 and Fig. 1 shos ha he Re and h are gradually decreased corresponding as high as Tube Effecive Lengh (L 1 ). Hoever, his graph also describes, due o umber of Baffles increase, Reynold umber increase. The resul able for Hea Load is shon in Fig. 13. Beeen shell diameer 30m and 330m, here are also a sligh rise in hea ransfer coefficien because of changing from urbulen flo o ransiion flo. Hea Transfer Coefficien in Shell (W/m K) b b3 b Lengh of Tube (mm) Fig. 1 A fac of Hea Transfer Coefficien on umber of Baffles and Lengh of Tube Hea Load (kw) b b3 b Shell Diameer (mm) Fig. 13 A fac of Hea Load on Shell Diameer TABLE II COMPARISO WITH IDUSTRIAL DATA Resul Indusrial Daa Calculaed Daa Shell diameer, m Tube lengh, m Toal no. of ubes Tube diameer, m umber of 4 4 Baffle Hea Load, kw Tube side pressure drop Shell side pressure drop V. DISCUSSIO AD COCLUSIO There are fe limiaions o be considered in program. To reduce size and cos of hea exchanger, U-Bend Exchangers 610

8 World Academy of Science, Engineering and Technology 008 are chosen. The arrangemens of ubes are only for a idely used riangular paern hich permis he use of more ubes. The limiaion of shell diameer is ihin he minimum 0.3 m and maximum 0.4 m. I is sill assumed ha here is no advanage in varying less han he alloable pressure drop and baffles ill be employed ihin he minimum (one fifh of he shell diameer) and maximum (inside diameer of he shell) spacing. These limiaions sem from he fac ha a ider spacing he flo ends o be axial raher han across he bundle and a closer spacing here is excessive leakage beeen baffles and he shell. If he shell side pressure drop is higher han he accepable limis, he baffles spacing is increased slighly, he shell side pressure drop ill be saisfacory. If he ube side pressure is no ihin accepable limis, he calculaion can be repeaed ih a revised value of oal number of ube because of he pressure drop depends on he square of he velociy. There are many ypes hea baffle. Among hem, segmenal baffle is seleced in his design. This ype of baffle is probably he mos popular. I is a circle of near shell diameer from hich a horizonal or verical porion has been cu. The cuou porion hich represens he free flo area for he shell side fluid is usually from 0 o 50 percen of he open shell area. In his design, 5 percen baffle cu is used according o he mehod of Wolverine. The limiaion of number of baffle is, 3 and 4. Shell diameer for calculaed design is nearly he same he exising design. Bu oal numbers of ubes are more han exising design because of ube diameer changes. Furhermore, use simple inser fla plae in ubes. By using of ube insers (fla plae) are highly effecive in laminar flo inside ubes. Tube insers fla plae in exising design is more confused han calculaed fla plae. In his program, ube diameer is limied o 1.7 mm, so his diameer is less han exising ube diameer 14mm. Because of hese facs, increase oal number of ube, hea ransfer area and hea load is more han limied hea load (83. kw). The ube and shell pressure drop for accepable limis is 0.6 and 0.3 bar. The calculaed pressure drop for ube and shell are and bar. The design is saisfied because he pressure drop for boh sides is loer han he limied pressure drop. So his compuer program is highly useful o design he liquid-o-liquid shell and ube ype hea exchanger. REFERECES [1] Frass, A.P and M.ecaic Ozisik, 1965, Hea Exchanger Design, John Wiley and Sons Inc. [] Max S.Peers and Klaus D. Timmerhuaus, 1958, Plan Design and Economics for Chemical Engineers, 4 h ed, McGra-Hill Book Company. [3] TEMA, 1999, Sandards of TEMA, 8 h ed, Turbular Exchanger Manufacurers Associaion, e York. [4] Kays, W.M and A.L.London, 1998, Compac Hea Exchangers, 3 rd ed, Krieger Publishing Malabar, FL. [5] E.A.Krasnoshchekov and A.S.Sukomel, 1977, Problems in Hea Transfer, MIR Publishers, Mosco. [6] Professor John R.Thom, 004, Wolverine Tube Hea Transfer Daa Book III, Wolverine Tube Inc,.Wolverine.com. [7] J.P. Holman, 1963, Hea Transfer, 8 h ed, McGra-Hill Book Company. [8] Dr. K. J. Bell and Dr. A.C.Muller, 1984, Wolverine Tube Hea Transfer Daa Book II, Wolverine Division of UOP Inc,.Wolverine.com. 611