Correlations of Flow Boiling Heat Transfer of R-134a in Minichannels:

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1 ENERGY SCIENCE AND TECHNOLOGY Vo. 1, No. 1, 011 PP ISSN [PRINT] ISSN [ONLINE] FANG Xiande 1,* SHI Rongrong 1 ZHOU Zanru 1 1 Institute of Air Conditioning and Refrigeration, Nanjing University of Aeronautics and Astronautics 9 Yudao St., Nanjing 10016, Cina. * Corresponding autor. Emai: xd_fang@yaoo.com Correations of Fow Boiing Heat Transfer of R-134a in Minicannes: Comparative Study Abstract: R-134a is one of te most widey used refrigerants, and minicanne refrigeration systems wit R-134a ave rapidy deveoped in many fieds, suc as ome, automobie and aircraft air conditioning systems, for ig efficiency operations to save energy and space. A number of correations for fow boiing ear transfer ave been proposed. Tere is some iterature to evauate existing correations for R-134a fow boiing eat transfer in minicannes. However, tey were ony based on te autors own experimenta data. Terefore, resuts are often not consistent, even controversia. Our efforts are devoted to deveop a better fow boiing eat transfer correation for R-134a in minicannes, and tis paper presents te first part of our efforts: A comparative study of existing correations for fow boiing ear transfer of R-134a in minicannes. From 9 pubised papers, 1158 data points of fow boiing eat transfer of R-134a in minicannes are coected. Eigteen fow boiing eat transfer correations, incuding amost a we-known ones, are reviewed and compared wit te data coected. It is found tat no correation as satisfactory accuracy. Te best one as a mean absoute reative deviation above 36%. It is interesting to note tat among te six best correations, one was deveoped for poo boiing and two were deveoped for conventiona cannes, and most of correations deveoped speciay for minicannes do not work quite we. More efforts soud be made to better understand te mecanism of fow boiing eat transfer in minicannes for deveoping better correations. Key words: R-134a; Fow boiing; Heat transfer; Correation; Minicanne Received 6 January 011; accepted 1 February

2 Nomencature Bo boiing number, q/( g G ) We Weber number C Cisom parameter X Martinei parameter Co convective number, (1/x-1) 0.8 ( g / ) x vapor quaity Co f confinement number, [ g( g ) D ] c p specific eat at constant pressure (J/kgK) Greek Symbos c p average specific eat at constant pressure terma expansion coefficient (1/K) (J/kgK) D inner diameter (m) aspect ratio: eigt to widt of canne cross-section D ydrauic diameter (m) terma conductivity (w/mk) F Reynods number factor increment f Moody friction factor canne surface rougness (m) F f fuid-surface parameter dynamic viscosity (Pas) Fr Froude number density (kg/m 3 ) G mass fux (kg/m s) surface tension (N/m) g acceeration due to gravity (m/s ) two-pase friction mutipier Gr Grasof number specific entapy (J/kg); eat transfer coefficient Subscripts (W/m K) g atent eat of vaporization (J/kg) crit critica point L tube engt (m) exp experimenta M moecuar mass, kg/kmo g saturated vapor Nu Nusset number go a fow taken as vapor p pressure (Pa) in canne inet difference in vapor pressure corresponding to saturated iquid p sat T sat P R reduced pressure, p/p crit o a fow taken as iquid Pr Prandt number m average Pr average Prandt number nb nuceate boiing q eat fux from tube wa to fuid (W/m ) out canne outet Re Reynods number pred predicted S suppression factor sat saturated state T temperature (K) sp singe-pase T R reduced temperature, T/T crit two-pase T sat supereat, T w - T sat t turbuent t temperature (C) w at inner wa temperature 1. INTRODUCTION HFC refrigerant R-134a is one of te most widey used refrigerant in many ome, automobie and aircraft air conditioning systems. Wit te increasing demand for energy conservation and space saving, te design of more efficient and compact air conditioning systems is increasingy important, resuting in wide appications of minicanne evaporators not ony in ig-tec sects suc as aeronautica and aerospace fieds, but aso in conventiona industries. Consequenty, fow boiing eat transfer in minicannes as received considerabe investigations in te ast 0 years and is sti an intense researc spot. A number of correations for fow boiing ear transfer ave been proposed, among wic most are empiricay formuated from data anaysis. However, fow boiing eat transfer of R-134a in minicannes remains a probem unsoved and controversia opinions are not uncommon. Unike fow in conventiona cannes, te mecanism of R-134a fowing in minicannes is sti not very cear. Kaew-On et a. (011) presented te experimenta resuts of fow boiing eat transfer caracteristics of R-134a in te muti-port minicanne eat excangers of te interna ydrauic diameter of 1.1 mm and 1. mm, respectivey. Te experimenta ranges are te eat fux of kw/m, mass fux of kg/m, and saturation pressure of 4-6 bar. Tey found tat te fow boiing regime corresponded to nuceate boiing, and tus te average eat

3 transfer coefficients increase wit increasing eat fux wie being independent of te vapor quaity and mass fux. Saisorn et a. (010) investigated experimentay fow boiing eat transfer of R-134a in a circuar mini-canne of 600 mm ong and 1.75 mm inner diameter (ID) in te range of te mass fux of kg/m s, eat fux of 1-83 kw/m, and saturation pressures of 8, 10, and 13 bar. Tey obtained te simiar findings wit tose of Kaew-On et a. (011). Siferaw et a. (007, 009) conducted R-134a fow boiing eat transfer experiments wit stainess stee tubes of 4.6 mm,.01 mm, and 1.1 mm ID in te parameter ranges of te mass fux of kg/m s, eat fux of kw/m, pressure of 6-1 bar, and vapor quaity up to 0.9, Tey found tat te oca eat transfer coefficient increased wit te eat fux and system pressure, but was independent of vapor quaity wen tis was ess tan about 40-50% in te 4.6 mm tube, 0-30% in te.01 mm tube, and about 50% in te 1.1 mm tube, wic coud be interpreted tat at ow quaity te fow boiing is dominated by nuceate boiing. Loca transient dryout was deduced wen te quaity was above tese vaues. Te effect of mass fux was observed to be insignificant. In and Jeong (009) investigated fow boiing eat transfer of R-134a in a singe circuar micro-canne of 0.19 mm ID under experimenta conditions of te eat fux of 10-0 kw/m, mass fux of kg/m s, saturation pressure of 9-11 bar, and vapor quaity of Tey found tat nuceate boiing was dominant eat transfer mecanism unti its suppression at ig vapor quaity and ten two-pase forced convection eat transfer became dominant. Bertsc et a. (008, 009a, 009b) investigated fow boiing eat transfer wit R-134a in muti-port rectanguar microcannes of ydrauic diameter of 1.09 and 4 mm. Te measured parameter ranges are te eat fux of 0-0 kw/m, mass fux of kg/m s, saturation temperature of 8-30 C and vapor quaity of Tey found tat nuceate boiing dominated te eat transfer, and tat eat transfer coefficients varied significanty wit eat fux and vapor quaity. Besides, tey observed tat for te 1.09 mm cannes te eat transfer coefficient first rose steepy as vapor quaity increased from a subcooed vaue, and ten dropped sarpy wit furter increases in vapor quaity, wit a peak at a vapor quaity of 0.. Findings about te effect of mass fux on eat transfer coefficient are not consistent. Bertsc et a. (008) first reported tat te eat transfer coefficient increased strongy wit increasing mass fux, but ater tey (Bertsc et a., 009b) found tat te eat transfer coefficient varied ony sigty wit mass fux. Saito et a. (007) presented te experimenta resuts of te eat transfer of R-134a fowing troug cannes wit tree different diameters of 1, 1.1, and 3.1 mm. Tey found tat te eat transfer coefficient for te 3.1 mm cannes depended upon bot eat fux and mass fux, wie te eat transfer coefficient for te 1 mm cannes increased wit increasing eat fux but was not significanty affected by mass fux. Moreover, for te sma cannes, te infuence of surface tension became a more important parameter wic resuted in te occurrence of dryout at ower quaity. Yan and Lin (1998) conducted experiments on fow boiing eat transfer coefficients and pressure drops of R-134a in a muti-port circuar tube wit an inner diameter of mm and a engt of 00 mm. Tey found tat for a iger eat fux, te eat transfer coefficient was iger except in te ig vapor quaity region and was ower in te ig vapor quaity region for a ig eat fux. At a ow eat fux, te eat transfer significanty increased for a sma rise in te mass fux, but at a iger eat fux te increase in te eat transfer coud be sigt and even reduced. Agostini and Bontemps (005) performed an experimenta study of upfow boiing of R-134a in vertica mini-cannes of a fat extruded muti-port tube composed of 11 parae rectanguar cannes (3.8 mm 1.47 mm) wit a ydrauic diameter of.01mm in te range of te mass fux of kg/m s, eat fux of kW/m, working pressure of 4 and 6 bar, and inet subcooing from 1 to 17K. Nuceate boiing was found to 3

4 be te dominant mecanism for q > 14kW/m and T sat > 3K. Te transition from nuceate boiing to supposed convective boiing occurred for Bo(1- x) regardess of te eat and mass fuxes. A investigations above ave one ting in common: Minicannes enance eat transfer compared wit conventiona cannes. Yan and Lins resuts indicate tat te eat transfer coefficients in sma tubes are iger tan tose of conventiona tubes by around 30 80%. Te effect of te saturated pressure on eat transfer is aso ess controversia: Te eat transfer coefficient is eiter iger at a iger saturated pressure (Saisorn et a., 010; Siferaw et a., 007, 009; Yan & Lin, 1998) or sigty varies wit te saturated pressure (Bertsc et a. 008, 009). A number of correations are proposed for fow boiing eat transfer. Bertsc et a. (009b) compared te measurements wit predictions from severa correations (Bennett & Cen, 1980; Bennett et a., 1980; Cooper, 1984; Gorenfo, 1993; Haynes & Fetcer, 003; Kandikar & Baasubramanian, 004; Lazarek & Back, 198; Lee & Lee, 001; Lee & Mudawar, 005; Liu & Winterton, 1991; Saito et a., 007; Sa, 198; Sumit et a., 003; Tome et a., 004; Tran et a., 1996; Yun et a., 006; Zang et a., 005; Warrier et a., 00). Tey found tat te correations wic deivered te owest errors were tat of Cooper (1984) deveoped for poo boiing and tose of Liu-Winterton (1991) and Tran et a. (1996) deveoped for conventiona cannes, and tat equations deveoped specificay for sma cannes did not predict te eat transfer coefficient better. Siferaw et a. (007, 009) compared severa existing correations (Kandikar & Baasubramanian, 004; Tome et a. 004; Zang et a., 004) wit teir experimenta data. Tey concuded tat te existing correations did not predict teir sma-diameter data to a satisfactory degree, and tat te tree-zone evaporation mode based on Tome et a. (004) sowed a better agreement, but it did not predict te effect of diameter and te partia dryout. Kaew-On et a. (011) compared te experimenta data wit severa existing correations (Cen, 1963; Kaew-On & Wongwises, 009; Kaew-On et a., 010; Kenning & Cooper, 1984; Kew & Cornwe, 1997; Lazarek & Back, 198; Maek & Coin, 1983; Tran et a., 1996; Warrier et a., 00; Yu et a., 00). Tey found tat te correations of Lazarek and Back, Maek and Coin, Kew and Cornwe, Yu et a., Kaew-On and Wongwises, and Kaew-On et a. sowed better agreement wit te experimenta data, but none ad a mean deviation ower tan 0%. Saisorn et a. (010) made a comparison of teir data wit correations of Cen (1963), Trant et a. (1996), Kandikar and Baasubramanian (004), and Coi et a. (007), and reported tat none of tem predicted we. Sun and Misima (009) compared correations of Cen (1963), Liu-Winterton (1991), Zang et a. (004), Saito et a. (005), Lazarek-Back (198), Kew Cornwe (1997), Kandikar (1990), Tran et a. (1996), Yu et a. (00), Warrier et a. (00), Kenning-Cooper (1989), Pamitran et a. (007), Cooper (1984), and Sun-Misima (009) wit a database incuding 505 data for 11 iquids covering diameter from 0.1 to 6.05 mm. Te resuts sow tat te Cen metod and te Cen-type correations are not suitabe for mini-cannes very muc, and tat te correations of Sun-Misima, Lazarek-Back, and Kew-Cornwe are te best tree metods, but none of tem as te mean absoute error ess tan 30.8%. From te brief review above, it is ceary seen tat fow boiing eat transfer of R-134a in minicanes needs more researc efforts, and tat satisfactory correations remain a probem. Te existing examinations of te correations for R-134a fow boiing eat transfer are ony based on te autor(s) own experimenta data, and tus it is predictabe tat te evauation resuts differ from one anoter, toug none found a compete satisfactory correation. Our effort is devoted to deveop a better fow boiing eat transfer correation for R-134a in minicannes. Tis paper presents te first part of te effort, wic incudes reviewing te existing correations for fow boiing eat transfer, coecting fow boiing eat transfer experimenta data of R-134a in minicannes, and conducting a compreensive evauation of te existing correations against te data bank. 4

5 . REVIEW OF FLOW BOILING HEAT TRANSFER COEFFICIENTS.1 Cen (1963) Correation By using te additive concept tat suggests tat te nuceate boiing and forced convection associated wit fow boiing eat transfer coud be added, Cen (1963) introduced two dimensioness factors, te suppression factor S tat accounts for te smaer effective supereat due to forced convection as compared to tat in a poo boiing case and te Reynods number factor F tat refects te increase in convective turbuence due to te presence of vapor pase. He proposed te foowing correation for fow boiing eat transfer coefficient of te turbuent regime (Zang et a. 004): = S F (1a) nb sp (1/ X tt 0.13) if 1/ X tt 0.1 F (1b) 1 if 1/ X tt S 1/( Re ) (1c) X tt 1 x x 0.9 g g 0.1 () ( 1 x) GD Re (3) nb c p, T sat psat g g (4) sp = 0.03Re Pr / D (5) Te Cen equation was found to work we for ow-pressure steam and some ydrocarbons and is taken as a bencmark in te iterature. Te appicabe range of vapor quaity of te Cen equation is Zang et a. (004) Correation In order to extend te Cen (1963) correation to minicannes and aminar regime, Zang et a. (004) modified te Cen correation wit te and nb remaining te same forms as Eq. (1a) and Eq. (4), respectivey, and S, F and sp isted in Tab. 1. Its appicabe range of vapor quaity is Tab. 1: Summary of S, F and sp in te Zang et a. (004) correation S S 1/( Re ) F ' C 1 F max F,1, F' 0.64, 1 X X 5 If Re 1000 and Reg 1000 C 10 If Re 000 and Reg if Re 1000 and Reg 000 C 0 if Re 000 and Reg 000 For oter regions of Re k, (k = or g), interpoate te above vaues of C. 1 f x g X f g x To be continued 5

6 Continued Tab. 1: Summary of S, F and sp in te Zang et a. (004) correation Wit te subscript k denoting eiter or g, te Moody friction factor is of te form 64 Rek for circuar canne and Re 1000 fk 96B Rek for rectanguar canne and Re Rek for Re B For 1000 Re k 000, interpoate te above vaues of f k. sp maxnusp,am, NuCoier for Re 000in verticacanne D sp maxnusp,am, Nusp,t for Re 300in orizaonta canne D Nusp,t for Re 300 bot in verticaand orizontacanne D 000 < Re < 300, interpoate te vaues of sp for vertica fow at Re = 000 and Re = Pr Coier 0.17 g Tw T D Nu = Re Pr Prw sp, t 0. 03Re Pr Nu = Nu sp,am =4.36 Nu sp, am for circuar canne = for rectanguar canne.3 Gungor-Winterton (1987) Correation For vertica fow at Compied from a database of over 3600 data points, incuding data for R-11, R-1, R-, R-113, R-114, and water, Gungor and Winterton (1987) proposed (ASHRAE 009) were sp is cacuated wit Eq.(5), = ) (6a) ( SS FF sp 0.86 S= Bo (6b) x F x 0.75 g 0.41 (6c) S (0.1Fro ) Fr if orizonta and o Fr 1 oterwise o 0.05 (6d) 1/ ) Fr o if orizonta and Fr 0.05 F o (6e) 1 oterwise Bo= q /( G g ) (7) Fr o G (8) gd Te Gungor-Winterton correation is appicabe to bot orizonta and vertica fows. 6

7 .4 Cooper (1984) Correation Cooper proposed te foowing correation for nuceate boiing eat transfer. Some iterature suggested it appy to fow boiing n R 5 R = 55P ( n P ) M q (9) nb Bertsc et a. Equation (009) Bertsc et a. (009) deveoped a composite correation for fow boiing eat transfer in minicannes from a database of 3899 data points covering 1 different wetting and non-wetting fuids, wit ydrauic diameters ranging from 0.16 to.9 mm and confinement numbers from 0.3 to 4.0. Te parameter ranges cover te mass fux of kg/m s, eat fux of kw/m, saturation temperature of C, and vapor quaity of 0-1. Te Bertsc et a. correation foowed te basic form of te Cen (1963) correation and is of te form nb 6 0.6Co f = (1 x) [1 80( x x ) e ] (10a) sp xsp, go ( 1 x) sp, o sp (10b) sp, ko RekoPrk D L k 3.66 (10c) / RekoPrk D L D were nb is cacuated wit te Cooper poo boiing equation (9), te subscript k denotes g or, and te surface rougness (according to DIN 476) soud be set equa to 1 m if unknown. Te confinement number Co f, te gas-ony Reynods number Re go, and te iquid-ony Reynods number Re o are defined as, respectivey Co f (11) g ( g ) D Re go GD g GD and Reo (1).6 Kandikar (1990) Correation Kandikar (1990) utiized te singe-pase, iquid-ony eat transfer coefficient to predict te nuceate boiing and convective boiing components of turbuent regime as given by te foowing equation (ASHRAE 009; Kandikar and Baasubramanian, 004): arger of, nb, cb (13a) = (13b) o , nb [ Co f ( Fro) Bo Ff ](1- x) , cb [ 1.136Co f ( Fro ) 667.Bo Ff ](1- x) = (13c) o 1 for Fro 0.04 f ( Fro ) = 0. 3 (13d) (5Fro ) for Fro x g Co= (14) x 7

8 o ( f/8) ReoPr ( / D) 1/ 11.7( f/8) ( Pr 1) /3 for 10 4 Re o (15) o ( f/8)( Reo 1000) Pr ( / D) 1/ 11.7( f/8) ( Pr 1) /3 for 3000 Re o 10 4 (16) - f (0.79n Re -1.64) (17) o Te vaues of te fuid-surface parameter, F f, are recommended in Tab.. Tab. : Recommended F f vaues in Kandikars fow boiing correation Fuid F f Fuid F f Water 1.00 R-134a 1.63 R R-15a 1.10 R R-31/R R-13B R141b 1.80 R-.0 R R Kerosene R F f = 1 for stainess stee tubes for a fuids..7 Kandikar-Baasubramanian (004) Correation Kandikar and Baasubramanian (004) extended te above Kandikar correation to aminar fow and mini- and micro-cannes. Te fow regions are cassified as turbuent region (Re LO 3000), transition region (1600 Re LO < 3000) and aminar region (Re LO < 1600). Tey considered te effect of tube orientation for fow boiing in sma diameter tubes negigibe, and tus deeted te Froude number effect in te above correation by setting f (Fr o ) = 1. As a resut, it foows tat = (18a) o , nb [ Co Bo Ff ](1- x) , cb [ 1.136Co 667.Bo Ff ](1- x) = (18b) were o is constant for te aminar region, o is cacuated wit Eq. (15) for te turbuent region and determined by inear interpoation in te transition region, and F f vaues are isted in Tab.. Te appicabe vapor quaity range is x <0.7~0.8.8 Yan-Lin (1998) Correation o C C4 0.8 ( C1 Co C3Bo Fro )(1 xm ) = (19a) were is assumed to be equa to /D. Te empirica constants C 1, C, C 3 and C 4 are assumed to be functions of te a iquid Reynods number Re o and reduced temperature T R. Tey can be expressed as m m,1 Cm, C m,3 o TR C = C Re (19b) were m = 1,, 3 and 4. Te best fitting vaues for te constants C m,1, C m, and C m,3 are isted in Tab. 3. 8

9 .9 Sa (198) Correation Tab. 3: Vaues of te constants in Yan-Lin correation m Co > < Co Co 0.15 C m,1 C m, C m,3 C m,1 C m, C m,3 C m,1 C m, C m, Sa (198) proposed tat te boiing eat transfer coefficient is te argest of tat given by te foowing equations: = 30Bo o (0a) 0.3 n 0.8 = 1.8[ Co(0.38Fr o ) ] o (0b) 0.3 n 0.15 F exp{.47[ Co(0.38Fr o ) ] } o = (0c) 0.3 n 0.1 F exp{.74[ Co(0.38Fr o ) ] } o = (0d) were o is cacuated as for te Kandikar (1990) correation, and 14.7Bo if Bo F (0e) 15.4Bo if Bo if orizonta wit Fro 0.04 or vertica n (0f) 1 if orizonta wit Fro Lazarek-Back (198) Correation Lazarek and Back (199) proposed a simpe fow boiing eat transfer correation based upon 738 experimenta data of R113 in a 3.15 mm ID tube = 30Reo Bo (1) D.11 Sun-Misima (009) Correation Based on te Lazarek Back correation and by introducing Weber number, Sun and Misima (009) proposed Reo Bo = () We ( / g ) D were te Weber number for iquid pase is defined as: G D We= (3).1 Kew-Cornwe (1997) Correation Kew and Cornwe modified te Lazarek Back equation to aow for an observed increase in te eat transfer coefficient wit te vapor quaity in arger tubes = 30Reo Bo (4) 1 x D

10 .13 Tran et a. (1996) Correation Tran et a. (1996) conducted fow boiing eat transfer experiments for R1 in sma cannes and proposed ,000Bo We 0.4 g = ( / ) (5).14 Yu et a. (00) Yu et a. (00) modified te Tran et a. correation. Te correation proposed in te paper is = 6,400,000Bo We ( / ) 0. g However, our assessment sows tat te above Yu form as far arge predictions. It migt be of te form ,000Bo We 0. g = ( / ) (6) Te Eq. (6) is used for te comparative study of tis paper..15 Warrier et a. (00) Correation Warrier et a. conducted experiments of bot singe-pase forced convection and subcooed and saturated nuceate boiing in sma rectanguar cannes using FC-84 and deveoped te foowing saturated fow boiing eat transfer correation: 1/ [1 6Bo 5.3(1 855Bo) x sp = ] (7) were sp is cacuated wit Eq. (5)..16 Kaew-On et a. (011) Kaew-On et a. modified te Kaew-On and Wongwises (009) correation and proposed = SBo We (8a) sp ( ) 3 S= (8b) C 1 =1 (8c) X X A C= e B (8d) A= f D (8e) B= 14.5f D (8f) X f f g 1 x g x (9) were te Moody friction factor, f, is cacuated wit te Haaand (1983) correation (Fang et a., 011) 1 f k 1.11 ( / D ) Re ] 1.8og[ (30) k were k denotes eiter or g, sp is cacuated wit Eq. (5)..17 Liu-Winterton (1991) Correation Liu and Winterton proposed te foowing equation for subcooed and saturated fow boiing: 10

11 ( Snb) ( Fsp = ) (31a) F xpr 1 g (31b) S= 1 ( F 0 Re ) (31c) were sp is given by te Dittus-Boeter correation, Eq. (5), nb is cacuated wit te Cooper (1984) poo boiing correation Eq. (9)..18 Kenning-Cooper (1989) Correation Kenning and Cooper pointed out tat te saturated fow boiing eat transfer coefficient depends primariy on oca parameters in te annuar fow regime and can be of te form 0.87 tt = (1 1.8X ) (3) sp were X tt is given by Eq. () and sp is given by Eq. (5)..19 Tome et a (004) Tome et a. proposed a tree-zone fow boiing mode to describe evaporation of eongated bubbes in microcannes, wic describes te transient variation in oca eat transfer coefficient during te sequentia and cycic passage of (a) a iquid sug, (b) an evaporating eongated bubbe and (c) a vapor sug. However, tis mode needs estimation of fow parameters, wic makes it difficut to be used. Besides, it does not predict te effect of diameter and te partia dryout (Siferaw et a., 007, 009). Hence, tis paper wi not introduce it in detai. 3. THE AVAILABLE EXPERIMENTAL DATA FOR FLOW BOILING HEAT TRANSFER OF R-134A IN MINICHANNELS Te 1158 experimenta data of fow boiing eat transfer of R-134a in minicannes from 9 papers (Tab. 4) are coected. A data were presented grapicay in te source papers. Tab. 4: Experimenta data sources of fow boiing eat transfer of R-134a in minicannes Reference Agostini and Bontemps (005) Bertsc et a. (009a, 009b) In and Jeong (009) Kaew-On et a. (011) Saisorn et a. (010) Siferaw et a. (007, 009) Yan and Lin (1998) Parameter range: T sat (C)/p sat (bar)/g(kg/m s)/ q(kw/m )/x Geometry range: D(mm)/L(mm)/(m)/Heigt(mm)/ Widt(mm)/Orientation and tube type Number of data points 54 */4-6/90-95/6-31.6/ /1100 /<1/3.8/1.47/Vertica upfow, muti-port rectanguar auminium tube 8.7-9/4-7.5/4-334/ / /9.53/</0.953/0.381/Horizonta muti-port 96 rectanguar copper tube. */11/ /10-0/ 0.19/31/*/*/*/Horizonta singe circuar stainess stee tube */4-6/ / 1.1/0 /*/1.5/1/; 1./0 /*/0.9/1.8/ /From A orizonta muti-port rectanguar auminium tube. */8-13/ / 1.75/600/*/*/*/Horizonta singe circuar stainess stee tube / /6-1/ 4.6/600/1.75/*/*/;.01/600/1.8/*/*/; /13-150/Up to /600/1.8/*/*/ 5-31/*/50-100/5-0/ A are orizonta singe circuar stainess stee tubes /00 /*/*/*/Horizonta muti-port circuar stainess stee tube * Not avaiabe or not appicabe. Te effect of te tube engt on te eat transfer of entrance section soud be considered

12 4. COMPARATIVE STUDY OF THE EXISTING CORRELATIONS AGAINST THE EXPERIMENTAL DATA Te 1158 experimenta data as indicated in Tab. 4 are used for te comparative study of te 18 eat transfer correations as described above, and te resuts are isted in Tab. 5, were te MRD is te mean reative deviation and te MARD is te mean absoute reative deviation. N 1 y( i) ca y( i) N 1 y( i) i 1 exp exp MRD (33) N 1 y( i) ca y( i) exp MARD N (34) 1 y( i) i Were yca is te cacuated vaue, yexp is te experimenta vaue, and N is te number of te data points. Tab. 5: Comparison between experimenta data and correation predictions Correations Data Errors Zang Gungor- Bertsc Kandiker ramanian Lin Kandikar-Baasub- Yansources % Cen Cooper Sa et a. Winterton et a Agostini and MRD Bontemps MARD Bertsc et a. MRD (009) MARD In and Jeong MRD MARD Kaew-On et MRD a. MARD Saisorn et a. MRD MARD Siferawa, et MRD a. MARD Yan and Lin MRD MARD Average MRD MARD * Data out of te appicabe conditions of te correation. Tab. 5: Comparison between experimenta data and correation predictions Data sources Errors Correations % Lazarek- Back Sun- Misima Kew- Cornwe Tran et a. Yu et a. Warrier et a. Kaew-On Liu- Winterton Kenning- Cooper Agostini and MRD Bontemps MARD Bertsc et a. MRD (009) MARD In and Jeong MRD MARD Kaew-On et MRD a. MARD Saisorn et a. MRD MARD Siferawa, et MRD a. MARD Yan and Lin MRD MARD Average MRD MARD From Tab. 5, te foowing can be seen: (1) None of te described correations predicts we. Te smaest MARD is greater tan 36%. Terefore, more work soud be done to generate better correations for fow boiing eat transfer of R-134a in minicannes. exp

13 () Te Gungor-Winterton (1987) correation performs best, wit a MRD of -5.4% and a MARD of 36.6%. Te correations of Sun & Misima (009), Tran et a. (1996), Cooper (1984), Bertsc et a (009), and Lazarek and Back (198) are te next five best ones, wit te MARD of 39.1%, 44.%, 44.3%, 44.7, and 45.1%, respectivey. (3) Te Cen-type correations, wic adopted te additive concept, generay do not work we, and te best correations generay ave simpe forms, except for te Bertsc et a (009) correation. 5. CONCLUSIONS (1) Te 18 correations for fow boiing eat transfer are reviewed, and 1158 data points of fow boiing eat transfer of R-134a in minicannes are coected from 9 pubised papers. Te correations are evauated against te coected data. () Among te 18 evauated correations, te smaest MARD is greater tan 36%, wic means tat tey can not predict experimenta data we, and tus te fow boiing eat transfer of R-134a in minicannes sti remains a probem. More researc efforts need to be made to better understand te mecanism of fow boiing eat transfer in minicannes to deveop better correations. (3) Te Gungor-Winterton (1987) correation is te best among te 18 evauated correations, and tose of Sun and Misima (009), Tran et a. (1996), Cooper (1984), Bertsc et a (009), and Lazarek and Back (198) are te next five best ones. (4) It is interesting to note tat among te six best correations, te Cooper (1984) correation was deveoped for poo boiing and te Gungor-Winterton (1987) and te Lazarek-Back correations were deveoped for conventiona cannes, and tat five in six of te best correations are in simpe non-additive forms. ACKNOWLEDGMENTS Tis work was funded by AVIC Cengdu Aircraft Design & Researc institute, Cina. REFERENCES [1] Agostini, B., Bontemps, A. (005). Vertica fow boiing of refrigerant R134a in sma cannes. Int. J. Heat and Fuid Fow, 6, [] ASHRAE (009). ASHRAE Handbook: Fundamentas. American society of eating, refrigerating, and air-conditioning engineers, Atanta, USA. [3] Bennett, D.L., Cen, J.C. (1980). Forced convective boiing in vertica tubes for saturated pure components and binary mixtures. AICE J. 6, [4] Bennett, D.L., Davies, M.W., Hertzer, B.L. (1980). Te suppression of saturated nuceate boiing by forced convective fow. American Institute of Cemica Engineers Symposium Series, 76, [5] Bertsc, S.S., Gro, E.A., Garimea, S.V. (008). Refrigerant fow boiing eat transfer in parae microcannes as a function of oca vapor quaity. Int. J. Heat and Mass Transfer, 51, [6] Bertsc, S.S., Gro, E.A., Garimea, S.V. (009a). A composite eat transfer correation for saturated fow boiing in sma cannes. Int. J. Heat and Mass Transfer, 5, [7] Bertsc, S.S., Gro, E.A., Garimea, S.V. (009b). Effects of eat fux, mass fux, vapor quaity, and saturation temperature on fow boiing eat transfer in microcannes. Int. J. Mutipase Fow, 35, [8] Cen, J. C. (1963). A Correation for Boiing Heat Transfer to Saturated Fuid in Convective Fow. ASME Paper, 63-HT-34, [9] Coi K.I., Pamitran, A.S., O, C.Y., O, J.T. (007). Boiing eat transfer of R-, R-134a, And CO in orizonta smoot minicannes. Int. J. Refrigeration, 30 (8), [10] Cooper, M.G. (1984). Heat fow rates in saturated nuceate poo boiing a wide ranging examination 13

14 using reduced properties. Adv. Heat Transfer, 16, [11] Fang, X. D., Xu, Y., Zou, Z. R. (011). New correations of singe-pase friction factor for turbuent pipe fow and evauation of existing singe-pase friction factor correations. Nucear Engineering and Design, in press. [1] Gorenfo, D. (1993). Poo boiing. In: VDI Heat Atas. Dussedorf, Germany: Ha-5. [13] Gungor, K.E., Winterton, R.H.S. (1987). Simpified gernara correation for saturated fow boiing and comparisons wit data. Cemica Engineering Researc and Design, 65, [14] Haaand, S.E. (1983). Simpe and expicit formuas for friction factor in turbuent pipe fow. Trans. ASME, J. Fuids Eng. 105, 89. [15] Haynes, B.S., Fetcer, D.F. (003). Subcooed fow boiing eat transfer in narrow passages. Int. J.Heat and Mass Transfer, 46, [16] In, S., Jeong, S. (009). Fow boiing eat transfer caracteristics of R13 and R134a in a micro-canne. Int. J. Mutipase Fow, 35, [17] Kaew-On, J, Wongwises, S. (009). Experimenta investigation of evaporation eat transfer coefficient and pressure of R410A in muti-port minicanne. Int. J. Refrigeration, 3, [18] Kaew-On, J, Sakamatapan, K., Wongwises, S. (011). Fow boiing eat transfer of R134a in te mutiport minicanne eat excangers. Experimenta Terma and Fuid Science, 35(), [19] Kandikar, S. G. (1990). A genera correation for two-pase fow boiing eat transfer coefficient inside orizonta and vertica tubes. J. Heat Transfer, 10, [0] Kandikar, S. G., Baasubramanian, P. (004). An extension of te fow boiing correation to transition, aminar, and deep aminar fows in minicannes and microcannes. Heat Transfer Engineering, 5(3), [1] Kenning, D.B.R., Cooper, M.G. (1989). Saturated fow boiing of water in vertica tubes. Int. J. Heat and Mass Transfer, 3, [] Kew, P.A., Cornwe, K. (1997). Correations for prediction of boiing eat transfer in sma-diameter cannes. Appied Terma Engineering, 17, [3] Lazarek, G.M., Back, S.H. (198). Evaporative eat transfer pressure drop and critica eat fux in a sma vertica tube wit R-113. Int. J. Heat and Mass Transfer, 5, [4] Liu, Z., Winterton, R.H.S. (1991). A genera correation for saturated and subcooed fow boiing in tubes and annui based on a nuceate poo boiing equation. Int. J. Heat and Mass Transfer, 34, [5] Lee, H.J., Lee, S.Y. (001). Heat transfer correation for boiing fows in sma rectanguar orizonta cannes wit ow aspect ratios. Int. J. Mutipase Fow, 7, [6] Lee, J., Mudawar, I. (005). Two-pase fow in ig-eat fux micro-canne eat sink for refrigeration cooing appications: part II eat transfer caracteristics. Int. J.Heat and Mass Transfer, 48, [7] Maek A., Coin, R. (1983). Ebuition de ammoniac en tube ong, transfert de caeur et ertes de carges en tubes vertica et orizonta. centre tecnique des. Industries Mecanniques, Senis France, CETIM , [8] Pamitran, A.S., Coi, K., O, J.T. O, H.K. (007). Forced convective boiing eat transfer of R-410a in orizonta mini-cannes. Int. J. Refrigeration, 30, [9] Saisorn, S., Kaew-On, J., Wongwises, S. (010). Fow pattern and eat transfer caracteristics of R-134a refrigerant during fow boiing in a orizonta circuar mini-canne. Int. J. Heat and Mass Transfer, 53, [30] Saito, S., Daiguji, H., Hiara, E. (005). Effct of tube diameter on boiing eat transfer of R-134a in orizonta sma-diameter tubes. Int. J. Heat and Mass Transfer, 48, [31] Saito, S., Daiguji, H., Hiara, E. (007). Correation for boiing eat transfer of R-134a in orizonta tubes incuding effect of tube diameter. Int. J. Heat and Mass Transfer, 50, [3] Sa, M.M. (198). Cart correation for saturated boiing eat transfer: equations and furter study. ASHRAE Transactions, 88,

15 [33] Siferaw, D, Huo, X., Karayiannis, T.G., Kenning, D.B.R. (007). Examination of eat transfer correations and a mode for fow boiing of R134a in sma diameter tubes. Int. J. Heat and Mass Transfer, 50, [34] Siferaw, D, Karayiannis, T.G., Kenning, D.B.R. (009). Fow boiing in a 1.1 Mm tube wit R134a: experimenta resuts and comparison wit mode. Int. J. Terma Sciences, 48, Sun, L, Misima, K. (009). An evauation of prediction metods for saturated fow boiing eat transfer in mini-cannes. Int. J. Heat and Mass Transfer, 5, [35] Sumit, B., Kaminaga, F., Matsumura, K. (003). Saturated fow boiing of water in a vertica sma diameter tube. Exp. Terma Fuid Science, 7, [36] Tome, J.R., Dupont, V., Jacobi, A.M. (004). Heat transfer mode for evaporation in microcannes, part I: presentation of te mode. Int. J. Heat and Mass Transfer, 47, [37] Tran, T., Wambsganss, M.W., France, D.M. (1996). Sma circuar- and rectanguar canne boiing wit two refrigerants. Int. J. Mutipase Fow,, [38] Warrier, G.R., Dir, V.K., Momoda, L.A. (00). Heat transfer and pressure drop in narrow rectanguar cannes, Exp. Terma Fuid Sci., 6, [39] Yan, Y. Y., Lin, T F. (1998). Evaporation eat transfer and pressure drop of refrigerant R-134a in a sma pipe. Int. J. Heat and Mass Transfer, 41, [40] Yu, W., France, D.M., Wambsganss, M.W., Hu, J.R. (00). Two-pase pressure drop, boiing eat transfer, and critica eat fux to water in a sma-diameter orizonta tube. Int. J. Mutipase Fow, 8, [41] Yun, R., Heo, J.H., Kim, Y. (006). Evaporative eat transfer and pressure drop of R410A in microcannes. Int. J. Refrigeration, 9, [4] Zang, W., Hibiki, T., Misima, K. (005). Correation for fow boiing eat transfer at ow iquid reynods number in sma diameter cannes. J. Heat Transfer, 17, [43] Zang, W., Hibiki, T., Misima, K. (004). Correation for fow boiing eat transfer in mini-cannes. Int. J Heat and Mass Transfer, 47,

A General Correlation to Predict The Flow Boiling Heat Transfer of R410A in Macro/Mini Channels

A General Correlation to Predict The Flow Boiling Heat Transfer of R410A in Macro/Mini Channels Purdue University Purdue e-pubs Internationa Refrigeration and Air Conditioning Conference Scoo of Mecanica Engineering 1 A Genera Correation to Predict Te Fow Boiing Heat Transfer of R1A in Macro/Mini