Journal of Power and Energy Systems

Transcription

1 Jurnal f Pwer an Energy Systems urbulent Heat ransfer fr Heatng f Water n a Shrt Vertcal ube* Kch HAA** an Nbuak NODA*** **Insttute f Avance Energy, Kyt Unv. Gkash, Uj, Kyt , Japan E-mal: hata@ae.kyt-u.ac.jp ***Natnal Insttute fr Fusn Scence 3-6 Orsh-ch, k, Gfu , Japan Abstract he turbulent heat transfer ceffcents fr the flw velctes (u=4.0 t 1 m/s), the nlet lqu temperatures ( n =96.5 t K), the nlet pressures (P n =810 t 1014 kpa) an the ncreasng heat nputs (Q 0 exp(t/τ), τ=10, 0 an 33.3 s) are systematcally measure by an expermental water lp. he Platnum test tubes f test tube nner ameters (=3, 6 an 9 mm), heate lengths (L=3.7 t 100 mm), rats f heate length t nner ameter (L/=5.51 t 33.3) an wall thckness (δ=0.3, 0.4 an 0.5 mm) wth surface rughness (Ra=0.40 t 0.78 µm) are use n ths wrk. he turbulent heat transfer ata fr Platnum test tubes were cmpare wth the values calculate by ther wrkers crrelatns fr the turbulent heat transfer. he nfluence f Reynls number (Re), Prantl number (Pr), Dynamc vscsty (µ) an L/ n the turbulent heat transfer s nvestgate nt etals an, the wely an precsely prectable crrelatn f the turbulent heat transfer fr heatng f water n a shrt vertcal tube s gven base n the expermental ata. he crrelatn can escrbe the turbulent heat transfer ceffcents btane n ths wrk fr the we range f the temperature fference between heater nner surface temperature an average bulk lqu temperature ( L =5 t 140 K) wth =3, 6 an 9 mm, L=3.7 t 100 mm an u=4.0 t 1 m/s wthn ±15 % fference. Key wrs: urbulent Heat ransfer, Heatng f Water, Shrt Vertcal ube. 1. Intructn he accurate expressn fr calculatn n turbulent heat transfer s necessary t clarfy the nset f subcle nucleate blng, subcle blng heat transfer an DNB (eparture frm nucleate blng), whse knwlege s mprtant t scuss the mechansm f subcle flw blng crtcal heat flux n a shrt vertcal tube. Many researchers have expermentally stue the turbulent heat transfer n ppes an gven the crrelatns fr calculatng turbulent heat transfer ceffcents (1)-(5). Dttus an Belter (1) : Nu = 0.03 Re Pr (1) Nusselt () : Nu / 3 = Re Pr () L *Receve 30 July, 007 (N ) [DOI: /jpes..318] Seer an ate (3) : Nu = 0.07 Re 0.8 Pr 1 / 3 µ µ w 0.14 (3) 318

2 Jurnal f Pwer an Petukhv (4) : Nu = ( f / )Re Pr 1 / / ( f / ) (Pr 3 1 ) (4) f = ( 3.64 lg (5) 10 Re 3.8 ) Gnelnsk (5) : Nu ( f / )(Re 1000 )Pr = (6) 1 / / ( f / ) (Pr 3 1 ) All prpertes n these equatns are evaluate at the average bulk lqu temperature, L, [=( n + ut )/], except µ w, whch s evaluate at the wall temperature. Fr many years, we have alreay measure the quas-steay state crtcal heat flux (CHF) t transent ne by expnentally ncreasng heat nputs, (Q 0 exp(t/τ), τ=19 ms t 33.3 s) fr the SUS304 test tubes wth the we range f expermental cntns t establsh the atabase fr esgnng the vertr f a helcal type fusn expermental evce, whch s Large Helcal Devce (LHD) lcate n Natnal Insttute fr Fusn Scence, Japan. An, we have gven the steay state an transent CHF crrelatns aganst utlet an nlet subclngs base n the effect f test tube nner ameter (), flw velcty (u), utlet an nlet subclngs ( sub,ut an sub,n ), rat f heate length t nner ameter (L/) an nn-mensnal expnental per [τu/{σ/g/(ρ l -ρ g )} 0.5 ] n CHF (6)-(16). Mre wely an precsely prectable crrelatn f turbulent heat transfer fr heatng f water n a shrt vertcal tube has been esre t clarfy the nset f subcle nucleate blng, subcle blng heat transfer an DNB fr the SUS304 test tubes. We have heate the SUS304 test tube wth an expnentally ncreasng heat nput supple frm a rect current surce an measure the average temperature f the SUS304 test tube wth resstance thermmetry partcpatng as a branch f a uble brge crcut fr the temperature measurement. Hwever, the relatnshp between the electrcal resstance an the temperature fr the test tube s nt rgly fxe at each expermental run, n case f ally test tube such as SUS304, because the test tube becmes very hgh temperature n the CHF experment. It s necessary t crrect the measure surface temperatures as cmpare wth the q versus L curve calculate by the wely an precsely prectable crrelatn f turbulent heat transfer fr each expermental run. he bjectves f present stuy are furfl. Frst s t measure the turbulent heat transfer ceffcents n Platnum test tubes wth varus test tube nner ameters, heate lengths an L/ fr the we range f test tube surface temperatures ( s ), nlet lqu temperatures ( n ) an flw velctes (u). Secn s t clarfy the nfluence f test tube nner ameter, L/, test tube surface temperature, lqu temperature an flw velcty n the turbulent heat transfer. hr s t erve the crrelatn f the turbulent heat transfer n a shrt vertcal tube base n the expermental ata. Furth s t scuss the mechansm f turbulent heat transfer n a shrt vertcal tube. Nmenclature C cnstant n Eq. (9) c specfc heat, J/kg K c p specfc heat at cnstant pressure, J/kg K test tube nner ameter, m f frctn factr fr smth tube G =ρ l u, mass flux, kg/m s h turbulent heat transfer ceffcent, W/m K I current flwng thrugh stanar resstance, A L heate length, m entrance length, m L e 319

3 Jurnal f Pwer an n expnent, r slpe n the lg-lg graph Nu nusselt number, h/λ P pressure, kpa P n pressure at nlet f heate sectn, kpa P pt pressure measure by nlet pressure transucer, kpa P ut pressure at utlet f heate sectn, kpa P pt pressure measure by utlet pressure transucer, kpa Pr =c p µ/λ, Prantl number Q heat nput per unt vlume, W/m 3 Q 0 ntal expnental heat nput, W/m 3 q heat flux, W/m r test tube nner raus, m r test tube uter raus, m R 1 t R3 resstance n a uble brge crcut, Ω Ra average rughness, µm Re =G/µ, Reynls number Rmax maxmum rughness epth, µm Rz mean rughness epth, µm S surface area, m Sc =c pl ( sub,ut ) cal /h fg, =c pl sub,ut /h fg, nn-mensnal utlet subclng Sc* =c pl sub,n /h fg, nn-mensnal nlet subclng temperature, K n nlet lqu temperature, K L =( n + ut )/, average bulk lqu temperature, K ut utlet lqu temperature, K ( ut ) cal calculate utlet lqu temperature, K s heater nner surface temperature, K sat saturatn temperature, K t tme, s L =( s - L ), temperature fference between heater nner surface temperature an average bulk lqu temperature, K sub,n =( sat - n ), nlet lqu subclng, K sub,ut =( sat - ut ), utlet lqu subclng, K u flw velcty, m/s V vlume, m 3 δ wall thckness, mm λ thermal cnuctvty, W/mK µ vscsty, Ns/m µ w vscsty at the temperature f the tube wall, Ns/m ρ ensty, kg/m 3 τ expnental per, s Subscrpt n ut l sub w wnh nlet utlet lqu subcle cntns wall wth n heatng. Expermental Apparatus an Meth 30

4 Jurnal f Pwer an Wat er El ectr magnet c Val ve Cnenser Pressur zer Vacuum Pump L qu e mp. St r age ank Level Gauge Heat er Pressure Gauge Ntrgen Gas Heater Cntrller Wat er Safety Val ve est Sect n Cl er Cl ng Wat er Safet y Val ve Dr a nage Pressure Gauge Level Gauge Expans n ank an Separat r By-pass Lp In Exchanger est ube mm Inner Dameter + 3mm + 6mm + + 9mm 1 mm + Pump Pr e- Heat er Dr a nage Flw Meter Oxygen Met er Degass ng Equ pment Fl w r ect n Fg. 1 Schematc agram f expermental apparatus. he schematc agram f expermental water lp cmprse f the pressurzer s shwn n Fg. 1. he lp s mae f SUS304 stanless steel an s capable f wrkng up t MPa. he lp has fve test sectns whse nner ameters are, 3, 6, 9 an 1 mm. est sectns were vertcally rente wth water flwng upwar. he three test sectns f the nner ameters f 3, 6 an 9 mm were use n ths wrk. he crculatng water was stlle an enze wth abut 5-MΩcm specfc resstvty. he crculatng water thrugh the lp was heate r cle t keep a esre nlet temperature by pre-heater r cler. he flw velcty was measure by a mass flw meter usng a vbratn tube. he flw velcty was cntrlle by regulatng the frequency f the three-phase alternatng pwer surce t the canne type crculatn pump. he water was pressurze by saturate vapr n the pressurzer n ths wrk. he pressure at the nlet f the test tube was cntrlle wthn P 170 Cu BL Flw rectn : hermcuple P : Pressure Gauge Cu :Cpper-electre-plate BL : Bakelte SUS304 est ube Cu SUS304 P L L+566 Flw rectn Fg. Vertcal crss-sectnal vew f 6 an 9 mm nner ameter test sectns. Fg. 3 SEM phtgraph f the Platnum test tube fr an nner ameter f 6 mm wth cmmercal fnsh f nner surface. 31

5 Jurnal f Pwer an Heat Input Cntrl Blck Heat Input S gnal Electrnc Swtch + - Amplfer D.C. Surce (3000A, 35V) Pwer Shut ff S gnal Shut ff e mperat ure Cmparatr Q Mult pler Dver VI VR V VI Data Prcessng Blck Dgtal C mputer est Heater Blck I RS VI D/A Cnverter A/D Cnverter R1 V R Amplfers r 0 a r r 3 b V VR VL VI VF VL VP VP Data Sgnal 8channels VR R est ube R3 Dsplay Pr nter Fg. 4 Measurement an ata prcessng system. ±1 kpa f a esre value by usng a heater cntrller f the pressurzer. he crss-sectnal vew f 6 an 9 mm nner ameter test sectns use n ths wrk s shwn n Fg.. he Platnum () test tubes fr the test tube nner ameters f 3, 6 an 9 mm wth the cmmercal fnsh f nner surface were manly use n ths wrk. Wall thckness f the test tube, δ, was 0.3, 0.4 an 0.5 mm. he nner surface cntns f the test tubes were bserve by the SEM phtgraph an nner surface rughness was measure by ky Semtsu C., Lt. s surface texture measurng nstrument (SURFCOM 10A). Fgure 3 shws the scannng electrn mcrscpe (SEM) phtgraph f the Platnum () test tube fr =6 mm wth cmmercal fnsh f nner surface. he values f nner surface rughness fr Ra, Rmax an Rz are measure 0.40,.0 an 1.50 µm fr =3 mm, 0.45,.93 an 1.93 µm fr =6 mm, an 0.78, 3.90 an.64 µm fr =9 mm respectvely. he slver-cate 5-mm thckness cpper-electre-plates t supply heatng current were slere t the surfaces f the bth ens f the test tube. he bth ens f test tube were electrcally slate frm the lp by Bakelte plates f 14-mm thckness. he test tubes were als thermally nsulate frm atmsphere wth a Bakelte blck f 10 mm we, 80 mm eep an L mm hgh. he test tube was heate wth an expnentally ncreasng heat nput supple frm a rect current surce (akasag Lt., NL R, DC 35 V-3000 A) thrugh the tw cpper electres shwn n Fg. 4. Heat transfer prcesses cause by expnentally ncreasng heat nputs, Q 0 exp(t/τ), were measure fr the test tube. he expnental per, τ, f the heat nput range frm 10 s t 33.3 s. hese prcesses were almst smlar t thse cause by steay-state heat nputs. he cmmn specfcatns f the rect current surce are as fllws. Cnstant-vltage (CV) me regulatn s %+3 mv f full scale, CV me rpple s 500 µv r.m.s. r better an CV me transent respnse tme s less than 00 µsec (ypcal) aganst 5 % t full range change f la. he average temperature f the test tube was measure wth resstance thermmetry partcpatng as a branch f a uble brge crcut fr the temperature measurement. he utput vltages frm the brge crcut tgether wth the vltage rp acrss the tw electres an acrss a stanar resstance were amplfe an then were sent va a D/A cnverter t a gtal cmputer. hese vltages were smultaneusly sample at a cnstant nterval rangng frm 60 t 00 ms. he average temperature f the test tube was calculate 3

6 Jurnal f Pwer an wth the a f prevusly calbrate resstance-temperature relatn. he heat generatn rate n the test tube was calculate frm the measure vltage fference between the ptental taps f the test tube an the stanar resstance. he surface heat flux s the fference between the heat generatn rate per unt surface area an the rate f change f energy strage n the test tube btane frm the fare average temperature versus tme curve as fllws: V q( t ) = Q( t ) ρ c (7) S t where ρ, c, V an S are the ensty, the specfc heat, the vlume an the nner surface area f the test tube, respectvely. he heater nner surface temperature was als btane by slvng the heat cnuctn equatn n the test tube uner the cntns f measure average temperature an surface heat flux f the test tube. Basc heat cnuctn equatn fr the test tube s as fllws: r + 1 r r Q + = 0 λ (8) hen ntegratn yels an the mean temperature f the test tube s btane. Qr 4λ Qr () r = + ln r + C λ (9), = π ( r r ) 1 r r π r Generatng heat n the tube s equal t the thermal cnuctn an the test tube s perfectly nsulate. q = ( r r ) Q λ = (11), = 0 r r = r r r r= r he temperature f the heater nner surface, s, can be escrbe as fllws: S qr = ( r ) = 4( r qr ( r r ) λ r ( r r lnr ) () r 1 1 4r r lnr r lnr ) λ r 4 4 ( r r ) In case f the 3, 6 an 9 mm nner ameter test sectns, befre enterng the test tube, the test water flws thrugh the tube wth the same nner ameter f the test tube t frm the fully evelpe velcty prfle. he entrance tube lengths, L e, are gven 40, 333 an 333 mm (L e /=80, 55.5 an 37). he values f L e / fr =3, 6 an 9 mm n whch the center lne velcty reaches 99 % f the maxmum value fr turbulence flw were btane rangng frm 9.8 t 1.9 by the crrelatn f Brkey an Hershey (17) as fllws: L e = 1 / Re (14) he nlet an utlet lqu temperatures were measure by 1-mm.., sheathe, K-type thermcuples whch are lcate at the centerlne f the tube at the upper an lwer stream pnts f 83 an 63 mm frm the tube nlet an utlet pnts. he nlet an utlet pressures were measure by the stran gauge transucers, whch were lcate near the entrance f cnut at upper an lwer stream pnts f 63 mm frm the tube nlet an utlet pnts. he thermcuples an the transucers were nstalle n the cnuts as shwn n Fg.. he nlet an utlet pressures fr =6 an 9 mm were calculate frm the pressures measure by nlet an utlet pressure transucers as fllws: Pn = Ppt {( Ppt ) ( Ppt ) } (15) wnh wnh L (10) (1) (13) 33

7 Jurnal f Pwer an ( P P ) L Put = Pn n pt (16) L Expermental errrs are estmate t be ±1 K n nner tube surface temperature an ± % n heat flux. Inlet flw velcty, nlet an utlet subclngs, nlet an utlet pressures, an expnental per were measure wthn the accuracy ± %, ±1 K, ±1 kpa an ± % respectvely. 3. Expermental Results an Dscussn 3.1 Expermental Cntns he ntal expermental cntns such as nlet flw velcty, nlet an utlet subclngs, nlet an utlet pressures, an expnental per fr the turbulent heat transfer experments were etermne nepenently each ther befre each expermental run. he expermental cntns were as fllws: Heater Materal Inner Dameter () 3, 6 an 9 mm Heate Length (L) 3.7, 66.5 an 100 mm fr =3 mm, 69.6 mm fr =6 mm, an 49.6 mm fr =9 mm L/ 10.9,. an 33.3 fr =3 mm, 11.6 fr =6 mm, an 5.51 fr =9 mm Wall hckness (δ) 0.5 mm fr =3 mm, 0.4 mm fr =6 mm, an 0.3 mm fr =9 mm Surface Cntn cmmercal fnsh f nner surface Surface rughness fr Ra, Rmax an Rz 0.40,.0 an 1.50 µm fr =3 mm, 0.45,.93 an 1.93 µm fr =6 mm, an 0.78, 3.90 an.64 µm fr =9 mm Inlet flw velcty (u) 4.0, 6.9, 9.9, 13.3, 17 an 1 m/s Inlet Pressure (P n ) t kpa Outlet Pressure (P ut ) t kpa Inlet Subclng ( sub,n ) 9.4 t K Outlet Subclng ( sub,ut ) 79.4 t K Inlet Lqu emperature ( n ) t K Stealy Increasng Heat Input (Q) Q 0 exp(t/τ), τ=10, 0 an 33.3 s 3. urbulent Heat ransfer Fgures 5, 6 an 7 shw the typcal examples f the turbulent heat transfer curves fr q (W/m ) Expermental Data =3 mm L=3.7 mm L/=10.9 P n =857.4 kpa n = K u=13.3 m/s Eq. (17) Nusselt Seer-ate Dttus-Belter Petukhv Gnelnsk Blng Intatn L (K) Fg. 5 Relatnshp between q an L [=( s- L)] wth an nner ameter f 3 mm, a heate length f 3.7 mm an a flw velcty f 13.3 m/s at an nlet pressure f 857 kpa. 34

8 Jurnal f Pwer an q (W/m ) Expermental Data =6 mm L=69.6 mm L/=11.6 P n = kpa n =30.68 K u=13.3 m/s Eq. (17) Nusselt Seer-ate Dttus-Belter Petukhv Gnelnsk q (W/m ) Expermental Data =9 mm L=49.6 mm L/=5.51 P n = kpa n = K u=13.3 m/s Eq. (17) Nusselt Seer-ate Dttus-Belter Petukhv Gnelnsk L (K) L (K) Fg. 6 Relatnshp between q an L [=( s- L)] wth an nner ameter f 6 mm, a heate length f 69.6 mm an a flw velcty f 13.3 m/s at an nlet pressure f 841 kpa. Fg. 7 Relatnshp between q an L [=( s- L)] wth an nner ameter f 9 mm, a heate length f 49.6 mm an a flw velcty f 13.3 m/s at an nlet pressure f 850 kpa. Platnum test tubes f =3, 6 an 9 mm, L=3.7, 69.6 an 49.6 mm, an L/=10.9, 11.6 an 5.51 respectvely wth the expnental per, τ, f arun 33.3 s at u=13.3 m/s. hese expermental ata are cmpare wth the values erve frm the crrelatns, Eqs. (1) t (6). he expermental ata fr =3 mm at the hgh heat flux pnt shwn n Fg. 5 are 17.6 t 53.8 % hgher than the values erve frm these crrelatns at a fxe temperature fference between heater nner surface temperature an average bulk lqu temperature ( L =cnstant), an 0 t 64 K lwer than the values erve frm these crrelatns at a fxe heat flux (q=cnstant). An thse fr =6 an 9 mm at the hgh heat flux pnt shwn n Fgs. 6 an 7 are 4.7 t 6.7 % an 3.8 t 60.5 % hgher, an 6 t 75 K an 15 t 41 K lwer respectvely. It s assume frm these facts that these crrelatns wul be evelpe frm the expermental ata wth a lng test tube an a lw range f L fr the esgn f heat-exchange equpment Influence f flw velcty, nner ameter, L/ an µ/µ w Fgure 8 shws the nfluence f the flw velcty n the turbulent heat transfer ceffcent, h, fr the nner ameter f 3 mm, the heate length f 66.5 mm an the L/ f h (W/m K) =3 mm L=66.5 mm L/=. P n = kpa n = K n=0.85 L 40 K 80 K 10 K u (m/s) Fg. 8 h vs. u fr an nner ameter f 3 mm an a heate length f 66.5 mm wth the L f 40, 80 an 10 K at nlet pressures f 83 t 933 kpa. 35

9 Jurnal f Pwer an h (W/m K) =3, 6 an 9 mm L=3.7, 69.6 an 99 mm L/=11 P n = kpa n = K u=13.3 m/s Extraplate Value n=-0.15 L 40 K 80 K 10 K (mm) Fg. 9 h vs. fr a flw velcty f 13.3 m/s wth the L f 40, 80 an 10 K at nlet pressures f 840 t 856 kpa. h (W/m K) =3 mm L= mm L/= P n = kpa n = K u=13.3 m/s n=-0.08 L 40 K 80 K 10 K L/ Fg. 10 h vs. L/ fr an nner ameter f 3 mm, heate lengths f 3.7 t 100 mm an a flw velcty f 13.3 m/s wth the L f 40, 80 an 10 K at nlet pressures f 856 t 904 kpa. h (W/m K) =6 mm L=69.6 mm L/=11.6 P n = kpa n = K n=0.14 u 4.0 m/s 6.9 m/s 9.9 m/s 13.3 m/s Nu /Re 0.85 /(µ/µw ) =6 mm L=69.6 mm L/=11.6 P n =809.5, an 878 kpa n =96.5, 30.7 an K u=13.3 m/s n=0.4 L 40 K 80 K 100 K 10 K 1 10 µ/µ w Fg. 11 h vs. µ/µ w fr an nner ameter f 6 mm an a heate length f 69.6 mm wth the flw velctes f 4 t 13.3 m/s at nlet pressures f 808 t 841 kpa Pr Fg. 1 Relatnshp between [Nu /Re 0.85 /(µ/µ w) 0.14 ] an Pr fr an nner ameter f 6 mm an a heate length f 69.6 mm wth a flw velcty f 13.3 m/s at nlet lqu temperatures f 96 t 353 K an nlet pressures f 809 t 878 kpa respectvely... he h fr the flw velcty f 4.0, 6.9, 9.9, 13.3, 17 an 1 m/s were shwn versus the flw velcty wth the temperature fference between the heater nner surface temperature an the average bulk lqu temperature, L, f 40, 80 an 10 K. he h fr sx fferent flw velctes becme lnearly hgher wth an ncrease n the flw velcty. he slpe, n, n the lg-lg graph kept almst cnstant abut 0.85 wth the L rangng frm 40 t 10 K. he effect f the nner ameter n the h was represente versus wth L as a parameter n Fg. 9. In the fgure, the h fr each L are almst prprtnal t n the range f the L frm 40 t 10 K. Fgure 10 s pltte n lg (h) versus lg (L/) graph t check the nfluence f L/ n h fr the L f 40, 80 an 10 K. he h fr each L becme lnearly lwer wth an ncrease n the L/ wth a smlar slpe, n, f he vscsty graent f the flu n the tube s taken nt accunt by means f the rat f µ/µ w, where µ s the vscsty f the flu at ts manstream temperature an µ w s ts vscsty at the temperature f the tube wall. As shwn n Fg. 11, the expnent, n, f µ/µ w s almst taken as 0.14 n the expressn fr the turbulent heat transfer ceffcent, h, fr the nner ameter f 6 mm, the heate length f 69.6 mm an the L/ f 11.6 n the range f the L frm 5 t 140 K. hs shws nearly the same tren f epenence n µ/µ w frst suggeste by Seer an ate (3) as shwn n Eq. (3). 36

10 Jurnal f Pwer an 3.3 urbulent Heat ransfer Crrelatn It has been clarfe that the turbulent heat transfer ceffcents, h, are almst prprtnal t u 0.85, -0.15, (L/) an (µ/µ w ) 0.14 n the range f the L frm 5 t 140 K base n the expermental ata Influence f Prantl number Fgure 1 shws the nfluence f Prantl number, Pr, n the values f [Nu /Re 0.85 /(µ/µ w ) 0.14 ] fr the nner ameter f 6 mm, the heate length f 69.6 mm an the L/ f 11.6 at nlet lqu temperatures ( n =96, 30 an 353 K) wth the temperature fference between the heater nner surface temperature an the average bulk lqu temperature, L, f 40, 80, 100 an 10 K. he values f [Nu /Re 0.85 /(µ/µ w ) 0.14 ] fr the Pr rangng frm.1 t 6.64 were shwn versus Pr wth the L as a parameter. he values f [Nu /Re 0.85 /(µ/µ w ) 0.14 ] becme lnearly hgher wth the ncrease n the Pr. he slpe, n, f the curve n the lg-lg graph s almst cnstant abut 0.4 smlar t the expermental ata fr L =40, 80, 100 an 10 K. he tren f Pr 0.4 epenence fr ur ata can als be seen fr the crrelatn, Eq. (1), erve by Dttus an Belter (1) Influence f Reynls number All the ata fr the we ranges f test tube nner ameters (=3, 6 an 9 mm), heate lengths (L=3.7 t 100 mm), L/=5.51 t 33.3, nlet lqu temperatures ( n =96 t 353 K), flw velctes (u=4.0 t 1 m/s) an temperature fference between heater nner surface temperature an average bulk lqu temperature ( L =5 t 140 K) are pltte n lg [Nu /Pr 0.4 /(L/) /(µ/µ w ) 0.14 ] versus lg (Re ) graph n Fg. 13 t etermne the fnal value f the expnent, n, fr Re. he fnal value f n was als gven 0.85 as the best ftte ne base n the expermental ata n ths wrk Crrelatn he turbulent heat transfer crrelatn s erve as fllws base n the effects f Re, Pr, L/ an µ/µ w clarfe n ths wrk. Nu = 0.0 Re 0.85 Pr 0.4 L 0.08 µ µ w 0.14 (17) Nu /Pr 0.4 /(L/) /(µ/µ w ) =3-9 mm L= mm L/= P n = kpa n = K u=4-1 m/s Eq. (17) +15% -15% n=0.85 L L/ n 3 mm 3.7 mm K 3 mm 66.5 mm K 3 mm 100 mm K 6 mm 69.6 mm K 6 mm 69.6 mm K 9 mm 49.6 mm K Re Fg. 13 Relatnshp between [Nu /Pr 0.4 /(L/) /(µ/µ w) 0.14 ] an Re fr nner ameters f 3, 6 an 9 mm an heate lengths f 3.7 t 100 mm wth flw velctes f 4 t 1 m/s an nlet lqu temperatures f 96 t 353 K at nlet pressures f 810 an 1014 kpa. 37

11 Jurnal f Pwer an All prpertes n the equatn are evaluate at the average bulk lqu temperature, L, [=( n +( ut ) cal )/], except µ w, whch s evaluate at the heater nner surface temperature. he utlet lqu temperature, ( ut ) cal, s calculate by the energy balance as fllws: ( ut ) cal 4Lq = n + (18) uc ρ pl l he curves erve frm Eq. (17) are shwn n Fgs. 5, 6, 7 an 13. Mst f the ata are wthn 15 % fference f Eq. (17) fr the we range f the temperature fference between heater nner surface temperature an average bulk lqu temperature ( L =5 t 140 K) wth =3, 6 an 9 mm, L=3.7 t 100 mm an u=4.0 t 1 m/s. 4. Cnclusns he turbulent heat transfer ceffcents, h, fr the flw velctes (u=4.0 t 1 m/s), the nlet lqu temperatures ( n =96.5 t K), the nlet pressures (P n =810 t 1014 kpa) an the ncreasng heat nputs (Q 0 exp(t/τ), τ=10, 0 an 33.3 s) are systematcally measure by the expermental water lp. he Platnum test tubes f test tube nner ameters (=3, 6 an 9 mm), heate lengths (L=3.7 t 100 mm), rats f heate length t nner ameter (L/=5.51 t 33.3) an wall thckness (δ=0.3, 0.4 an 0.5 mm) wth surface rughness (Ra=0.40 t 0.78 µm) are use. Expermental results lea t the fllwng cnclusns. 1) he h fr u=4.0 t 1 m/s becme lnearly hgher wth an ncrease n the flw velcty. he slpe, n, n the lg-lg graph kept almst cnstant abut 0.85 wth the L f 40, 80 an 10 K. ) he h fr =3, 6 an 9 mm are almst prprtnal t fr the L f 40, 80 an 10 K. 3) he h fr L/=5.51 t 33.3 becme lnearly lwer wth an ncrease n the L/ wth a smlar slpe, n, f fr the L f 40, 80 an 10 K. 4) he expnent, n, f µ/µ w s almst taken as 0.14 n the expressn fr the turbulent heat transfer ceffcent, h. 5) he slpe, n, f the curve n the lg [Nu /Re 0.85 /(µ/µ w ) 0.14 ] versus lg (Pr) graph s almst cnstant abut 0.4 smlar t the expermental ata fr L =40, 80, 100 an 10 K. 6) he fnal value f n n the lg [Nu /Pr 0.4 /(L/) /(µ/µ w ) 0.14 ] versus lg (Re ) graph was als gven 0.85 as the best ftte ne base n the expermental ata n ths wrk. 7) he turbulent heat transfer crrelatn, Eq. (17), s erve base n the effects f Re, Pr, L/ an µ/µ w. 8) Mst f the ata are wthn 15 % fference f the turbulent heat transfer crrelatn, Eq. (17), fr the we range f the temperature fference between heater nner surface temperature an average bulk lqu temperature ( L =5 t 140 K) wth =3, 6 an 9 mm, L=3.7 t 100 mm an u=4.0 t 1 m/s. Acknwlegments hs research was perfrme as a LHD jnt research prject f NIFS (Natnal Insttute fr Fusn Scence), Japan, NIFS05KFRF015, 005. References (1) Dttus, F., W., an Belter, L., M., K., Unv. Calf. (Berkeley) Pub. Eng., Vl., (1930), p () Nusselt, W., Der Wärmeaustausch zweschen Wan un Wasser m Rhr, Frsch. Geb. Ingeneurwes., Vl., (1931), p (3) Seer, E. N., an ate, C. E., Heat ransfer an Pressure Drp f Lqus n ubes, In. Eng. Chem., Vl. 8, (1936), pp (4) Petukhv, B. S., Heat ransfer an Frctn n urbulent Ppe Flw wth Varable 38

12 Jurnal f Pwer an Physcal Prpertes, Avances n Heat ransfer, New Yrk, Acaemc Press, (1970), pp (5) Gnelnsk, V., New Equatns fr Heat an Mass ransfer n urbulent Ppe an Channel Flw, Internatnal Chemcal Engneerng, Vl. 16, N., (1976), pp (6) Hata, K., Shtsu, M., an Na, N., Crtcal Heat Fluxes f Subcle Water Flw Blng aganst Outlet Subclng n Shrt Vertcal ube, Jurnal f Heat ransfer, rans. ASME, Seres C, Vl. 16, (004), pp (7) Hata, K., Kmr, H., Shtsu, M., an Na, N., Crtcal Heat Fluxes f Subcle Water Flw Blng aganst Inlet Subclng n Shrt Vertcal ube, JSME Internatnal Jurnal, Seres B, Vl. 47, N., (004), pp (8) Hata, K., Kmr, H., Shtsu, M., an Na, N., Influence f Dsslve Gas Cncentratn n Subcle Flw Blng Crtcal Heat Flux n Shrt Vertcal ube, Prceengs f 1th Internatnal Cnference n Nuclear Engneerng, Paper N. ICONE , (004), pp (9) Hata, K., Shtsu, M., an Na, N., Subcle Flw Blng Crtcal Heat Flux n Shrt Vertcal ube (Influence f Inner Surface Rughness), Prceengs f 004 ASME Internatnal Mechancal Engneerng Cngress an RD&D Exp, Paper N. IMECE , (004), pp (10) Hata, K., an Na, N., Subcle flw blng heat transfer an crtcal heat flux n shrt vertcal tube wth mrrr fnshe nner surface, Prceengs f 11th Internatnal pcal Meetng n Nuclear Reactr hermal Hyraulcs, Paper N. NUREH11-81, (005), pp (11) Hata, K., an Na, N., hermal Analyss n Flat-Plate ype Dvertr Base n Subcle Flw Blng Crtcal Heat Flux Data aganst Inlet Subclng n Shrt Vertcal ube, Jurnal f Heat ransfer, rans. ASME, Seres C, Vl. 18, (006), pp (1) Hata, K., an Na, N., hermal Analyss n Mn-Blck ype Dvertr Base n Subcle Flw Blng Crtcal Heat Flux Data aganst Inlet Subclng n Shrt Vertcal ube, Plasma an Fusn Research, he Japan Scety f Plasma Scence an Nuclear Fusn Research, Vl. 1, N. 017, (006), pp (13) Hata, K., Shtsu, M., an Na, N., Crtcal Heat Flux f Subcle Water Flw Blng fr Hgh L/ Regn, Nuclear Scence an Engneerng, Vl. 154, N. 1, (006), pp (14) Hata, K., Shtsu, M., an Na, N., Influence f Heatng Rate n Subcle Flw Blng Crtcal Heat Flux n a Shrt Vertcal ube, JSME Internatnal Jurnal, Seres B, Vl. 49, N., (006), pp (15) Hata, K., Shtsu, M., an Na, N., ransent Crtcal Heat Fluxes f Subcle Water Flw Blng n a Shrt Vertcal ube Cause by Expnentally Increasng Heat Inputs, Prceengs f 13th Internatnal Heat ransfer Cnference, Syney, Australa, Paper N. IHC13-BOI-07, (006), pp (16) Hata, K., Shtsu, M., an Na, N., Influence f est ube Materal n Subcle Flw Blng Crtcal Heat Flux n Shrt Vertcal ube, Jurnal f pwer an Energy Systems, Vl. 1, N. 1, (007), pp (17) Brkey, R. S., an Hershey, H. C., ransprt Phenmena, McGraw-Hll, New Yrk, (1988), p