Heat Transfer and Pressure Drop

8/6/2019 Heat Transfer and Pressure Drop

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Heat Transfer and Pressure DropCharacterist ics of Laminar Flow in a CircularTube Fi t ted wi th Regular ly SpacedTwi s t ed- Tape E l em ent sS . K . S a h aResearch ScholarU . N . G a i t o n d eAssociate ProfessorA . W . D a t eProfessorMechanical Engineering Department,Indian Institute of Technology,Powai, Bombay, India

I I L am i na r f l ow hea t t r ans f e r and p r e s s u r e d r op cha r ac t e r i s t i c s i n a c i r cu l a rt ube f i t ted w i t h r egu l a r l y s paced t w i s ted - t ape e l em en t s conn ec t ed by t h i n c i r -cu l a r r ods w e r e i nves t i ga t ed expe r i m en t a l l y . T hes e cha r ac t e r i s t i c s a r e gov -e r ned by R eyn o l ds num b er , P r and t l num ber , t w i s t ra t i o , s pace ra t i o , and r od -t o - t ube d i am e t e r r a t i o . C o r r e l a t i ons f o r f r i c t i on f ac t o r and N us s e l t num ber a r ea l s o r epo r t ed . I t i s s how n t ha t on t he ba s i s o f bo t h cons t an t pum pi ng pow erand cons t an t hea t du t y , r egu l a r l y s paced t w i s t ed - t ape e l em en t s pe r f o r m s i gn i f i -can t l y be t t e r than f u l l - l eng th t w i s t ed t apes a t h i gh R e yno l ds num ber s , h i ghtwis t s , and smal l spacings .K e y w o r d s : laminar flo w, circular tube, twisted tapes

I N T R O D U C T I O NA m o n g t h e m a n y t e c h n i q u e s ( b o t h p a s s i v e a n d a c t i v e ) i n v e s t i -g a t e d f o r a u g m e n t a t i o n o f h e a t t r a n s f e r r a t e s i n s i d e c i r c u l a rt u b e s , f u l l - le n g t h t w i s t e d - t a p e i n s e r t s t h a t i m p a r t a h e l i c a l p a t ht o t he f l o w h a v e b e e n s h o w n t o b e v e r y e f f e c t i v e , p a r ti c u l a rl yw h e n l a m i n a r f l o w o f h i g h P r a n d t l n u m b e r f l u i d s is c o n s id e r e d[ 1 ]. F i g u r e l a s h o w s t h e l a y o u t o f a f u ll - le n g t h t w i s t e d - t a p ei n s e r t i n s id e a c i r c u l a r t u b e . T h e e x p e r i m e n t a l w o r k o f H o n ga n d B e r g l e s [ 2 ] , d u P l e s s i s [ 3 ] , a n d S u k h a t m e e t a l . [ 4 ] a n d t h en u m e r i c a l w o r k o f D a t e [ 5 ] h a v e s h o w n t h a t i n th e c a s e o f h i g hP r a n d f l n u m b e r f l u i d s i n l a m i n a r f l o w t h e h e a t t r a n s f e r r a t ei n c r e a s e s c o n s i d e r a b l y f o r a m o d e r a t e i n c r e a s e i n p r e s s u r ed r o p . A r e c e n t s u r v e y b y N a n d e k a u n a r a n d M a s l iy a h [ 6]r e p o r t e d s i m i l a r c h a r a c t e ri s t ic s f o r s e v e r a l o t h e r t y p e s o f d u c t si m p a r t i n g h e l i c a l f l o w .I n t h i s p a p e r , i n s t e a d o f a f u l l - l e n g t h t w i s t e d t a p e , t w i s t e d -t a p e e l e m e n t s c o n n e c t e d b y t h i n c i r c u l a r r o d s a r e c o n s i d e r e d .F i g u r e l b s h o w s t h e g e o m e t r y in v e s t i g a t e d . T h e t w i s t e d - t a p ee l e m e n t s o f le n g t h H ( p i tc h l e n g t h f o r 1 8 0 " r o t a t io n o f t h et a p e ) a re f o l l o w e d b y a f r e e s p a c e o f l e n g t h S , w h e r e t h en o n a x i s y m m e t r i c s w i r l f l o w g e n e r a t e d b y t h e t a p e e l e m e n td e c a y s , o n l y t o b e a g a i n a u g m e n t e d b y t h e t a p e e l e m e n t t h a tf o ll o w s . T h e p h a s e a n g l e b e t w e e n s u c c e s s iv e t a p e e l e m e n t s i s0 " . T h e d i r e c t io n o f t w i st i m p a r t e d t o e a c h s u c c e s s iv e e l e m e n ti s a l s o th e s a m e . B o t h t h e p h a s e a n g l e a n d t h e d i r e c t i o n o f tw i s ta r e p a r a m e t e r s t h a t a r e o u t s i d e t h e s c o p e o f th i s p a p e r . A l s o t h ef m e f f e c t o f t h e t a p e e l e m e n t s i s d e h ' b e r a t e l y s u p p r e s s e d . T h ef i n g e o m e t r y c o n s i d e r e d h e r e t h u s i m p a r t s a p e r i o d i c i t y t o t h eh e l i c a l f l o w . T h e o b j e c t i v e o f p r o v i d i n g f r e e s p a c e s b e t w e e nt w i s t e d - t a p e e l e m e n t s i s t o e x a m i n e w h e t h e r t h e p r e s s u r e d r o pa s s o c i a t e d w i t h t h e f u l l - l e n g t h t w i s t e d t a p e c a n b e r e d u c e d

w i t h o u t s e r i o u s l y i m p a i r i n g t h e h e a t t r a n s f e r a u g m e n t a t i o nr a t e s .L a m i n a r f l o w r e s u l t s o f e x p e r i m e n t a l i n v e s t i g a t io n s c a r r i e do u t w i t h w a t e r a s t h e w o r k i n g f l u id a r e r e p o r t e d . H e a t t r a n s f e rd a t a w e r e o b t a i n e d i n a n e l e c t r i c a l l y h e a t e d t e s t s e c t i o n g i v i n ga n a x i a l l y a n d c i r c u m f e r e n t i a l l y c o n s t a n t w a l l h e a t f l u x .E x p e r i m e n t s w e r e c o n d u c t e d o v e r t h e fo l lo w i n g r a n g e s o fi n d e p e n d e n t p a r a m e t e r s :R e y n o ld s n u m b e r 500


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L a min a r F lo w in a T u b e w i th T wis te d T a pe s 3 1 1

_ 1 2 .D I R E C T I O N IO F F L O W

t . . . Ai

!|;-A

T A P E

- T U B E

D I R E C T I O N O FF L O W

S E C T I O N A - A( a )

H " - : S _ _ H _ _

r T . - -(b)

Figu re 1 . ( a ) Layo ut o f a fu ll - length twisted- tape inse r t ins ide a c i r cu la r tube . (b ) Geom etry underinvestigation.

I n a ll t h e e x p e ri m e n t s , t w i s te d t a p e s w e r e m a d e o f 0 . 4 m mth ic k s t ain le ss s t e e l s tr ip , t h e w id th o f wh ic h wa s 1 m m le s sth a n th e in s id e d ia me te r o f th e t e s t s e c t io n ro b e . T h e s t rip sw e r e t w i s t ed o n a l a t h e b y m a n u a l r o t a ti o n o f t h e c h u c k . T h etwis t e d s t r ip s we r e h e a te d p e r io d ic a l ly b y f l a me to r e l a x th e

s t r e s s e s t o p r e v e n t t h e m f r o m b u c k l i n g a n d u n t w i s t i n g w h e nt h e y w e r e r e m o v e d f r o m t h e l at h e. T h e r o d e n d s w e r e s l o t t edto r e c e iv e th e tw i s t e d - t a p e e l e me n t s .T h e t e s t s e c t io n f o r p r e s s u r e d r o p t e s t s c o mp r i s e d a n a c r y l i c

t u be 1 . 85 m l o n g, 1 3 m m I . D . , a n d 2 0 m m O . D . . P r e ss u re

~ ~ " I

I I 0 j 1.6oo _ ~ o 3 6 20 0 ! e o o ~ 8 4 o ? s o ! s o 2 TA L L D I M E N S I O N S IN m m

Fig ure 2 . Exper imen ta l se tup . 1 , Ove rhead tank; 2 , leve l ind icator ; 2 , over f low to sump; 4 , rubberhose ; 5 , cen tr i fuga l pump; 6 , ro tamete r s ; 7 , r educer ; 8 , f lange ; 9 , ca lming sec t ion ; 10 , tes t sec t ion ;11, exit section; 12, r iser ; 13, f low outlet to sump; 14, needle valve.


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312 S .K . Saha e t a l .

Figu re 3. He at transfer test section. 1, Test tube; 2 , fiberglasstape insulation; 3, fiberglass insulated nichrome wire; 4, glasswool blanket insulation; 5, thin G.I. cylinder; 6, asbestos rope. ALL DIMENSION5 IN m mt a p s w e r e m a d e o f 3 0 m m l o n g , 3 m m I . D . , 4 . 5 m m O . D .ac ry l i c tube . T hreads we re cu t on one end o f the t aps , anddri l led holes on the tes t sec t ion were thread ed in ternal ly by ' 0 'BA taps . T he th readed po r t ion o f e ach p re s s u re t ap wascove red w i th T e f lon t ape be fo re i t was in s e r ted in to a t ap pe dhole on the tube to prevent leakage . Addi t ional ly , r ig idi ty ofthe t aps was ens u red by us ing Ara ld i t e . In a l l , 16 t aps we rep rov ided , the f ir s t s ix be ing 65 mm apa r t and the re s t 130 m mapa r t . T he p re s s u re t aps we re connec ted by f l ex ib le PVCtub ing to a manom e te r v i a a heade r (G . I . p ipe , 1 .25 m long ,25 . 4 mm nomina l d i ame te r ) .P re s s u re d rops we re meas u red by m eans o f a ve r t i c a l U- tubema nom eter with dibutyl phthala te (sp . gr . 1 .047) as themanome t r i c f lu id . T h i s ens u red a rea s onab ly accu ra te mea -s u remen t o f the low p re s s u re d rops encoun te red a t l owR eyno lds numbers .

The heat t ransfer tes t sec t ion is shown in Fig . 3 . I tcompr i s ed a 1 . 84 m long , 11 mm I . D . , and 12 m m O. D .s tainless s tee l tube (304 SS). The tu be was un iform ly heated bypass ing a l te rnat ing current f ro m a s tabi l ized three-ph ase sourceth rough 30 SW G n ich rome w i re hav ing 16 oh rns /m re s i s tancewound a round the tube . T he u ich rom e wi re was cove red w i thfiberglass insula t ion. To k eep the current to less than 2 A , thehea te r was made in th ree s ec t ions , e ach s ec t ion hav ing fou rpa ra l l e l hea te r s . Au to t rans fo rmers we re us ed to regu la t e theheat f lux suppl ied to the tes t sec t ion.Coppe r (30 SWG) -cons tan tan the rmocoup le s we re us ed tomeas u re the ou t s ide wa l l t empe ra tu re o f the tube . T hethe rmocoup le s we re s i lve r s o lde red and were t aken f i r s tth rough a pe r iphe ra l g roov e abou t 5 mm long and then rad ia l lyout through the heater wire turns and the insula t ion tha ts u r rounded the t e s t s ec t ion . T wen ty -one thennocoup le s we rep rov ided on the ou t s ide wa l l o f the tube . T he f i r s t s even werel o ca t ed 1 0 m m , 5 5 m m , 1 00 m m , 1 55 m m , 2 1 0 r a m , 2 6 5 m m ,and 320 m m f ro m the po in t whe re hea t ing s t a r ted . T he rea f t e rthe rema in ing the rmocoup le s we re p laced 110 mm apa r t .T ow ard the downs t ream end o f the t e st s ec t ion , t h ree the rmo -coup le s we re p laced a long the pe r iphe ry o f the tube to meas u rethe c i rcumfe ren ti a l t empe ra tu re va r i a t ion , wh ich was found tobe negligible.Ax ia l conduc t ion lo s se s we re p reven ted b y us ing po ly te tra -f luorce thylene spacers pos i t ioned between brass f langes . Ther ad ia l hea t l o s s was m i n i ~ by wi nd ing asbes to s rope (100m m ove ra l l d i ame te r ) and pu t ting a g l a s s woo l b l anke t (50 m mth ick ) a round the a s bes tos rope . T he a s bes tos rope was w ound

on a G . I . cy l inde r ( s p l it i n two ha lves ) 70 mm in d iame te r toprotec t the e lec tr ica l connect ions . The space between theheater wire and the G. I . cyl inder was a lso f i l led with glasswoo l .

T he the rmocoup le ou tpu t was meas u red by a 5 . 5 d ig i tHewle t t -Packa rd d ig it a l mu l t ime te r hav ing a 1 pV re s o lu t ionvia a 36-point se lec tor switch. The pow er input was ca lcula tedf rom m eas u red va lue s o f the vo l t age and re s i st ance . T hecur ren t was a l s o meas u red to p ro v ide a c ros s -check .T he in l e t and ou t l e t wa te r bu lk t empe ra tu re s we re a l s omeas u red by the rmocoup le s . T he in l e t bu lk t empe ra tu re wasmeas u red by one the rmocoup le , whe rea s the ou t l e t bu lktempera tu re was meas u red by means o f two the rmocoup le ss t a tioned 150 mm apa r t i n the m ix ing s ect ion . T he ave rag e o fthe two read ings was t aken a s the t rue bu lk t em pe ra tu re a t t heou tl et . T he f in e f fec t o f the t apes was s uppre s s ed by cove r ingthe edges of the tapes with an insula t ing tape .

O P E R A T I N G P R O C E D U R EP r e s s u r e D r o p T e s t sT he p re s s u re d rop t e s t s we re pe r fo rmed in the ac ry l i c tube .T he fu l ly deve loped f r i c tion fac to r was de fm ed a s

f i = ~ [ ( A P z ) / P O 2 ] ( D i / z ) (1 )where

0 m/pAc (2 )and AP z i s the p re s s u re d rop o ve r a l eng th z .T he p re s s u re t aps on the tube w e re s o loca ted tha t i n the ca s eo f regu la r ly s paced tw i s t ed t apes the d i s t ance be tween the t apscove red e i the r the l eng th H o f the t ape e l emen t o r the l eng th Hof the t ape e l emen t p lus the s pace S be tw een two cons ecu t ivetape e l emen t s . T hus the deve lopmen t l eng th fo r the pe r iod i -ca l ly he l ica l f low could be ident i f ied .For regu la r ly s paced tw i s t ed - t ape e l emen t s , t he f low wasfound pe r iod ica l ly fu l ly deve loped , and the fu l ly deve lopedpre s s u re g rad ien t was typ ica l ly meas u red ove r the l a s t t h reecyc le s (each cyc le cons i st ing o f one t ape modu le and one s pacemodule) to ca lcula te the ful ly developed fr ic t ion fac tor .Be fo re the p re ss u re d rop m eas u remen t s we re t aken , the t e s ts ec tion was f reed o f a i r bubb le s by ven t ing them th rough ther i s e r s ec tion a t t he end o f the t e s t s ec t ion . F low was t aken f rom


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Lam inar Flow in a Tub e with Twisted Tape s 313the ove rhead t ank whe re a cons tan t wa te r l eve l was ma in -t a ined . T yp ica l ly 5 min was requ i red fo r s e t t l emen t o f f lowaf te r e ach change o f mas s f low ra t e . P re s s u re d rops we remeas u red by a manom e te r , and mas s f low ra te s we re meas u redby a ro tame te r . T h e ro tame te r was ca l ib ra t ed and was found toread accura te ly within : t: 3 %.H e a t T r a n s f er T e s t sT he hea t t r ans fe r t e s t s we re pe r fo rmed in the s t a in le s s s t e e ltube . T he l eng th -ave raged Nus s e l t numb er was de f ined a s

N u ' K D i ( x - -- ~ - ~ /L ) ( L o T ~ - T b z , ] \ k ] (3)w h e r e

Q = V 2 R = r n C p ( T b o - T b s ) ( 4 )In mos t c a s e s , t he va lue s o f Q ca lcu la t ed by the two m e thodsin E q . (4 ) ag reed to w i th in 3 %. I f t he d i s ag reemen t exceeded5 %, the da ta we re d i s ca rded . T he a r i thme t i c mean o f the twova lues o f Q was t aken a s the t rue va lue . T he w a l l t empe ra tu reT ~ a t any z in E q . (3) was d i rec t ly meas u red , w he rea s T b~ wasobta ined by in terpola t ion. Al l f lu id propert ies were evaluated

a t (Tbi + Tbo)/2 . A the rm a l s t e ady s t a te was gene ra l ly reachedin 20 -25 ra in .An uncerta inty analys is conducted a long the l ines sugges tedby Kl ine and M cCl in tock [7 ] s howed tha t t he unce r t a in t i e sinvo lved in the f r i c t ion fac to r s we re w i th in 5 % whe rea s thos einvo lved in the e s t ima t ion o f Nus s e l t num ber w e re w i th in 2 %.R E S U L T S A N D D I S C U S S IO N

C o n f i r m a t o r y T e s tsBe fo re the re s u l ts fo r the ca s e o f r egu la r ly s paced tw i s t ed t apesa re repor t ed , da ta a re p re s en ted fo r thos e ca s e s fo r wh ich we l l -es tabl ished corre la t ions are avai lable . These cases are1. Flow in a p la in tube2. Flow in a tube with ful l - length twis ted-tape insertsThe es tabl ished corre la t ions for these cases are as fol lows .

P l a i n T u b eJ~= 16/Rei

From Ref . 8 ,N u i = 4.364 + 0.2633 ( z * ) - " 5 6 e x p ( 4 1 . 0 z * ) ,

(S )

z * > 0 . 0 0 1 5( 6 )

S t r a i g h t T a p e ( y = o % s = 0 ) F r o m R e f . 9 ,2~ = 46.45/Re~ (7)

F r o m R e f . 3 ,Nui = 4.405 [1 + 0.0517 (Z *) - 1.5]0-333 Z * < 0 . 0 3 5 ( 8 )

T wis ted T a p e ( y < ~ , s = 0 ) [ 3 ]f i / f e = [1 + (Re J 70 y 1.3)1.5]0.333 (9 )

w h e r e

an d

3.0949(0.9692 + ~ r / 2 G ) 2fe = Re~ (2y 2/x )(G - 1) - 0.03077] 3 (10)

G = (4y 2 + x 2 ) / 2 y (11)An add i tiona l co r re la t ion ba s ed on the num er ica l r e s u lt s o fDa te [5 ] w i th the co r rec t ion fo r t ape th i cknes s s ugges ted byShah and London [9] is

= 46.45/Re~, R e J y


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3 1 4 S . K . Saha et a l .

F i g u r e 4 . F r i c t i o n f a c t o r d a t a f o r t h e p l a in t u b e a n d t h es t r a ight t ape .

0 .20

0.100.08

0 " 0 50 .040 .03

0 ,02

0.010 " 0 0 8

0 . 0 0 5

0 , 0 0 3

l i I I I ! I I

5TRAtGHT TAPEI o PLA IN TUBE

~ y : o o ~ s = O( e q n . 7 )

( e q n , 5 ) -J

6 1 D i = 4 I 1 3 0

I I i i i I I Ix 102 5x lO 2 I03

R e i3 x 1 0 3

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o~ O vO /y&0 ~ ..o 6 A ~ - - 3 .1 ,6o

0 ~ ~ 5-0V - - 7 . 5O - - 1 0 . 0

I I I f f I I I i I3 0 4 0 5 0 6 0 7 0 8 0 9 0 I 0 0 1 5 0 2 0 0

R e i / y l " 3F i g u r e 5 . F r i c t io n f a c t o r d a t a f o r f u l l- l e n g t h t w i s t e d t a p e ( s = 0 ) .

I3 0 0 4 0 0


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L a m i n a r F l o w in a T u b e w i t h T w i s t e d T a p e s 3 1 5

z

1.5

1 3x 10 2

i I I I I Iy =a % ~ s = O - - I

~ 0 0/ 0 0 .

: . . . . . I( e q n , 6 )

P r ~ 5~ / D i = 4 1 1 1 0

l I I I l I I i5 x 1 0 2 1 0 3 2 x l ,

R e i

F i g u r e 6 . N u s s e l t n u m b e r d a t a f o r t h e p l a i n ro b e a n d t h e3 s t r a ight t ape .

z

, t: f3 0

2 0

15lO

I I I I I w I I l I I l I ! | I I | I | I I I

s = O ~ 1 0 i = 4 1 1 1 0

A A 6 A- ( e q n . 1 6 ) _ V A ~ V A

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I l I I a I l I i I i I I I I I3 x 1 0 3 6 x l0 3 10/~ 3 x 1 04 6 x 1 0 4 1 0 5 3 x l0 S

R e s ) 1 . 7 8P r ( TF i g u r e 7 . N u sse l t n u m b e r d a t a f o r f u ll - l e n g th t w i s t e d t a p e ( s = 0 ) .

I I I !

7 x D $


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3 1 6 S . K . S a h a e t a l .32

280

24 0

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A - R e i : 9 9 5 . ~ ' ( . ~ "O - R e i = 1741 J " "

" = o

I I i I i I i i i i i i i I I I200 400 600 80 0 !000 1200 14 O0 1600Z ( m m )

Figure 8 . A x i a l p r e s s u r e d r o p r e s u l t s f o r a t y p i c a l c a s e o f y = 1 0 a n d s = 1 0 .

R e s u l t s f o r R e g u l a r l y S p a c e d T w i s t e d T a p e sA x i a l V a r i a t io n of Pressure F i g u r e 8 s h o w s t y p i c a l p r e s -

s u r e d r o p m e a s u r e m e n t s f o r t w o d i f f e re n t R e y n o l d s n u m b e r sf o r y = 1 0 a n d s = 1 0. T h e p r e s s u r e d r o p d a t a h a v e b e e np l o t t e d i n m i l l i m e t e r s o f m a n o m e t r i c f l u i d to d e m o n s t r a t e w i t hc l a r i t y t h e n a t u r e o f v a r i a t i o n o f t h e a x i a l p r e s s u r e d r o p . I t i so b s e r v e d t h a t t h e p r e s s u r e v a r i e s l i n e a r l y b e y o n d a c e r t a i na x i a l l e n g t h . F o r e x a m p l e , a t R e i = 1 7 4 1 , t h e d e v e l o p m e n tl e n g t h i s f o u n d a s z = 9 0 0 r a m , a n d a t R e i = 9 9 5 , z = 6 5 0m m , o r ( z / D i ) / R e i = 0 . 0 3 9 7 6 a n d 0 . 0 5 0 2 5 , r e s p e c t i v e l y .T h e s e f i g u r e s s u g g e s t t h a t i n t h e c a s e o f r e g u l a r l y s p a c e dt w i s t e d - t a p e e l e m e n t s , t h e d e v e l o p m e n t l e n g t h f o r a g i v e n ya n d s i s a f u n c t i o n o f R e y n o l d s n u m b e r . F o r a p l a i n t u b e , t h ed e v e l o p m e n t l e n g th i s 0 . 0 5 D ~ R e / , a n d D a t e [ 1 0 ] h a s s h o w nt h a t th e d e v e l o p m e n t l e n g t h is s h o r t e r f o r f u l M e n g t h t w i s t e dt a p e s . T h u s , t h e o r d e r s o f m a g n i t u d e o f t h e d e v e l o p m e n tl e n g t h s m e a s u r e d h e r e a r e i n a c c o r d w i t h e x p e c t a t i o n . S i m i l a rt r e n d s h a v e a l s o b e e n o b s e r v e d a t o t h e r v a l u e s o f y a n d s .

F r i c t i o n F a c t o r R e s u l t s F i g u r e s 9 a , 9 b , 9 c , a n d 9 d s h o wt h e v a r i a t io n o f f r i c t i o n f a c t o r w i t h R e y n o l d s n u m b e r f o r y =1 0 , 7 . 5 , 5 , a n d 3 . 4 6 , r e s p e c t i v e l y , a n d d i ff e r e n t v a l u e s o f s . I t

i s t o b e n o t e d t h a t d a t a f o r s = 0 c o r r e s p o n d t o th e f u l l - l e n g t ht w i s t e d t a p e .

F o r f i n i t e v a l u e s o f y , t h e f r i c t i o n f a c t o r i n c r e a s e s a s t h es p a c i n g b e t w e e n t h e t a p e e l e m e n t s is r e d u c e d . H o w e v e r , t h ec a s e o f s = 0 i s n o t n e c e s s a r i l y a l i m i t i n g c a s e o f t h e s p a c ed i s t a n c e . T h i s i s a p p r e c i a t e d f r o m t h e f a c t t h a t f r i c ti o n f a c t o r sf o r f i n i te s c a n b e e i t h e r l a r g e r o r s m a l l e r t h a n t h o s e f o r t h ec a s e o f s = 0 . I t w o u l d n o r m a l l y b e e x p e c t e d t h a t f o r a l l s > 0 ,t h e f r ic t i o n f a c t o r s h o u l d b e l o w e r t h a n t h a t f o r s = 0 , s i n c e t h ea m o u n t o f s o l i d s u r f a c e o f f e r i n g r e s i s t a n c e t o f l u i d f l o w i sr e d u c e d . T h i s e x p e c t a t i o n i s s u b s t a n t i a l ly s a ti s f i e d f o r s = 1 0f o r a l l v a l u e s o f y a n d f o r s = 7 . 5 f o r y = 1 0 a n d y = 7 . 5 .H o w e v e r , f o r y < 5 a n d f o r s = 5 a n d s = 2 . 5 , t h e v a l u e s o ff r i c t io n fa c t o r , i n f a ct , e x c e e d t h o s e f o r s = 0 . T h i s s u g g e s t st h a t t h e p r e s s u r e l o s s a s s o c i a t e d w i t h t h e m o m e n t u m c h a n g et h a t o c c u r s w h e n t w o n o n a x i s y m m e t r i c v e l o c i t y p r o f i le si s s u i n g f r o m t h e t w i s t e d - t a p e e l e m e n t s e c t i o n m i x i n t h ed e c a y i n g s w i r l s e c t i o n i s m u c h g r e a t e r t h a n t h e p r e s s u r e l o s st h a t w o u l d h a v e b e e n e n c o u n t e r e d h a d t h e t a p e b e e n p r e s e n t .A l s o , t h e l e a d i n g - e d g e l o s s e s a s s o c i a t e d w i t h t h e t w i s t e d - t a p es e c t i o n c a n b e c o n s i d e r a b l e . S i n c e f r i c t i o n f a c t o r s f o r d e c a y i n gs w i r l s i n t h e e n t r a n c e l e n g t h a r e q u i t e l a r g e , t h e s e e x p e r i m e n t a l


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318 S . K . Saha e t a l .r e s u l ts c a n , in f a c t , b e e x p e c te d , p a r t i c u la r ly f o r s ma l l v a lu e so f s . F o r l a r g e s , wh e r e th e s w i r l p e r h a p s d e c a y s mo r es u b s ta n t i a l ly , t h e a s s o c ia t e d mo me n tu m- c h a n g e p r e s s u r e lo s sd o e s n o t e x c e e d th e p r e s s u r e lo s s d u e to f r i c t io n th a t wo u ldh a v e b e e n e n c o u n te r e d w i th th e f u l l - l e n g th t a p e .

T h e a b o v e - me n t io n e d fig u r e s s h o w a n o th e r imp o r ta n t r es u l t .A t r a n s i t io n l ik e v a r i a t io n o f f r i ct io n f a c to r i s o b s e r v e d f o r f u l l -l e n g th tw i s t e d t a p e s ( s = 0 ) f o r Re y n o ld s n u mb e r s o f 1 3 0 0 -1 5 0 0 . A l th o u g h th e c r i t i c a l Re y n o ld s n u mb e r f o r a p l a inc i r c u la r tu b e i s a b o u t 2 3 0 0 , a s o me wh a t lo we r c r i t i c a lRe y n o ld s n u mb e r i s e x p e c te d f o r th e s w i r l in g f lo w in an o n c i r c u la r d u c t [ 6 ]. F o r f in it e v a lu e s o f y , h o w e v e r , t h et r a n s it io n a p p e a r s to b e a t s o me w h a t h ig h e r Re y n o ld s n u m b e r swh e n s i s l a r g e a n d a t s ma l l e r Re y n o ld s n u m b e r s w h e n s i ssmall .

N u s s e l t N u m b e r R e s u l t s F ig u r e s 1 0 a , 1 0 b , 1 0 c , a n d 1 0 ds h o w th e v a r i a t io n o f Nu i w i th Re i f o r d i f f e r e n t v a lu e s o f s a t y= 1 0 , 7 . 5 , 5 . 0 , a n d 3 . 1 8 , r e s p e c t iv e ly . I t i s a l s o s ee n f r o mth e s e f ig u r e s th a t s = 0 d o e s n o t s ig n i f y a l imi t in g c a s e o f fin i tes p a c in g s ( s > 0 ) b e twe e n th e tw i s t e d - t a p e e le me n t s ; N u s s e l tn u mb e r s f o r s > 0 a r e f o u n d to b e b o th g r e a te r a n d s ma l l e rth a n th o s e fo r s = 0 .F ig u r e s 1 0 a a n d 1 0 b s h o w te n d e n c ie s s imi la r to th o s ed i s c u s s e d in re l a t io n to th e f r ic t io n f a c to r r e s u lt s . Ho we v e r , t h er e s u lt s f o r y _< 5 a re wo r th o b s e r v in g . He r e i t is s e e n th a tc o m p a r e d to th e f u l l -l e n g th tw i s t e d t a p e ( s = 0 ) th e Nu s s e l tn u m b e r i s g r e a te r f o r a ll v a lu e s o f s , w h e r e a s F ig . 9 c s h o ws as ma l l e r f r ic t io n f a c to r f o r l a r g e r v a lu e s o f s ( s > 5 ) a n d h ig h e rRe y n o ld s n u mb e r s . F u r th e r , t h e in c r e a s e in h e a t t r a n s f e r i sg r e a te r th a n th e in c re a s e in p r e s su r e d r o p . T h e t a p e w i th y =3 . 1 8 d o e s n o t s e e m t o p e r f o r m b e t t er t ha n t he t ap e w i t h y = 5f o r a n y s in t e r ms o f Nu s s e l t n u mb e r . Ho we v e r , t h e f r i c t io nf a c to r in c r e a se s f o r s _ 5 w i th y = 3 . 4 6 i s l e s s th a n th a t w i th y= 5 . T h i s o b s e r v a t io n i s p a r t i c u la r ly t r u e a t h ig h e r R e y n o ld sn u mb e r s .T h u s in l a min a r f lo w , c o mp a r e d to v a lu e s a c h ie v e d w i thf u l l - l e n g th tw i s t e d t a p e s , a r e d u c t io n in p r e s s u r e d r o p w i tha u g m e n ta t io n in h e a t tr a n s f e r i s p o s s ib le w i th r e g u la r ly s p a c e d

twis t e d - ta p e e l e me n t s a t s ma l l e r v a lu e s o f y ( _< 5 ) a n d l a r g e rRe y n o ld s n u m b e r s ( Re i > 1 0 0 0 ) .C O R R E L A T I O N S

T h e c o r r e l a t io n s f o r r e g u la r ly s p a c e d tw is t e d - t a p e e l e me n t sh a v e b e e n d e v e lo p e d o n th e b a s i s o f th o s e th a t a r e we l la c c e p te d f o r f u l - l e n g th tw i s te d t a p e s . T h u s wh e n s = 0 th ec o r r e l a t io n s f o r r e g u la r ly s p a c e d tw is t e d - t a p e e l e me n t s a u to -ma t i c a l ly r e d u c e to th e c o r r e l a t io n s f o r f u l l - l e n g th tw i s t e dta p e s . T h e l e a s t s q u a r e s c u r v e - f i t ti n g me th o d h a s b e e n u s e d tod e v e lo p th e c o r r e l a t io n s .C o r r e l a t i o n s f o r F r ic t i o n F a c t o rCo r r e la t io n s h a v e b e e n d e v e lo p e d o n th e b a s i s o f th o s e o f S h a ha n d L o n d o n [ 9 ]. T h e y a r e v a l id f o r

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p o w e r r e q u i r e me n t s o f e x i s t in g h e a t e x c h a n g e r s ( h a v in g f u l l-l e n g th tw i s t e d t ap e s ) w i th o u t a r e d u c t io n in h e a t d u ty . T h e h e a tt r a n s f e r r a t in g o f a n e x i s tin g c o m p a c t h e a t e x c h a n g e r c a n a l s ob e i m p r o v e d w i t h o u t an i n c r e as e i n p u m p i n g p o w e r .

C O N C L U S I O N S1 . E x p e r ime n ta l d a ta o n l a min a r f lo w f r i c t io n f a c to r a n dN u s s e l t n u m b e r h a v e b e e n p r e s e n t e d f o r t h e c a s e o f ac i r c u la r tu b e f i t t e d w i th r e g u la r ly s p a c e d tw is t e d - t a p ee le me n t s .2 . I t is s h o wn th a t p r e s s u r e d r o p a n d h e a t t r a n s f e r c h a r a c te r i s -t i c s a r e s u c h th a t th e c a s e o f fu l l - l e n g th tw i s t e d t a p e ( s = 0 )i s n o t a l imi t in g c a s e o f th e g e o me t r y w i th r e g u la r ly s p a c e d

twis t e d - t a p e e l e me n t s ( f in i t e s ) . F r i c t io n f a c to r a n d N u s s e l tn u m b e r f o r s > 0 c a n b e b o th g r e a te r a n d s ma l l e r th a n f o r s= 0 . T h i s i s b e c a u s e th e p r e s s u r e lo s s e s a s s o c ia te d w i th th ed e c a y i n g n o n a x i s y m m e t r i c s w i f t i n t h e s p a c e b e t w e e n t a p ee le me n t s c a n , u n d e r c e r t a in c i r c u ms ta n c e s ( in th e c a s e o fs ma l l s ) , b e g r e a te r th a n th e p r e s s u r e d r o p th a t wo u ld b ee n c o u n t e r ed i f t h e s a m e s p a c e l e ng t h w e r e o c c u p i e d b y atw is t e d t a p e . S imi la r a r g u me n t s a p p e a r to a p p ly w i thr e s p e c t to th e h e a t t r a n s f e r r e s u l t s wh e r e th e f lu id mix in ge f f e c t in th e s p a c e r e g io n a p p e a r s to b e g r e a te r th a n wo u ldh a v e b e e n a c h ie v e d i f a tw i s t e d t a p e we r e p r e s e n t .3 . F o r s > 7 . 5 , t h e me a s u r e d f r i c t io n f a c to r i s a lwa y s f o u n d tob e l es s th a n th e v a lu e f o r s = 0 . A l th o u g h a t y = 1 0 a n d y= 7 . 5 th e r e i s a c o r r e s p o n d in g r e d u c t io n in th e Nu s s e l tn u m b e r , t h i s r e d u c t io n i s s ma l l e r th a n th a t o b s e r v e d f o r th ef r i c t io n f a c to r . A t y _< 5 , o f c o u r s e , t h e r e i s a n imp r o v e -me n t in h e a t t r a n s f e r . T h u s i t c a n b e c o n c lu d e d th a tr e g u la r ly s p a c e d tw is t e d - t a p e e l e me n t s a p p e a r to b e mo r ea t t r ac t ive than fu l l - length twis ted tapes in ce r ta in s i tua t ions .4 . T h e p r o p o s e d c o r r e l a t io n s p r e d ic t t h e e x p e r ime n ta l d a ta f o rf r i c t io n f a c to r a n d Nu s s e l t n u mb e r s a t i s f a c to r i ly .5 . O n t h e b a s is o f c o n s t an t p u m p i n g p o w e r a n d c o n s t a n t h e a td u ty , r e g u la r ly s p a c e d tw is t e d - t a p e e l e me n t s a r e f o u n d top e r f o r m s ig n i f i c a n t ly b e t t e r th a n f u l l - l e n g th tw i s t e d t a p e s .

The present s tud y was sponsored by the Coun cil of Scientif ic andIndustrial Research, Governm ent of Ind ia, through g rant CSIR 23(158)/86-EMR-II.

N O M E N C L A T U R EAc f lo w c r o s s - s e c t io n a l a r e a , m 2D~ in te r n a l d i a m e te r o f th e t e s t t u b e , n u n

Dh h y d r a u l i c d ia me te r o f th e t e s t t u b e , m md r o d d i a m e t e r , m mf f u l ly d e v e lo p e d fr i c t io n f a c to r b a s e d o n in te r n ald ia me te r o f th e tu b e , d ime n s io n le s sH p i t c h f o r 1 8 0 " r o ta t io n o f tw i s t e d t a p e , m mh le n g th - a v e r a g e d h e a t t r a n s f e r c o e f f i c i e n t , W / ( m 2K )k f l u id t h e r m a l c o n d u c t i v it y , W / ( m K )L l e n g th o f th e t e s t s e c t io n , mr n ma s s flo w r a t e o f th e f lu id , k g / s

N u i a x i al l y a v e r a g e d N u s s e l t n u m b e r b a s e d o nin te rn a l d i a m e te r o f th e tu b e , d ime n s io n le s sA P z p r e s s u re d r o p o v e r a l e n g t h z , N / m 2

P r P r a n d t l n u m b e r o f th e f lu id , d ime n s io n le s sQ h e a t in p u t to th e t e s t s e c t io n , WR r e s i s ta n c e o f th e h e a te r e l e me n t , o h m s

R e i R e y n o l d s n u m b e r b a s e d o n in t e rn a l d i a m e t e r o fth e tu b e , d ime n s io n le s sR es s w i f t f l o w R e y n o l d s n u m b e r [ = ( 4 m h r ) ( D i -4 / i ) ] , d ime n s io n le s s

S s p a c e l e n g th , ms s p a c e r a t io ( = S / D ~ ) , d ime n s io n le s s

Tbi i n l e t b u lk m e a n t e mp e r a tu r e o f th e f lu id , * CT bo o u t l e t b u lk me a n t e mp e r a tu r e o f th e f lu id , * C

O f lu id me a n a x ia l v e lo c i ty , m/sV v o l t a g e o u tp u t f r o m th e a u to s ta t, Vy tw is t r a t io ( = H / D i ) , d ime n s io n le s sz ax ia l leng th , m

z * n o n d im e n s io n a l a x ia l l e n g th [ = z / ( D s Re i P r ) ] ,d ime n s io n le s s

G r e e k S y m b o l st a p e th i c k n e s s , mm0 p h a s e a n g le , d e gp f lu id d e n s i ty , k g / m 3# f lu id v i s c o s i ty , k g / ( m s )

REFERENCESI. Bergles, A. E ., Techniques o Augmen t Heat Transfer, in Handbookof Heat Transfer Applications, 2nd ed., W . M. R ohsenow , J. P.Hartnett, and E. N . C ranic, Eds., pp. 3.1-3.80, McCn'aw-Hill, NewYork, 1985.2. Ho ng, S. W ., and Bergles, A. E. , Augmentation of Laminar Flow


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322 S . K . S a h a e t a l.Hea t T r ans f e r i n T ubes by M eans o f T wis t ed - T ape I ns er ts , . L H e a tTransfer , Trans. A SM E , 9g(2) , 251-256, 1976.

3. du Plessis , J . P . , L amin ar Flow and Hea t Transfer in a Smooth Tubewith a Twis ted-Tape Inser t , Ph.D. Thes is , Un ivers i ty of Stel len-bosch, South Afr ica, 1982.

4. Sukhatme, S. P. , Gai tonde, U. N. , Shidore, C. S. , and Kunc ol ienkar ,R. S. , Forced Convect ion Heat Transfer to a Viscous Liquid inL aminar F low in a T ube wi th a T wis t ed T ape , 9 th Nat iona l Hea t andM as s T r ans f e r C onf er ence , I . I . Sc . , B anga lo r e , I nd ia , Paper No .HM T 7-87, 1987.

5. Date, A. W. , Predict ion of Ful ly-Developed Flow in a TubeContaining a Twis ted-Tape, In t . J . Heat Mass Transfer , 17(8),845-859, 1974.

6. Nandakumar, K. , and Masl iyah , J . H. , Sw ir l Flow Genera ted byTwis ted Pipe and Tape Inser ts , in E n c y c l op e d i a o f F l u i d M e c h a n -ics, N. P. Cherem is inoff , Ed. , Vol . 2 , pp. 691-706 , Gu lf Publ . Co. ,Hous ton, Tex. , 1986,

7. Kl ine, S. J . , and McClintock, F. A. , Descr ibing Unce r taint ies inSingle Sample Exper iments , M e c h . E n g . , 75, 3-8, 1953.

8 . Gr igu l l, U . , and T r a t z , H . , T her mis eher E in l auf i n Aus geb ide te rL aminar R ohr s t r omung , In t . J . Heat Mass Transfer , 8 , 6 6 9 - 6 7 8 ,1965.

9 . Shah , R . K. , and L ondon , A. L . , L am inar F low For ced C onvec t ion inDucts , in Ad va n ces in Hea t Tra n s fe r , Vol. 1, Suppl. 1, T. F. Irvine ,J r . , and J . P . Har tnet t , Eds . , pp. 379-381, 1978.

10. Date, A. W . , Predict ion of Fr ict ion and Heat Transfer Character is t icsof Flow in a Tube Containing a Twis ted-Tape, Ph.D . Thes is , Impe r ialCol lege, Univers i ty of Londo n, 1972.

11. Bergles, A . E. , Blumenk rantz, A. R. , and Taborek , J ., Perform anceEvaluat ion Cri ter ia for Enhan ced Heat Transfer Surfaces, Prec. Int .Hea t and M as s T r ans f e r C onf er ence , Vo l . 2 , pp . 239- 243 , 1974.

Received Novem ber 15, 1988; revised Febru ary 6, 1989

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