esferas congeladas

8/18/2019 esferas congeladas

1/5

H ea t transfer characteristics d urin g air precooling of strawberries

D . R . G i i e m e s , M . E . P i r o v a n i a n d J . H . D i P e n t i m a

I n s t i t u t o d e T e c n o l o g i a d e A l i m e n t o s , U n i v e r s i d a d N a c i o n a l d e l L i to r a l , C . C o r r e o s 4 2 8 ,

3 0 0 0 S a n t a F e , A r g e n t i n a

R e c e i v e d 6 J a n u a r y 1 9 8 8 ; r e v is e d 1 8 J u l y 1 9 8 8

He at transf er chara cteristics during air prec oolin g of strawberries were studied. Effective surface hea t transfer

coefficients were determ ined an d a

N u - R e

correla t ion w hich includes the effect of mois ture e vapor at ion w as

developed. The m ean value of f ilm coefficients obtaine d for s t rawberries were 16 to 25 ~ higher than those

pred ic ted by the cor re la tion o f McA dam s for sphe res coo led on ly by convec t ion . F ur the rm ore , a geom et ry

analysis fo r strawberries was carried ou t when de term ining surface heat transfer coefficients. It was conclu ded

that for pract ical appl icat ions s t rawberries may be acceptably considered as spheres, s ince correct ion for

anomalous shape does not cause significant differences.

Keywords: foo d products;hea t transfer; precooling;strawberries)

C a r a c t e r i s t i q u e s d u t r a n s f e r t d e c h a l e u r a u c o u r s d e l a

p rrr f rigrrat ion p a r a i r d e s f ra i ses

n a btudib les caract~ristiques du tran sfert de chaleu r au cours de la prbrbfrigbration p ar air des fraises. L es

coefficients effecti fs d e transfe rt de chaleu r superficiel on t btb d~terminbs e t une corrblation N u - R e c ompr e nan t

l ' influence d e l '~vaporation d'eau a btb btablie. La valeur mo yen ne des coefficients pell iculaires obte nus po ur les

fraises b ta i t supbrieure d e 16 ~ 25 ~ ce lle pr~vue par la corrblat ion de M c Ad am s pour des sphbres re froid ies par

convect ion pure . D e plus , une analyse gbom~tr ique des f ra ises a ~tb e ffectube en dbterminant les coef fic ients de

transfe rt de chaleur superficiel . O n a conclu que pour les applications pratiqu es les frais es pouv aient ~tre

considbrbes de fa fon acceptable com me des sphbres puisque la correc t ion pour les forme s anorma les ne donne pas

de diffbrences significatives.

(Mots cl~s: produits alimentaires; transfert de chaleur; p rrr6frigrration; fraises)

T h e f re e z in g o f s t r a w b e r r i es b y I Q F t e c h n o l o g y

( i n d i v i d u a l l y q u i c k f r e e z in g ) p r e s e n t s s o m e d i f f i cu l t ie s d u e

t o t h e t e n d e r n e s s a n d h i g h p e r i s h a b i l i t y o f t h e s e f r u i t s 1 .

T h e r e f o r e , t h e r e i s a t r e n d t o p r e c o o l t h e m i n o r d e r t o

i n c r e a se t h e i r f ir m n e s s , t o p r o d u c e a h i g h q u a l i t y p r o d u c t .

P r e c o o l i n g i m p r o v e s e f fi c ie n c y o f t h e f r e ez i n g o p e r a t i o n ,

a n d f r e e z e r c a p a c i t y i s i n c r ea s e d d u e t o s h o r t e r d w e l l

t im es .

A w a y t o a t t a i n t h a t p u r p o s e i s t o u s e a t u n n e l w h e r e a i r

i s f o r c e d u p t h r o u g h t h e s t r a w b e r r i e s m o v i n g

c o n t i n u o u s l y o n a b e l t c o n v e y o r . W h e n f r u it s a r e

p r e c o o l e d b y t h i s m e t h o d , h e a t i s r e m o v e d b y c o n v e c t i v e

h e a t t r a n s f e r f r o m t h e p r o d u c t s u r f a c e t o t h e c o o l i n g

m e d i u m w h i l e m o i s t u r e e v a p o r a t i o n p r o d u c e s a n

a d d i t i o n a l c o o l i n g e f f e c t2-4.

H e a t t r a n s f e r c h a r a c t e r i s t i c s d u r i n g a i r - c o o l i n g o f

s t r a w b e r r ie s a r e i m p o r t a n t f o r a p r o p e r d e s i g n

a n d

o p e r a t i o n o f s u c h s y st e m s . E m p i r i c a l e q u a t i o n s t o p r e d i c t

s u r f a c e h e a t t r a n s f e r c o e f f i c i e n t s a r e o n l y v a l i d w h e n h e a t

t r a n s f e r i s b y c o n v e c t i o n 5 .

T h e b e s t w a y t o a c c o u n t f o r th e e v a p o r a t i o n c o o l i n g

e ff e ct i s t h r o u g h a s e p a r a t e f u n c t i o n b a s e d o n t h e

e v a p o r a t i o n c o e f fi c ie n t f o r t h e

p r o d u c t a n d

t h e

t e m p e r a t u r e a n d h u m i d i t y o f t h e a ir . H o w e v e r , t h is is

m o r e c o m p l i c a t e d a n d i s h a r d e r t o c o m m u n i c a t e t o t h e

r e f r i g e r a t i o n i n d u s t r y . H e n c e , e f f e c ti v e s u r f a c e h e a t

t r a n s f e r c o e f f i c i e n t s w h i c h i n c l u d e t h e e f f e c t o f m o i s t u r e

e v a p o r a t i o n w e r e p r o p o s e d . A p r o b l e m w i t h t h e e f fe c ti v e

' h ' is t h a t i t c h a n g e s w i t h t h e h u m i d i t y l ev e l o f t h e c o o l i n g

a i r . T h i s i s n o t a s c r i t i c a l w i t h s i n g l e p r o d u c t s a s i t i s w i t h

p r o d u c t s i n b u l k o r l a r g e c o n t a i n e r s .

E f f e c ti v e v a l u e s o f s u r f a c e h e a t t r a n s f e r c o e f f i c ie n t s (h )

o r

N u - R e

t y p e c o r r e l a t i o n s f o r t h e c o o l i n g o f m a n y f r u it s

a n d

v e g e t a b le s h a v e b e e n r e p o r t e d 6 -a . H o w e v e r , d a t a

r e f e r r e d t o s t r a w b e r r i e s i n p a r t i c u l a r a r e s c a r c e .

T h e r e f o r e , t h e o b j e c t iv e s o f th i s s t u d y w e r e t o d e t e r m i n e

t h e e f f ec t i ve v a l u e s o f s u r f a c e h e a t t r a n s f e r c o e f f i c ie n t s

d u r i n g a i r p r e c o o l i n g o f s t r a w b e r r i e s a n d t h e e f f ec t o f

m o i s t u r e e v a p o r a t i o n o n t h e m , t o d e v e l o p a N u - R e

c o r r e l a t i o n w h i c h i n c l u d e s t h e e f fe c t o f m o i s t u r e

e v a p o r a t i o n a n d t o p e r f o r m a g e o m e t r i c a n a l y s i s u s i n g

a c r y l ic p la s t ic m o d e l s , in o r d e r t o c o n s i d e r a n o m a l o u s

s t r a w b e r r y s h a p e s.

M a t e r i a ls a n d m e t h o d s

T h e o r e t i c a l c o n s i d e r a t io n s

C o r r e l a t i o n t o e s t i m a t e s u r f a c e h e a t t r a n s f e r

c oe f f i c i e n t s . T o e s t i m a t e s u r f a c e h e a t t r a n s f e r

c o e f f i c ie n t s (h ) in f o r c e d - a i r c o o l i n g o f a s p h e r e , t h e w e l l -

k n o w n r e l at i o ns h i p o f M c A d a m s w a s u s e d :

N u = 0 . 3 7 R e ° ' 6 (1)

w h e r e N u i s t h e N u s s e l t n u m b e r ( h D / k a ) a n d R e i s the

R e y n o l d s n u m b e r

( Dv ap~ / 1~) .

0140--7007/89/030169~)5503.00

© 1989 Butterworth & Co (Publishers) Ltd and IIR Rev . Int . Fro id 1 9 8 9 Vol 1 2 Ma i 16 9


2/5

Air p recoo l ing o f strawberries:

D .

R. Gilemes

et a l .

N o m e n c l a t u r e

A Di m ens i on l ess d i s t anc e r a t i o , (Area 1 ) /h i 2

B D i m e n s i o n l e s s d i s t a n c e r a t i o , ( A r e a 2 ) /h i 2

B i B i o t n u m b e r

C F u n c t i o n f r o m t h e g e n e r a l e q u a t i o n p r e s e n -

t e d b y S m i t h

et al.

C , ( x ) F u n c t i o n o f th e g e o m e t r y , p o si ti o n a n d B i o t

n u m b e r

D D i a m e t e r f o r s p h e r e s o r ( 2.l ) f o r a n o m a l o u s

s h a p e s ( m )

F o F o u r i e r n u m b e r

G G e o m e t r y i n d ex

h Sur face hea t t r ans fe r coef f i c i en t

( W m - 2 ° C - 1)

k T h e r m a l c o n d u c t i v i ty ( W m - 1 o c - 1)

/ Ch arac t e r i s t i c l eng t h (m)

M ~ S q u a r e o f t h e f ir s t r o o t o f t h e t r a n s c e n d e n -

t a l e q u a t i o n a p p r o p r i a t e t o t h e g i v e n

g e o m e t r y

N u N u s s e l t n u m b e r

r C o r r e l a t i o n c o e f f ic i e n t

R O u t s i d e r a d i u s o f s p h e r e s ( m )

R e R e y n o ld s n u m b e r

R~q Eq u i va l e n t r ad i u s (m)

t T e m p e r a t u r e ( °C )

T D i m e n s i o n l e s s t e m p e r a t u r e r a t i o a s a f u n c -

t i o n o f t im e a n d p o s i t i o n w i t h i n t h e s o l i d

v Vel oc i t y (m s - t )

W W a t e r c o n t e n t ( ~o b y w e i g h t )

x G e n e r i c a l p o s i t i o n

Greek le t ters

T h e r m a l d i f fu s i v it y ( m 2 s - ~

0 Ti m e ( s)

2 , n t h r o o t o f t h e t r a n s c e n d e n t a l e q u a t i o n

k t Vi scos i t y (kg m - 1 s - l )

p D e n s i t y ( k g m - 3 )

Subscr ip t s

a Ai r

acr Acry l i c p l as t i c

s S t r a w b e r r i e s

i I n i ti a l u n i f o r m t e m p e r a t u r e o f t h e p r o d u c t

Iv C o n s t a n t t e m p e r a t u r e o f s u r r o u n d i n g

e n v i r o n m e n t

1

Exper im enta l m e thod to de term ine sur face heat t rans fer

coefficients. A m e t h o d w h i c h in v o l ve s th e m e a s u r e m e n t

o f t h e t e m p e r a t u r e v a r i a t i o n d u r i n g t h e t r a n s i e n t c o o l i n g

o f a b o d y w a s u s e d . T h e t e m p e r a t u r e r e s p o n s e a s a

f u n c t i o n o f t i m e a t a n y p o s i t i o n w i t h i n a s p h e r e

u n d e r g o i n g t r a n s i e n t h e a t e x c h a n g e t a k e s t h e f o l l o w i n g

f o r m 9 :

T - t - t o o _ ~ , C . ~. ,e x p ( - A z . ) ~ O / R z (2)

t i - - too .= t

w h e r e t h e t r a n s c e n d e n t a l r o o t e q u a t i o n i s :

B i = 1 - 2 . c o t 2 . ( 3)

Af t e r F o = 0 .20 t he se r ies so l u t i on c onve rges r a p i d l y ,

a n d t h e t e m p e r a t u r e r a t i o c a n b e e v a l u a t e d a c c u r a te l y b y

t h e u s e o f t h e f i rs t te r m o n l y . T h e t e c h n i q u e t o e v a l u a t e h

f r o m c o o l i n g c u r v e s i n v o l v e s t h e a s s u m p t i o n t h a t t h e

s e c o n d a n d h i g h e r te r m s i n t h e s u m m a t i o n o f E q u a t i o n ( 2)

a r e n e g l i g ib l e a f t e r s o m e t i m e h a s e l a p s e d . T h e r e f o r e , t h e

e q u a t i o n b e c o m e s :

T t - t o o - C l , x e X p ( - 2 ~ ) o ~ O / R 2

(4)

t i - - t ~

A s t r a i gh t l i ne wi t h a s l ope o f - 2 2 c t / R 2 i s o b ta i n e d b y

p l o t t i n g th i s e q u a t i o n o n s e m i - l o g p a p e r . T h e n , t h e

e x p e r i m e n t a l c o o l i n g c u r v e i s a l s o p l o t t e d o n s e m i - l o g

p a p e r . F r o m t h e s l o p e o f t h i s l i n e a n d t h e p r o p e r t i e s o f t h e

p r o d u c t , 22 c a n b e e v a l u a t e d . F r o m 21 a n d E q u a t i o n ( 3) ,

t h e B i o t n u m b e r a n d h c a n b e c a l c u la t e d .

F o r t h o s e c a s e s i n w h i c h w a t e r l o s s o c c u r s , t h e h e a t

t r ans fer coef f i c i en t s wi l l be ' e f f ec t i ve ' , because t hey wi l l

i n c l u d e e v a p o r a t i v e c o o l i n g .

Geom etry analys i s . T h e c o r r e c t i o n f o r n o n - s p h e r i c a l

s h a p e o f s tr a w b e r ri e s w a s m a d e b y a p p l y i n g t h e

p r o c e d u r e d e v e l o pe d b y S m i t h et al .l o,a 1. I t i s b a s e d o n a

d i m e n s i o n a l p a r a m e t e r d e f i n e d a s t h e ' c h a r a c t e r i s t i c

a )

~ o r t h o g o n a t a re a 1

b ) ~ o r th o c j o n a l r e a 2

F ig u r e 1 C r o s s - s ec t io n o f a t y p ica l s t r aw b er r y in th e ( a ) p o la r p l an e

an d ( b ) eq u a to r i a l p l an e

Figure 1 Cou pe transversale d'une fra ise ty pe dans (a) le plan polaire et

(b) le plan bquatorial

l e n g t h ' ( 1 ), w h i c h i s o r i g i n a t e d b y t w o o r t h o g o n a l p l a n e s

t h a t p a s s th r o u g h t h e p o i n t o f m a x i m u m t e m p e r a t u r e

( ' th e r m a l c e n t r e ' ) o f t h e f r u i t (Figure 1) .

T h e y a l s o d e f i n e a g e o m e t r y i n d e x , G , w h i c h i s

c a l c u l a t e d b y E q u a t i o n ( 5 )

1 3 3

G = ~ + ~ - ~

8B z

5)

w h e r e A = o r t h o g o n a l a r e a 1/nl 2 a n d B = o r t h o g o n a l a r e a

2/n l 2. T h e g e o m e t r y i n d e x f o r a s p h e r e i s 1 , d e c r e a s i n g a s

t h e s p h e r e b e c o m e s e c c e n t r ic .

F u r t h e r m o r e , t h e p r o c e d u r e i n v o l v e s a f i rs t t e r m

a p p r o x i m a t i o n o f th e i n f i n i te s e ri e s s o l u t io n s , w h e r e

t e m p e r a t u r e

versus

t i m e r e l a t i o n d u r i n g t r a n s i e n t h e a t

t r a n s f e r is g i v e n b y E q u a t i o n ( 6) :

T = C e x p ( -M ~ F o ) (6)

S m i t h et al. ~°'1~ d e v e l o p e d a m o n o g r a p h w h i c h

1 7 0 I n t. J . R e f ri g . 1 9 8 9 V o l 1 2 M a y


3/5

c o r r e l a t e s M ~ w i t h G a n d B i . M 1 c a n b e c a l c u l a t e d f r o m

t h e r m a l d i f f u si v i ty a n d t h e s l o p e o f t h e l o g a r i t h m i c

t e m p e r a t u r e r a t i o v e r s u s t i m e p l o t d u r i n g c o o l i n g t e s t s .

R a w m a t e r i a l

S t r a w b e r r i e s ( v a r . T u f t s ) f r o m C o r o n d a d i s tr i c t ( S a n t a F e

p r o v i n c e ) , w e r e u s e d . T h e f r u i t s w e r e s e l e c t e d t o o b t a i n

s a m p l e s o f u n i f o r m c h a r a c t e r i s ti c s a n d s iz e .

E x p e r i m e n t a l p r o c e d u r e

T h e h e a t t r a n s f e r c o ef f ic i e n ts (h ) a n d N u s s e l t n u m b e r s

w e r e e v a lu a t e d f r o m p r o p e r t i e s o f t h e p r o d u c t a n d t h e

a c r y l i c m o d e l , a c c o r d i n g t o t h e f o l l o w i n g p r o c e d u r e .

F o r t h e s p h e r i c a l s h a p e :

1 . T h e c h a r a c t e r i s ti c l e n g t h o f e a c h t e s t s p e c i m e n

a s s u m e d t o b e t h e r a d i u s o f a s p h e r e o f e q u i v a l e n t v o l u m e ,

w a s d e t e r m i n e d ;

2 . 2 ~ f r o m e x p e r i m e n t a l c o o l i n g c u r v e s a n d t h e

r e s p e c t i v e B i n u m b e r f r o m t a b le s 9 , w e r e o b t a i n e d ; a n d

3 . t h e s u r f a c e h e a t t r a n s f e r c o e f f i c ie n t h f r o m t h e v a l u e o f

B i

n u m b e r , w a s c a l c u l a t e d .

F o r t h e a n o m a l o u s s h a p e :

1 . T h e g e o m e t r y in d e x ( G ) a n d t h e c h a r a c t e r is t i c l e n g t h

(1) o f e a c h t e s t s p e c i m e n w e r e d e t e r m i n e d ;

2 . M ~ f r o m t h e s e m i - l o g p l o t o f t e m p e r a t u r e v e r s u s t i m e

w a s e v a l u a t e d ; a n d

3 . u s i n g t h e n o m o g r a p h , t h e r e c ip r o c a l o f t h e B i ot

n u m b e r a n d t h e v a l u e o f t h e r e s p e c t iv e s u r fa c e h e a t

t r a n s f e r c o e f f ic i e nt w e r e o b t a i n e d .

C o o l i n g t e s t s w e r e p e r f o r m e d i n a tu n n e l w h e r e a i r w a s

f o r c e d u p t h r o u g h t h e s t r a w b e r r i e s o r a c r y l ic m o d e l ,

p l a c e d o n a w i r e b e l t. B o t h s t r a w b e r r i e s a n d a c r y l ic m o d e l

w e r e c o o l e d s i n g l y . I n c o m m e r c i a l p r a c t i c e s t r a w b e r r i e s

a r e p l a c e d c l o s e t o g e t h e r , s o t h a t h i g h e r e f f e c ti v e h v a l u e s

t h a n

t h e e x p e r i m e n t a l v a l u e s o b t a i n e d a r e e x p e c t e d , a s

a c t u a l a i r v e l o c i ti e s a t t h e s u r f a c e a r e g r e a t e r t h a n t h e

a p p r o a c h i n g v e l o c i t y u s e d i n t h e t es t s.

T h e a c r y l ic p la s t i c m o d e l w a s t u r n e d o n a l a t h e s o t h a t

i ts s h a p e a n d s iz e w e r e a s s i m i l a r a s p o s s i b l e t o t h e

s t ra w b e r r ie s ( c h a r a ct e ri s ti c le n g t h , l = 0 . 0 1 2 m a n d

e q u i v a l e n t r a d i u s , R~q = 0 . 0 1 4 5 m ) .

T e m p e r a t u r e w a s m e a s u r e d u s in g ty p e K - A W G N o . 3 0

t h e r m o c o u p l e s c o n n e c t e d t o a m u l t i c h a n n e l d i g i t a l

Air preco ol ing of s trawberr ies: D. R. GOemes e t a l

e l e c tr o n i c t h e r m o m e t e r w i t h a n a c c u r a c y o f 0. I ° C . E a c h

t h e r m o c o u p l e w i r e w a s i n s e r te d n e a r t h e c e n t r e o f t h e

s a m p l e . T h e r m o c o u p l e e n t r a n c e w a s s e a l e d a p p r o -

p r i a t e ly . S a m p l e s w e r e a l l o w e d t o e q u i l i b r a t e i n a i r t o a

u n i f o r m t e m p e r a t u r e o f a b o u t 3 0 °C . C o o l i n g t e s ts

c o n t i n u e d u n t i l t h e s a m p l e h a d c o o l e d t o w i t h i n I ° C o f a i r

t e m p e r a t u r e . A i r f l o w r a t e s w e r e m e a s u r e d w i t h a h o t w i r e

a n e m o m e t e r . T h e e x p e r i m e n t a l a i r v e lo c i ti e s w e r e 1 .3 , 3. 0

a n d 4 .5 m s - 1 a n d t e m p e r a t u r e r a n g e d f r o m 0 t o 2 ° C .

T h e r e l a t i v e a i r h u m i d i t y w a s d e t e r m i n e d f r o m d r y -

b u l b a n d w e t - b u l b t e m p e r a t u r e v a l u e s . E x p e r i m e n t a l

v a l u e s r a n g e d f r o m 8 8 t o 9 0 ~ o.

T h e r m a l p r o p e r t i e s o f th e s t r a w b e r r i e s a n d a c r y l ic

p l a s ti c m o d e l w e r e d e t e r m i n e d i n a p r e v i o u s s t u d y 12 b y

t h e t r a n s i e n t m e t h o d 1 3 . T h e y w e r e : k s = 0 .4 6 W m - ~° C - 1 ;

k a c r = 0 . 2 0 8 W m - l o c l; ~ s = l . 2 6 x 1 0 - V m 2 s - X ; a nd

cq~r = 1 .207 x 1 0- 7 m 2 s - 1 . T hese va l u es agr e e w i t h da t a

f ou nd i n t he l i t e r a t u r e s, 14,1 s .

M o i s t u r e c o n t e n t o f s tr a w b e r r ie s w a s d e t e r m i n e d b y

d r y i n g t h e s a m p l e i n a ir a t 6 0 ° C u n t il c o n s t a n t w e i g h t w a s

o b t a i n e d . S p e c if ic g r a v i t y w a s m e a s u r e d b y w a t e r

d i s p l a c e m e n t . W e i g h t l o ss e s in t h e s a m p l e s w e r e

d e t e r m i n e d f r o m v a l u e s o f th e i r w e i g h t s b e f o r e a n d a f t e r

t h e c o o l i n g t e s t s .

R e s u l t s a n d d i s c u s s io n

T a b l e 1 s h o w s a v e r a g e s u r f a c e h e a t t r a n s f e r c o e f f i c i e n t s h

o b t a i n e d f r o m t h e t h r e e d i f fe r e n t a ir v e l o c it ie s . T h e v a l u e s

o f h f o r s p h e r e s ( f r o m E q u a t i o n (1 )) a r e a v e r a g e s o f th e

s in g l e v a l u e s c o r r e s p o n d i n g t o e a c h e x p e r i m e n t a l

c o n d i t i o n . V a l u e s p r e d i c te d b y E q u a t i o n (1 ) o f M c A d a m s

f o r s p h e re s a n d t h o s e o b t a i n e d f o r t h e a c r y l i c p l a s ti c

m o d e l w i t h s i m i l a r d i m e n s i o n s w e r e n o t f o u n d t o b e

s i g n i f i c a n t l y d i f f e r e n t ( P ~ < 0 . 0 5 ) . V a l u e s o b t a i n e d f o r

s t r a w b e r r i e s a s s u m e d a s s p h e r e s a n d t h o s e o b t a i n e d b y

c o r r e c ti o n f o r a n o m a l o u s s h a p e w e r e n e i th e r f o u n d t o b e

s i gn i f i ca n t l y d i f f e r en t ( P ~< 0 .05) .

O n t h e o t h e r h a n d , s i g n i f i c a n t d i f f e r e n c e s ( P ~ < 0 . 0 5 )

w e r e f o u n d b e t w e e n p r e d i c t e d v a l u e s fo r sp h e r e s o r

e x p e r i m e n t a l v a l u e s f o r t h e a c r y li c m o d e l a n d t h e m e a n

v a l u e s f r o m s t r a w b e r r i e s . T h e l a t t e r w e r e 1 6 t o 2 5 ~o h i g h e r

t h a n t h o s e p r e d i c te d b y E q u a t i o n (1 ) o f M c A d a m s f o r

s p h e r e s a n d t h e e x p e r i m e n t a l v a l u e s f o r th e a c r y l i c p la s t ic

m o d e l . T h e d i f fe r e n c e m a y b e m a i n l y a t t r i b u t e d t o t h e

Table 1 Surfaceheat transfer coefficients h) obtained from fo rced-aircooling of acrylicplastic mod el and strawberries (each value s an average of 4 to

6 runs)

Tableau 1 Coefficients de transfert de chaleur superficiel (h) obtenus it partir du refroidissement par courant d'air force d'un mo dble en matikre plastique

acrylique et de fraises (chaque valeur reprbsente une moyenne de 4 it 6 essais)

Air velocity (m s- 1)

1.3 3.0 4.5

h CV h CV h CV

(W m- 2 oc - ~ ) ( %) ( W m - 2 of - , ) ( %) ( W m - 2 of 1) ( %)

Spheres (pred icted by Equ ation 1) 39.6 8.3 64.9 7.0 83.9 3.9

Acrylic plastic mo del 37.8 14.7 68.9 7.0 81.9 14.6

Strawberries

assumed as spheres 47.8 10.9 82.5 14.0 102.1 15.9

corre cted for ano ma lous shap e 44.5 12.6 78.3 13.9 106.4 14.5

CV: Co efficient of variation (standard d eviation/mean value)× 100

Average air temp erature during cooling tests: 1.4°C

Sphe res (for Eguatio n 1): f-=_/~q= 0.012 m; _acrylicplastic model: l= 0.012 m; Req = 0.0145 m; G = 0.76

Strawberries: l=0.0116 m; Req=0.0131 m; G =0.83; jrs=95 2; 1~=90 .5 %

R e v I n t F r o i d 1 9 8 9 V o l 1 2 M a i 1 7 1


4/5


5/5

200

Z

I

6 0

40

+

2 0

10 I

1000

2

I I I I t I I

4000 10O00

Reynolds number

2

Figure 4 Nusselt-Reynolds correlation for forced-air precooling of the

acrylic plastic model (---) and McAdams relationship for spheres

( ). +, Experimental data

Figure 4 Correlation entre les nombres de Nusselt et de Reynolds pour

la pr~rbfrig~ration par eourant d air forcb du modble en mati~re plastique

acrylique ( - - - ) et relation de McAdams pour des spheres ( ).

+,

Rbsultats expbrimentaux

C o n c l u s i o n s

For practical applications, s trawberries can be acceptably

considered as spheres, because the correction for

an om al ous shape does no t cause significant differences.

This com ment is l imited to s trawberries of Tufts variety

or others of similar shape because there are some varieties

that are very large and fiat , and perhaps cannot be

modelled as spheres.

The air cooling of s trawberries involves, to some

extent, an evaporation cooling effect. To take this effect

into account, 'effective' surface heat transfer coefficients

must be used.

It should be interesting for future work to evaluate

moisture losses as a function of time and air velocity, in

order to describe the combined heat and mass transfer

process more accurately.

Air preco ol ing o f strawberr ies: D. R. GS emes e t a l .

A c k n o w l e d g e m e n t

This work was supported by the Secretaria de Estado de

Ciencia y T~cnica de la Repfiblica Argentina

R e f e r e n c e s

1 Conroy,R., Ell is, R. F. Precooling berries improves quality

shortens fluidized reezing ime Food Processing (1981) 42 82-83

2 Fockens,F. H., Meffert, H. F. Moisture loss of horticultural

products during precooling with cold air

12bne Congr~s

International du Froid Madrid (1967) 731-741

3 Ansarl , . A., Charan, V. Varma, H. K. Heat and mass transfer

analysis in air-cooling of spherical food products lnt J Refrio

(1984) 7 194-197

4 Feldrnan,C. Transfert de chaleur et de masse entre une sphere et

de l'air a basse temperature CTGREF No 6 Memoire (March

1976)

5 McAdams,W. Heat Transmission McGraw Hill Book Co., New

York, Toronto, London (1954)

6 Are¢ , J., Sweat, V. E. Survey of published heat transfer

coefficients encountered in fo od refrigeration processes

ASH RAE Trans (1980) 86(2)

7 Kopdman, I., Blaisdell,J. L, Ptlug, . J. Influenceof fruit size and

coolant velocity on the cooling of Jonathan apples in water and

air ASHRAE Trans (1966) 72(1) 209-216

8 Mi nh , . V, Perry, J. S, Bennett, A. H. Forced air precooling of

white potatoes in bulk

ASHRAE Trans

(1969) 75(II) 87-94

9 L u i k u v ,A. V. Analytical Heat Diffusion Theory Academic Press,

New York and London (1968)

10 Sm it h, L E., Nelson, G. L, Henrickson, R. L. Analyses on

transient heat transfer from anomalous shapes

Trans ASAE

(1967) 10 236-245

11 Smith,R. E., Nelson, G. L., Henriekson, R. L. Applications of

geometry analysis of anomalous shapes to problems in transient

heat transfer Trans ASAE (1968) 11 296-302

12 Di Pentima, J. H., Giiemes,D. R. Difusividad rrmica de acrilico

y de frutillas preparadas de diferentesmaneras, unpublished data

(1985)

13 Gaffney,. J., Baird, C. D., Eshleman,W. D. Review and analysis

of the transient method for determining thermal diffusivity of

fruits and vegetablesASHRAE Trans (1980) 86(2) 261-280

14 Sweat,V. E. Experimental values of thermal conductivity of

selected fruits and vegetablesJ Food Sci (1974) 39 1080-1083

15 Perry,R., Chilton, C.

Chemical Engineers Handbook

5th Ed.

McGraw Hill Kogakusha Ltd, Tokyo (1973)

16 S a s tr y ,S. K . Zuritz, C. A., Anantheswaran, R. C. Interaction

between heat and mass transfer in foods ASHRAE Trans (1985)

91(2)

R e v . I n t. F r o i d 1 9 8 9 V o l 1 2 M a i 1 7 3

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