doc vs internet + libraryrepository.unika.ac.id/15903/2/unicheck steaming the...u, % heat transfer...
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1. https://www.deepdyve.com/lp/de-gruyter/heat-transfer-during-steaming-of-bread-gQhjtWRnCt 3.05%2. https://core.ac.uk/display/41383651 3.05%3. https://www.european-mrs.com/2014-spring-symposium-f-european-materials-research-society 0.71%4. https://www.pubfacts.com/search/zirconium%20tetratert-butoxide/2 0.59%5. https://docplayer.nl/50496718-Vlaanderen-is-open-ruimte-mestrapport-2016-vlaamse-land-maatsch… 0.29%6. https://www.slideshare.net/rmakaha/ms-office-package-practical-questions 0.29%7. https://www.deepdyve.com/lp/elsevier/two-dimensional-cfd-modelling-and-simulation-of-an-industria… 0.24%8. http://www.villaalbadetormes.com/registros/perfil_contratante/Proyecto%20Renov.%20y%20Mejor… 0.2%9. http://foodhaccp.com/memberonly/newsletter761.html 0.18%10. https://www.scribd.com/document/362923622/Baking 0.18%11. http://khotib-makalahti.blogspot.com/2009/10/pengujian-performansi-voip-pada.html 0.16%12. http://media.collegeboard.com/digitalServices/pdf/ap/bio-manual/Bio_Lab13-EnzymeActivity.pdf 0.16%13. https://searchworks.stanford.edu/?per_page=100&q=Schofield+reference+collection.&search_fie… 0.16%14. http://www.readbag.com/rdi-ku-ac-th-ku-journal-sciences-doc-ku422 0.16%15. https://www.uts.edu.au/staff/wenshan.guo-1 0.16%16. http://www.asturias.es/Astursalud/Ficheros/AS_Salud%20Publica/As_Vigilancia/Informes%20epi… 0.16%17. http://onlinelibrary.wiley.com/doi/10.1111/1574-6968.12151/full?globalMessage=0 0.16%18. http://minds.jacobs-university.de/uploads/papers/Mantas_Lukosevicius_PhD_thesis.pdf 0.16%19. https://www.bbvaresearch.com/KETD/fbin/mult/WP_1130_tcm346-270043.pdf 0.15%20. https://www.esrl.noaa.gov/gmd/publications/browse.php?year=2014 0.15%21. http://www.public.asu.edu/~etcamach/AMSSI/reports/neuron.pdf 0.15%22. http://salis.org/resources/newbooks_archive_current.htm 0.15%23. https://www.containerstore.com/s/closet/shoe-storage/view-all-shoe-storage/12-pair-shoe-organiz… 0.15%24. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P1006YOO.TXT 0.15%25. https://library.umd.umich.edu/newbooks/2007/july.php 0.15%26. http://www.niisk.com/spezrada/Dissertacija.pdf 0.15%27. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=91024W54.TXT 0.15%28. https://en.wikibooks.org/wiki/Chemical_Principles/Gas_Laws_and_the_Kinetic_Theory 0.15%29. http://www.euskadi.eus/contenidos/informacion/escuela_vasca_deporte/es_9258/adjuntos/Mikel%… 0.15%30. http://wiener.math.csi.cuny.edu/~verzani/Projects/Tutorials/simpleR/stat.html 0.15%31. https://www.slideshare.net/schcherban/c-44312280 0.15%32. http://www.diva-portal.org/smash/get/diva2:901740/FULLTEXT01.pdf 0.15%33. https://latierrayelhombre.files.wordpress.com/2012/11/cuadernillo-de-pruebas-saber-111.pdf 0.15%34. https://searchworks.stanford.edu/?f%5Btopic_facet%5D%5B%5D=Education&per_page=100 0.15%
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https://www.deepdyve.com/lp/de-gruyter/heat-transfer-during-steaming-of-bread-gQhjtWRnCthttps://core.ac.uk/display/41383651https://www.european-mrs.com/2014-spring-symposium-f-european-materials-research-societyhttps://www.pubfacts.com/search/zirconium+tetratert-butoxide/2https://docplayer.nl/50496718-Vlaanderen-is-open-ruimte-mestrapport-2016-vlaamse-land-maatschappij-vlm-be.htmlhttps://www.slideshare.net/rmakaha/ms-office-package-practical-questionshttps://www.deepdyve.com/lp/elsevier/two-dimensional-cfd-modelling-and-simulation-of-an-industrial-a54x5zrNA2http://www.villaalbadetormes.com/registros/perfil_contratante/Proyecto+Renov.+y+Mejora+SANEAMIENTO+ALBA.pdfhttp://foodhaccp.com/memberonly/newsletter761.htmlhttps://www.scribd.com/document/362923622/Bakinghttp://khotib-makalahti.blogspot.com/2009/10/pengujian-performansi-voip-pada.htmlhttp://media.collegeboard.com/digitalServices/pdf/ap/bio-manual/Bio_Lab13-EnzymeActivity.pdfhttps://searchworks.stanford.edu/?per_page=100&q=Schofield+reference+collection.&search_field=search&sort=year-deschttp://www.readbag.com/rdi-ku-ac-th-ku-journal-sciences-doc-ku422https://www.uts.edu.au/staff/wenshan.guo-1http://www.asturias.es/Astursalud/Ficheros/AS_Salud+Publica/As_Vigilancia/Informes+epidemiol%C3%B3gicos/Informe+TB+2007-08.pdfhttp://onlinelibrary.wiley.com/doi/10.1111/1574-6968.12151/full?globalMessage=0http://minds.jacobs-university.de/uploads/papers/Mantas_Lukosevicius_PhD_thesis.pdfhttps://www.bbvaresearch.com/KETD/fbin/mult/WP_1130_tcm346-270043.pdfhttps://www.esrl.noaa.gov/gmd/publications/browse.php?year=2014http://www.public.asu.edu/%7Eetcamach/AMSSI/reports/neuron.pdfhttp://salis.org/resources/newbooks_archive_current.htmhttps://www.containerstore.com/s/closet/shoe-storage/view-all-shoe-storage/12-pair-shoe-organizer/123d?productId=10008147https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P1006YOO.TXThttps://library.umd.umich.edu/newbooks/2007/july.phphttp://www.niisk.com/spezrada/Dissertacija.pdfhttps://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=91024W54.TXThttps://en.wikibooks.org/wiki/Chemical_Principles/Gas_Laws_and_the_Kinetic_Theoryhttp://www.euskadi.eus/contenidos/informacion/escuela_vasca_deporte/es_9258/adjuntos/Mikel+Izquierdo.pdfhttp://wiener.math.csi.cuny.edu/%7Everzani/Projects/Tutorials/simpleR/stat.htmlhttps://www.slideshare.net/schcherban/c-44312280http://www.diva-portal.org/smash/get/diva2%3A901740/FULLTEXT01.pdfhttps://latierrayelhombre.files.wordpress.com/2012/11/cuadernillo-de-pruebas-saber-111.pdfhttps://searchworks.stanford.edu/?f%5Btopic_facet%5D%5B%5D=Education&per_page=100https://corp.unicheck.com/
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Library sources: 10 sources found
Food Bioprocess Technology Impact of Green Tea Extract.pdf 1.63%Green Tea Catechins Reduced the Glycaemic Potential of Bread.pdf 1.61%Green Tea Catechins Reduced the Glycaemic Potential of Bread (1).pdf 1.61%11 ICEF (Hal 647).pdf 1.08%
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A Study on Bifidobacterium lactis Bb12 Viability in Bread du.pdf 0.4%Green Tea Catechins During Food Processing and Storage.pdf 0.4%A Study on Bifidobacterium lactis Bb12 Viability in Bread du (1).pdf 0.4%2. Results and Discussions.docx 0.15%Vicky Widia Yusrina-13.70.0146-22 MARET.docx 0.15%15.I1.0019_Joshua Adi Nugraha P-KP-21 JUNI-F.docx 0.15%
Library omitted sources: 2 sources found
Heat Transfer during Steaming of Bread.pdf 100%Heat Transfer during Steaming of Bread.pdf 100%
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V i c t o r i a K . A n a n i n g s i h , E d d a Y . L . S i m , X i a o D o n g C h e n a n d W e i b i a o Z h o u *
H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
A b s t r a c t : U n d e r s t a n d i n g o f h e a t t r a n s f e r d u r i n g s t e a m i n g
i s i m p o r t a n t t o o p t i m i z e t h e p r o c e s s i n g o f s t e a m e d b r e a d
a n d t o p r o d u c e d e s i r e d q u a l i t i e s i n t h e f i n a l p r o d u c t .
P h y s i c o c h e m i c a l c h a n g e s o c c u r d u r i n g s t e a m i n g o f t h e
d o u g h w h i c h m i g h t b e i m p a c t e d u p o n b y t h e h e a t t r a n s -
f e r s y s t e m . I n t h i s s t u d y , a m a t h e m a t i c a l m o d e l w a s
d e v e l o p e d t o d e s c r i b e t h e h e a t t r a n s f e r s y s t e m i n t h e
b r e a d b e i n g s t e a m i n g t h r o u g h o u t t h e h e a t i n g p r o c e s s .
T h e F o r w a r d E u l e r m e t h o d w a s e m p l o y e d f o r s o l v i n g
t h e t h r e e - d i m e n s i o n a l p a r t i a l d i f f e r e n t i a l e q u a t i o n s e t
f o r h e a t t r a n s f e r t o p r o d u c e t e m p e r a t u r e p r o f i l e s a t a
n u m b e r o f i n d i v i d u a l l o c a t i o n s i n t h e s t e a m e d b r e a d
d u r i n g i t s s t e a m i n g . A l l t h e c o m p a r i s o n s b e t w e e n t h e
m o d e l - p r e d i c t e d v a l u e s a n d t h e e x p e r i m e n t a l r e s u l t s p r o -
d u c e d r o o t m e a n s q u a r e e r r o r v a l u e s r a n g e d f r o m 1 . 3 9 1 t o
3 . 5 4 5 a n d R2 v a l u e s o f a l l g r e a t e r t h a n 0 . 9 3 . T h e r e f o r e , i t
i s c o n f i r m e d t h a t t h e m o d e l h a s a g o o d p e r f o r m a n c e a n d
c a n b e u s e d t o p r e d i c t t e m p e r a t u r e p r o f i l e s i n t h e b r e a d
d u r i n g s t e a m i n g .
K e y w o r d s : h e a t t r a n s f e r , m a t h e m a t i c a l m o d e l , s t e a m e d
b r e a d , f i n i t e d i f f e r e n c e m e t h o d
* C o r r e s p o n d i n g a u t h o r : W e i b i a o Z h o u , F o o d S c i e n c e a n d
T e c h n o l o g y P r o g r a m m e , c / o D e p a r t m e n t o f C h e m i s t r y , N a t i o n a l
U n i v e r s i t y o f S i n g a p o r e , 3 S c i e n c e D r i v e 3 , S i n g a p o r e 1 1 7 5 4 3 ;
N a t i o n a l U n i v e r s i t y o f S i n g a p o r e ( S u z h o u ) R e s e a r c h I n s t i t u t e , 3 7 7
L i n Q u a n S t r e e t , S u z h o u I n d u s t r i a l P a r k , J i a n g S u 2 1 5 1 2 3 , P e o p l e s’
R e p u b l i c o f C h i n a , E - m a i l : c h m z w b @ n u s . e d u . s g
V i c t o r i a K . A na n i n g si h , F o o d S c i e n ce a n d T e c h no l o g y P r o g ra m m e ,
c / o D e p a r t me n t o f C h e m i st r y , N a t i on a l U n i v e r s i ty o f S i n g a p or e ,
3 S c i e n c e D r iv e 3 , S i n g a p o r e 1 1 7 54 3 ; D e p a r t me n t o f F o o d
T e c h n ol o g y , S o e g i j ap r a n a t a C a th o l i c U n i v er s i t y , J a l a n P a wi y a t a n
L u h u r I V / 1 , S e m a r an g 5 0 2 3 4 , I n d o n es i a , E - m a i l : k r i s t in a @ u n i ka . a c . id
E d d a Y . L . S i m , F oo d S c i e n c e a n d T e c h n ol o g y P r o g r am m e ,
c / o D e p a r t me n t o f C h e m i st r y , N a t i on a l U n i v e r s i ty o f S i n g a p or e ,
3 S c i e n c e D ri v e 3 , S i n g a p or e 1 1 7 5 4 3 , E- ma i l : u 0 3 0 62 4 5 @ n us . e d u . s g
X i a o D o n g C h e n , D e p a r t m e n t o f C h e m i c a l a n d B i o c h e m i c a l
E n g i n e e r i n g , X i a m e n U n i v e r s i t y , F uj i a n , C h i n a , E - m a i l : x d c @ x m u . e d u . c n
1 I n t r o d u c t i o n
S t e am e d b re a d , o r c al l e d “m a n t o u”, i s a t ra d i ti on a l s ta p le
f o od i n n or t h er n C hi n a ( i. e . th e r e gi on n o r th o f t he Y a n gt z e
R i v er ) a nd r e p r e se n ts a r o un d 7 0 % o f t h e e n d u sa g e o f
f l ou r p r o du c e d i n th i s r e g io n a n d a l e s se r p r op o rt i o n i n
t h e s o ut h [ 1 ] . A mo n g s i mi la r p r o du c ts w i d e l y e mb r ac e d b y
p e o pl e i n K o re a , Ja p a n a n d So u th e a st A s i an c o u nt r i es a r e
a v a r i e t y o f s t e a m e d b r e a d s w i t h d i f f e r e n t f i l l i n g s ( o r c a l l e d
s t ea m ed b u n s) . T h e m a j or s t e ps f o r p ro d u ci n g t h es e p ro -
d u ct s i nc l ud e m a ki n g d ou g h of w he a t f lo u r of l o we r p ro -
t e in c o n t e nt c o mp a r e d to b a k e d b r ea d , d iv i d in g t h e d ou g h
i n to s m a l l p ie c e s a nd m o u l di n g t h em a n d f i na l l y st e a mi n g
t h e d ou g h p ie c e s u s in g o nl y s a t u ra t ed s t e am i n t h e
a b se n c e o f an y d r y h e at .
S t e a m i n g , w h i c h i s n o t t o b e c o n f u s e d w i t h t h e p r o -
c e s s o f i n j e c t i n g s o m e s t e a m d u r i n g b a k i n g , i s a p r o c e s s
t h a t r e s u l t s i n a s e r i e s o f p h y s i c a l , c h e m i c a l a n d b i o -
c h e m i c a l c h a n g e s i n a p r o d u c t , s u c h a s v o l u m e e x p a n -
s i o n , c o n d e n s a t i o n o f w a t e r o n t h e p r o d u c t s u r f a c e
f o l l o w e d b y t h e f o r m a t i o n o f a n o u t e r e l a s t i c s k i n ( n o t
c r u s t ) , p r o t e i n d e n a t u r a t i o n a n d s t a r c h g e l a t i n i z a t i o n .
T h e s y s t e m i s c h a r a c t e r i z e d b y s i m u l t a n e o u s h e a t a n d
w a t e r t r a n s p o r t p r o c e s s e s w i t h i n t h e p r o d u c t a s w e l l a s
b e t w e e n t h e p r o d u c t a n d t h e e n v i r o n m e n t i n s i d e t h e
s t e a m e r . A t t h e b e g i n n i n g , h e a t t r a n s p o r t f r o m t h e e n v i r -
o n m e n t ( i . e . s a t u r a t e d s t e a m ) t o t h e p r o d u c t s u r f a c e
o c c u r s m a i n l y t h r o u g h c o n v e c t i o n a c c o m p a n i e d b y l a t e n t
h e a t o f c o n d e n s a t i o n o f s t e a m . A f t e r w a r d s , w h i l e c o n d u c -
t i o n a t t h e s u r f a c e i s t h e m a j o r m o d e o f h e a t t r a n s f e r , f o r
b r e a d i n s i d e , c o n d u c t i o n f r o m t h e s u r f a c e t o t h e b r e a d
c r u m b c e n t r e i s d o m i n a t i n g a n d t h e l a t e n t h e a t o f c o n -
d e n s a t i o n c o n t r i b u t e s a l o n g a c o l d f r o n t w h i c h m o v e s
t o w a r d s t h e c e n t r e . D e p e n d i n g o n t h e a c t u a l t y p e o f
t h e p r o d u c t t o b e m a d e a n d t h e t y p e o f s t e a m e r u s e d ,
r e l a t i v e c o n t r i b u t i o n s b y t h e v a r i o u s m e c h a n i s m s o f
h e a t t r a n s f e r c a n b e a d j u s t e d t o a c h i e v e a d e s i r e d q u a l i t y
i n t h e f i n a l p r o d u c t . D u e t o t h e h i g h e n e r g y c o n s u m p t i o n
o f t h e s t e a m i n g p r o c e s s , i t i s c r u c i a l t h a t t h e o p e r a t i n g
c o n d i t i o n o f a s t e a m e r i s o p t i m i z e d t o r e d u c e t h e
e n e r g y c o n s u m p t i o n a s w e l l a s t o i m p r o v e p r o d u c t
q u a l i t y , s i m i l a r t o b a k i n g s y s t e m s [ 2 ] , i . e . p o s s i b l e m i n i -
m u m a m o u n t o f s t e a m u s e d p e r k g o f d r y m a t e r i a l
p r o c e s s e d .
B o t h e x p e r i m e n t a l a n d m a t h e m a t i c a l m o d e l l i n g
a p p r o a c h e s a r e o f t e n u s e d f o r t h i s p u r p o s e . I n t h e f o r m e r
a p p r o a c h , t h e p r o c e s s i s s i m u l a t e d i n a l a b o r a t o r y o r
p i l o t - s c a l e s e t - u p t o g e n e r a t e v a l u a b l e d a t a o n t h e s y s t e m
b e h a v i o u r [ 3 ] . W h i l e c a r e f u l e x p e r i m e n t a l d a t a a r e i n d i s -
p e n s a b l e i n v a l i d a t i n g t h e p r o c e s s , h o w e v e r , u n l i k e
k n o w l e d g e o b t a i n e d t h r o u g h m a t h e m a t i c a l m o d e l s , t h e y
c a n n o t b e e a s i l y g e n e r a l i z e d . M a t h e m a t i c a l m o d e l l i n g ,
d o i 1 0 . 1 5 1 5 / i j f e - 2 0 1 3 - 0 0 2 3 I n t e r n a t i o n a l J o u r n a l o f F o o d E n g i n e e r i n g 2 0 1 4 ; 1 0 ( 4 ) : 6 1 3 6 2 3–
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w h i c h i s o f t e n b a s e d o n k n o w n p h y s i c a l a n d c h e m i c a l
p r i n c i p l e s , i s i m p o r t a n t i n r e d u c i n g t h e t i m e a n d c o s t s
i n v o l v e d i n e x p e r i m e n t a t i o n . M o d e l s c a n a l s o b e u s e d f o r
t h e d e s i g n , o p t i m i z a t i o n a n d c o n t r o l o f t h e p r o c e s s .
P a u l u s [ 4 ] d e s c r i b e d t r a n s p o r t m o d e l s a s o n e o f t h e
m a i n c h a r a c t e r i s t i c s o f t h e m o d e l l i n g o f i n d u s t r i a l c o o k -
i n g . I n r e c e n t y e a r s , t h e r e h a s b e e n g r o w i n g i n t e r e s t f o r
t h e m o d e l l i n g o f s i m u l t a n e o u s h e a t a n d w a t e r t r a n s f e r s
i n b a k i n g [ 5–7 ] . Z h o u [ 8 ] p r e s e n t e d s e v e r a l h e a t a n d m a s s
t r a n s f e r m o d e l s d u r i n g b a k i n g w h i c h i n v o l v e d t h e r m o -
p h y s i c a l p r o p e r t i e s o f p r o d u c t t h a t a r e c h a n g i n g d u r i n g
t h e b a k i n g p r o c e s s , e . g . d e n s i t y , s p e c i f i c h e a t , t h e r m a l
c o n d u c t i v i t y a n d t h e r m a l d i f f u s i v i t y .
T h e r m o p h y s i c a l p r o p e r t i e s a r e e s s e n t i a l t o d e v e l o p -
i n g m o d e l s f o r h e a t t r a n s f e r . T h e r m o p h y s i c a l p r o p e r t i e s
o f d o u g h a n d b a k e r y p r o d u c t s f o r b a k e d g o o d s w e r e
r e p o r t e d b y B a i k e t a l . [ 9 ] , M a r c o t t e [ 1 0 ] a n d Z u n i g a
a n d L e - B a i l [ 1 1 ] . T h e r m a l c o n d u c t i v i t y , s p e c i f i c h e a t a n d
m a s s d i f f u s i v i t y a r e s o m e o f t h e i m p o r t a n t t h e r m o p h y s i -
c a l p r o p e r t i e s e s s e n t i a l f o r t h e m o d e l l i n g o f h e a t a n d
m a s s t r a n s f e r d u r i n g b o t h b a k i n g a n d s t e a m i n g
p r o c e s s e s .
S o f a r , r e l a t i v e l y f e w s t u d i e s o n s t e a m e d b r e a d h a v e
b e e n r e p o r t e d i n t h e l i t e r a t u r e [ 1 , 1 2 ] . T h e o r e t i c a l m o d e l -
l i n g o f t h e h e a t t r a n s f e r s y s t e m f o r s t e a m i n g b r e a d h a s
n o t b e e n r e p o r t e d , i n c o n t r a s t t o m a n y s t u d i e s o n b a k e d
b r e a d [ 1 0 , 1 3 , 1 4 ] . T h i s s t u d y a i m e d t o d e v e l o p a m a t h e -
m a t i c a l m o d e l f o r t h e h e a t t r a n s f e r i n s t e a m e d b r e a d
d u r i n g i t s s t e a m i n g p r o c e s s .
2 M a t e r i a l s a n d m e t h o d s
2 . 1 B r e a d f o r s t e a m i n g
T h e s t u d y w a s c a r r i e d o u t o n n o r t h e r n - s t y l e s t e a m e d
b r e a d . S o f t o r l o w - p r o t e i n “m a n t o u” f l o u r ( B a k e K i n g ,
H o n g K i n g E x t r a S p e c i a l F l o u r , S i n g a p o r e ) w a s p u r c h a s e d
f r o m a l o c a l s u p e r m a r k e t . T h e d o u g h f o r m u l a t i o n i n p e r -
c e n t a g e o f f l o u r w e i g h t w a s 5 8 % w a t e r , 1 % y e a s t ( D r y
b a k e r’s y e a s t , S a f - i n s t a n t , F r a n c e ) , 1 % s a l t ( P a g o d a ,
C h i n a ) a n d 1 % s u g a r ( S i s , A u s t r a l i a ) . M i x i n g w a s d o n e
i n a s p i r a l m i x e r ( V a r i m i x e r ® W A G - R N 2 0 , E u r o p e ) c o m -
p r i s i n g o n e l o w - s p e e d m i x i n g s t e p ( 6 m i n , 1 0 0 r p m ) . T h e
t e m p e r a t u r e o f t h e d o u g h a f t e r k n e a d i n g w a s 2 3 0 . 5 ° C .
D o u g h w a s l e t t o r e s t f o r 1 0 m i n a t a m b i e n t t e m p e r a t u r e
o f a r o u n d 2 2 ° C a n d w a s t h e n s h e e t e d a n d f o r m e d i n t o
h e m i s p h e r i c a l p i e c e s u s i n g a m o u l d e r ( D r R O B O T I I ,
N e t h e r l a n d s ) . T h e m o u l d e d d o u g h p i e c e s w e r e w e i g h e d
t o b e 5 0 g t o e n s u r e c o n s i s t e n c y . T h e h e m i s p h e r i c a l
d o u g h p i e c e s w e r e p l a c e d o n t h e p l a s t i c t r a y s o f a s t e a -
m e r ( P h i l l i p s , H - R C 1 9 , S i n g a p o r e ) , a n d t h e n t h e t r a y s
w e r e p l a c e d i n t o a p r o o f i n g c a b i n e t ( E U R O F O U R S®
M s 0 1 T 0 3 - 2 , F r a n c e ) f o r 3 0 m i n a t 4 0 ° C a n d a r e l a t i v e
h u m i d i t y o f 8 0 % . T h e h e m i s p h e r i c a l d o u g h p i e c e s a f t e r
p r o o f i n g w e r e s t e a m e d f o r v a r i o u s p r e - d e t e r m i n e d
s t e a m i n g p e r i o d s . A t e a c h s t e a m i n g o p e r a t i o n , e i g h t
p i e c e s o f p r o o f e d s a m p l e s w e r e f i t t e d i n t o t h e s t e a m e r
e a c h t i m e .
2 . 2 S t e a m i n g a n d t e m p e r a t u r em e a s u r e m e n t s
S t e am i ng w a s c ar r i ed o u t i n a c o n ve nt i o n al , e le c t ri c al l y
o p e ra te d s t e am e r ( 3 t i er s t e am e r, T e f a l , B er k sh i re , U K ) a t
a n e q ui l i br i um s u r r ou n di n g t e mp er a t ur e o f 1 00 ° C i n t h e
s t ea m er . T h e st e a me r h ad t h r ee t r a y s w h i c h we r e s ta c ke d
o n t o p of e a c h o t h er . D u e to t h e h i g h p ow e r e ff i ci e n cy a n d
t h e sm a l l s i z e o f th e s t ea me r , t he t e mp e ra t u re o f t he t o p
t r ay r e a c he d a n e qu i l ib r i um t e mp e r at u r e a s fa s t a s t h e
b o tt o m t ra y . I n t h e l id o f t h e s te a me r , t h re e s ma l l h o l es
w e re p r e se nt w h ic h s e rv e d t o r e gu l at e t h e i n si d e p re s su r e
o f t h e s te a m e r. T h es e h o l e s w er e a l so u s e d t o i n se r t u p t o
n i n e K- t yp e t h e rm o c o up le s o f 0 . 3 m m i n d i am e t e r t hr o ug h
t h e l id a n d p l ac e t h e m at d i f f e re n t p os i ti o n s i n th e d o ug h
p i e ce s i n si d e t he s t e am e r d u ri n g s te a mi n g , t h ro u g h th e
e n ti r e s ti p u l at e d st e a m in g p r o ce ss .
A s s h o w n i n F i g u r e 1 , t h e t h e r m o c o u p l e s w e r e s p e c i -
f i c a l l y p l a c e d a t e i g h t d i f f e r e n t l o c a t i o n s o f t h e d o u g h /
s t e a m e d b r e a d , n a m e l y t h e c e n t r e ( p o i n t 1 ) , t h e b o t t o m ,
f o u r o t h e r d i f f e r e n t l o c a t i o n s i n t h e c r u m b o f t h e d o u g h
( p o i n t s 2–5 ) , d i r e c t l y a b o v e t h e d o u g h ( i . e . s u r r o u n d i n g )
a n d j u s t u n d e r t h e b r e a d s k i n ( i . e . s u r f a c e ) . I t w a s e a r l i e r
o b s e r v e d t h a t t h e t e m p e r a t u r e p r o f i l e s y i e l d e d f r o m t h e
p o i n t s o n a n d u n d e r t h e b r e a d s k i n w e r e v e r y s i m i l a r d u e
t o t h e r a p i d t h e r m a l c o n d u c t i o n t h r o u g h t h e s k i n . H e n c e ,
t h e p o i n t s w e r e t a k e n a s o n e ( i . e . t h e s u r f a c e p o i n t ) .
2 . 3 M o i s t u r e m e a s u r e m e n t s
T h e d e t e r m i n a t i o n o f b r e a d m o i s t u r e d i s t r i b u t i o n d u r i n g
s t e a m i n g a t d i f f e r e n t t i m e s w a s a c h i e v e d b y s a m p l i n g a t
t h e l o c a t i o n s o f p o i n t s 2 & 3 , p o i n t s 4 & 5 , b o t t o m , c e n t r e
a n d s u r f a c e . T h e s t e a m e d b r e a d s a m p l e s w e r e d i v i d e d
i n t o s e v e r a l p o r t i o n s , a n d t h e i r m o i s t u r e s w e r e
6 1 4 V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
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d e t e r m i n e d u s i n g a g r a v i m e t r i c m e t h o d [ 1 5 ] b y w e i g h i n g
a s a m p l e b e f o r e a n d i m m e d i a t e l y a f t e r a n o v e n d r y i n g .
M o i s t u r e m e a s u r e m e n t s w e r e d o n e i m m e d i a t e l y a f t e r
s t e a m i n g w i t h o u t c o o l i n g t h e f i n a l p r o d u c t . T h i s w a s t o
e n s u r e t h a t t h e m o i s t u r e c o n t e n t s o f t h e b r e a d s a m p l e s
d u r i n g t h e s t e a m i n g p r o c e s s w e r e m o r e a c c u r a t e l y d e t e r -
m i n e d , a s t h e g r a v i m e t r i c a n a l y s i s w a s d o n e w i t h o u t
c o o l i n g w h e n w a t e r l o s s b y e v a p o r a t i o n w a s s t i l l c o m -
p a r a t i v e l y s m a l l . A f t e r d r y i n g , t h e s a m p l e s w e r e c o o l e d i n
a d e s i c c a t o r a n d w e i g h e d b y a n a n a l y t i c a l b a l a n c e ( s e n -
s i t i v i t y 0 . 0 0 1 g ) . T h e w e t - b a s e d m o i s t u r e c o n t e n t (M % ) o f
a s a m p l e w a s c a l c u l a t e d b y t h e d i f f e r e n c e b e t w e e n t h e
m a s s b e f o r e (mi ) a n d a f t e r ( m f) d r y i n g u s i n g t h e e q u a t i o n :
M m( % ) ¼ ( i – mf ) 1 0 0 / mi .
2 . 4 M a t h e m a t i c a l m o d e l l i n g o f h e a t t r a n s f e rd u r i n g s t e a m i n g
T he d o u gh /s t e ame d b r e ad p ie c e is m o d e lle d a s a t h re e -
d i me ns io n al h e mi sp h e re of r a di us R . The dough pieces at a
u n i f o r m t e m p e r a t u r e Ti a n d a u n i f o r m m o i s t u r e c o n t e n t W0
w er e t ak en o u t of t h e pr o of e r a nd p l ac e d i n to t he s te a me r
w h i c h w a s a t T0 a n d i ts r e la ti v e h um id i ty ( R H) w a s t a ke n
a s 10 0 % ( i. e. f u ll s te a m) a t ro om p r e ssu r e ( i.e . 1 a tm ).
H e a t t r a n s f e r i n s i d e t h e d o u g h c a n b e t r e a t e d a s a
h e a t c o n d u c t i o n p r o c e s s d e s p i t e t h a t c o n d u c t i o n w a s n o t
t h e o n l y m e c h a n i s m f o r h e a t t r a n s f e r i n t h e d o u g h .
A n o t h e r m e c h a n i s m w a s t h r o u g h w a t e r v a p o u r d i f f u s i o n
f r o m o u t e r l a y e r s t o w a r d s d o u g h c e n t r e ( F i g u r e 1 ) . W a t e r
v a p o u r c a n d i f f u s e f r o m t h e o u t s i d e e n v i r o n m e n t , w h i c h
c o n s i s t s o f 1 0 0 % w a t e r v a p o u r , t o w a r d s t h e c e n t r e o f t h e
d o u g h ; m e a n w h i l e w a t e r v a p o u r a l s o c o n d e n s e s a t t h e
s u r f a c e o f s t e a m e d b r e a d f r o m w h e r e m o i s t u r e i s t r a n s -
f e r r e d e i t h e r v i a l i q u i d w a t e r d i f f u s i o n o r w a t e r v a p o u r
d i f f u s i o n t o w a r d s t h e c e n t r e . H o w e v e r , i t w a s n o t e d t h a t
t h e f o r m a t i o n o f s k i n m i g h t h a v e s i g n i f i c a n t l y r e s t r i c t e d
t h e d i f f u s i o n o f w a t e r v a p o u r f r o m o u t s i d e t o b r e a d . T h i s
w a s s i m i l a r t o t h e f u n c t i o n o f c r u s t o b s e r v e d b y v a r i o u s
i n v e s t i g a t o r s d u r i n g t h e i r s t u d y o f b a k e d b r e a d , w h i c h
r e s t r i c t e d t h e d i f f u s i o n o f w a t e r v a p o u r f r o m b r e a d i n s i d e
t o w a r d s e n v i r o n m e n t [ 1 6 , 1 7 ] .
I n t h i s s t u d y , t w o m a j o r a s s u m p t i o n s w e r e m a d e :
( 1 ) I n t h e m o d e l , o n l y h e a t c o n d u c t i o n w a s t a k e n i n t o
c o n s i d e r a t i o n n e g l e c t i n g t h e e f f e c t s o f m a s s t r a n s f e r
d u e t o t h e c o m p u t a t i o n a l e f f i c i e n c y a n d t h e c o m p l e x i t i e s
i n v o l v e d i n m o d e l l i n g t h e m t o g e t h e r . H e a t t r a n s f e r w a s
c a r r i e d o u t b y c o n d u c t i o n d u e t o t h e t e m p e r a t u r e
g r a d i e n t r e s u l t e d f r o m c o n v e c t i o n a n d c o n d e n s a t i o n o n
t h e s u r f a c e . ( 2 ) T h e t o t a l a p p a r e n t v o l u m e w a s t a k e n a s
c o n s t a n t d u r i n g s t e a m i n g ( i . e . m a t e r i a l e x p a n s i o n w a s
i g n o r e d ) . T h e v a l i d i t y o f t h e s e a s s u m p t i o n s f o r t h e s y s t e m
w i l l b e e v a l u a t e d b y e x a m i n i n g h o w w e l l t h e m o d e l o u t -
p u t s a r e a g r e e a b l e t o t h e e x p e r i m e n t a l d a t a .
F i g u r e 1 T o p : S c h e m a t i c d i a g r a m o f t h e c r o s s - s e c t i o n o f s t e a m e d b r e a d a n d l a b e l l e d l o c a t i o n s f o r t e m p e r a t u r e m e a s u r e m e n t s . B o t t o m :
M e c h a n i s m o f h e a t a n d m a s s t r a n s f e r i n t h e s t e a m e d b r e a d
V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d 6 1 5
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T h e c om p l et e d es c r i pt i on o f a m a t h em a ti c al m o d e l f o r
t h e a b ov e- m e n ti on e d s ys t e m i s p re se n t ed i n t h e f o ll o wi n g
s e ct i on s .
2 . 4 . 1 G o v e r n i n g e q u a t i o n
H e at t r an s fe r e qu a t io n i n C a rt e s i an c o or d in at e s i s g i v en b y
@T
@t¼ α @
2 T
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@2 T
@y2þ
@2 T
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¼ αÑ2 T ð Þ1
α ¼ λρCC pp
w h e r e T i s t e m p e r a t u r e ( ° C ) , λ i s t h e r m a l c o n d u c t i v i t y(W m−1 ° C−1 ) , ρ i s d e n s i t y ( k g m−3 ) , C p i s s p e c i f i c h e a t(J k g−1 ° C−1 ) , a n d α i s t h e r m a l d i f f u s i v i t y ( m2 s−1 ) . A s s u m et h a t ρ a n d C p w e r e c o n s t a n t d u r i n g t h e s t e a m i n g p r o c e s sw h o s e v a l u e s a r e 5 4 4 k g m−3 a n d 2 , 3 1 0 J k g−1 ° C−1 . T h e n ,
λ w a s o b t a i n e d t h r o u g h o p t i m i z a t i o n o f t h e m o d e l b ym i n i m i z i n g t h e r o o t m e a n s q u a r e e r r o r ( R M S E ) b e t w e e n
t h e e x p e r i m e n t a l a n d m o d e l l e d v a l u e s . I t w a s f o u n d t o b e
a r o u n d 0 . 8 0 W m−1
° C−1
.
2 . 4 . 2 B o u n d a r y c o n d i t i o n s
T h e r e w e r e t w o b o u n d a r i e s t a k e n i n t o c o n s i d e r a t i o n i n
t h i s s t u d y . T h e t e m p e r a t u r e o f t h e d o u g h / b r e a d s u r -
r o u n d i n g s w a s t a k e n t o b e 1 0 0 ° C t h r o u g h o u t t h e s t e a m -
i n g p r o c e s s . S i n c e t h e s a m p l e w a s p l a c e d o n a p e r f o r a t e d
s o l i d p l a t e w h i c h a l l o w e d a c o n t i n u o u s a c c e s s o f s t e a m t o
t h e b o t t o m o f t h e d o u g h / b r e a d , t h e b o t t o m a n d t o p s u r -
f a c e s o f b r e a d w e r e a l s o t a k e n t o b e a t 1 0 0 ° C . T h i s w a s
d u e t o c o n d e n s a t i o n o f v a p o u r a t d o u g h s u r f a c e a t t h e
b e g i n n i n g s o t h a t t h e t e m p e r a t u r e d i f f e r e n c e s b e t w e e n
t h e m w e r e c l o s e t o z e r o a t a l l t i m e s d u r i n g s t e a m i n g .
I n o t h e r w o r d s , t h e t e m p e r a t u r e a t t h e s u r r o u n d i n g s
a n d t h e d o u g h s u r f a c e s ( i . e . t o p a n d b o t t o m ) w a s t h e
s a m e ( 1 0 0 ° C ) . T h i s a s s u m p t i o n w a s s u b s e q u e n t l y v e r i f i e d
b y t h e e x p e r i m e n t a l r e s u l t s .
2 . 4 . 3 N u m e r i c a l m e t h o d
T h e n um e r i ca l m et h od u s e d t o s o lv e t h e p ar t i al d i f fe r e nt i al
e q ua t i on , i . e . e q. ( 1 ) w a s t h e F or w ar d E u l er m e t h od . I t w a s
a p pl i e d v i a a f i ni t e d if fe r e nc e a n al ys i s. T h e f i ni te d i ff e r -
e n c e s c h e me w a s t o a p p r o xi ma t e th e d e ri v at i ve s u s i ng
c h a ng e s t h a t o cc ur a t f i ni t e i nt e rv a l s. T o d er i ve t h e f in i te
d i ff e re n c e e qu a t io n s, t h e d o u gh w a s s p l it i n t o g r i d p oi n t s
w i th e q ui s p ac e d i nt e rv a ls t h a t we r e i mp os e d o n a r ec t an -
g u l ar d o m ai n . E ac h t e mp e ra t u re r e a d in g o n t h e g ri d i s
d e n ot e d b y Ti , j , k . T h e g r i d sp a ci n g s i z es i n t h e x- , y- and
z- di r e ct i on s a r e d en o te d b y h x, hy a n d hz r e sp e ct i ve l y . Th e
g r i d p oi nt s a r e n u mb e re d i , j a n d k l a b el l i ng t h e p os i ti o n s
o n t h e g ri d i n t h e x- , y- and z- d ir e ct i o ns , r e sp e c ti v e ly ,
a c co r di n g t o C ar t es i a n c oo rd i n at e s.
U n d e r t h e c e n t r a l d i f f e r e n c e s c h e m e , t h e - d i r e c t i o nx
s e c o n d - o r d e r d e r i v a t i v e t e r m i n t h e r i g h t - h a n d s i d e
o f e q . ( 1 ) , i . e . @2 T@x 2 c a n b e a p p r o x i m a t e d b y e q . ( 2 ) a s
f o l l o w s :
@2 T
@x2
Ti1; ;j k 2 Ti j; ;k þ Tiþ1;j k;
h x2 ð2Þ
w h e r e h x i s t a k e n t o b e t h e s t e p - s i z e o f x. S i m i l a r a p p r o x -
i m a t i o n s c a n b e d o n e f o r t h e y- a n d z- d i r e c t i o n s e c o n d -
o r d e r d e r i v a t i v e s .
T h e d i f f e r e n c e e q u a t i o n f o r a g r i d p o i n t ( )i , j , k
l o c a t e d i n s i d e t h e b o u n d a r y i s d e r i v e d b y c o n s i d e r i n g
t h e g r i d p o i n t ( i , j , k ) a n d s i x s u r r o u n d i n g g r i d p o i n t s .
T h e F o r w a r d E u l e r m e t h o d e v a l u a t e s T i j , k, a t a f u t u r e
t i m e s t e p (t þΔt ) u s i n g t h e f o l l o w i n g e q u a t i o n :
@T
@t¼
Tðt þ ΔΔtÞ TðtÞ
ΔΔt
w h e r e T(t ) a n d T(t þΔt ) a r e t e m p e r a t u r e a t t i m e a n dtt i m e ( i s t i m e s t e p . S u b s t i t u t i n g e q st þΔt ) , r e s p e c t i v e l y . ΔΔt( 2 ) a n d ( 3 ) i n t o e q . ( 1 ) r e s u l t s i n ( f o r s i m p l i c i t y ,
o n l y x- d i r e c t i o n d e r i v a t i v e i s s h o w n f o r i l l u s t r a t i o n
p u r p o s e ) :
Tðt þ ΔΔtÞ TðtÞΔΔt
ji; ;j k ¼ αTi1;j;k 2 Ti j; ;k þ Ti j kþ1; ;
h x2 ð Þ4
E q u a t i o n ( 4 ) i s s u b s e q u e n t l y s o l v e d f o r T(t þΔt ) t oo b t a i n t h e T i , j , k v a l u e a t a f u t u r e t i m e s t e p . T h i s s c h e m e
i s c a l l e d a n e x p l i c i t m e t h o d b e c a u s e , i f T i , j , k a t t a r e
g i v e n f o r a l l t h e g r i d p o i n t s , T i , j , k f o r t h e n e w t þΔt f o ra n y g r i d p o i n t c a n b e i m m e d i a t e l y c a l c u l a t e d b y s i m p l y
u s i n g e q . ( 4 ) .
I t w a s n o t e w o r t h y t h a t t h e t i m e s t e p Δt o f t h e e x p l i c i tm e t h o d m u s t s a t i s f y
ΔΔt 0:5 h x
2
α ð Þ5
O t h e r w i s e , i n s t a b i l i t y o f t h e s o l u t i o n w i l l h a p p e n . H e n c e ,
n o m a t t e r h o w s l o w t h e p h y s i c a l c h a n g e o f t h e s y s t e m i s ,
ΔΔt m u s t b e e q u a l t o o r s m a l l e r t h a n 0:5 h x2
α . T h i s a l s o m e a n st h a t ΔΔt m u s t b e c o m e i n c r e a s i n g l y s m a l l e r i f h x i s r e d u c e d .
6 1 6 V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
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A p r o g r a m b a s e d o n t h e a b o v e - m e n t i o n e d F o r w a r d
E u l e r m e t h o d w a s i m p l e m e n t e d u s i n g M a t l a b , a n d t h e
m o d e l w a s s i m u l a t e d f o r a p e r i o d o f 2 0 m i n . T h e R M S E
b e t w e e n t h e m o d e l l e d r e s u l t s a n d t h e e x p e r i m e n t a l
r e s u l t s w a s m i n i m i z e d t h r o u g h a d j u s t i n g m o d e l p a r a -
m e t e r s . I n p a r t i c u l a r , λ v a l u e i n e q . ( 1 ) w a s u s e d a s a ni n p u t i n t h e o p t i m i z a t i o n s y s t e m t o m i n i m i z e t h e o u t p u t ,
i . e . t h e R M S E v a l u e .
3 R e s u l t s a n d d i s c u s s i o n
3 . 1 M o i s t u r e p r o f i l e s
F i g ur e 2 p re se n t s th e m oi s tu r e p ro fi l e s at d i ff e re n t
p o i nt s o f m e as u re m e nt i n t h e s t e am e d b re a d . M o is t u re
c o n te nt s t h r o ug ho u t t h e b re a d i n cr e as e d w i th s t e a mi n g
t i me . A l so , t h e m o is t ur e c o n te nt b e c a m e re l a ti v e ly
l o we r a s th e m ea s ur e m e nt p oi n t mo v e d f ur t h er a wa y
f r om t h e s u rf a c e. H e n ce , i t c a n b e s u gg e st e d t h at w a t er
d i ff u s io n o c cu r re d f r o m t h e o ut si d e t o wa r d s t he i n s id e o f
t h e b re a d t o i ts c e n tr e . A s s h o wn i n F i gu r e 2 , t h e mo i s tu r e
c o n te nt s d ur i n g th e e nt i re b r e ad s t ea mi n g p ro c e ss f e ll
w i th i n a re l a t iv e ly n a rr o w ra n g e , h e n ce m o i st u re t r an s f er
a n d i ts i mp a c t on h e at t r an s fe r w e re a s su m e d t o be n e g li -
g i bl e i n t h e c u rr e nt m o d e l d ev e l op ed f o r h e a t tr a n sf e r .
T h e i n c r e a s e i n m o i s t u r e c o n t e n t w i t h s t e a m i n g t i m e
w a s d u e t o c o n d e n s a t i o n o f w a t e r a t t h e s u r f a c e o f b r e a d .
T h e s a t u r a t e d s t e a m i n t h e s u r r o u n d i n g s a l s o p r e v e n t e d
e v a p o r a t i o n o f w a t e r f r o m t h e b r e a d , r e s u l t i n g i n a s u r -
f a c e o f h i g h m o i s t u r e c o n t e n t . T h e h i g h w a t e r c o n t e n t a t
t h e b o t t o m o f t h e s t e a m e d b r e a d w a s d u e t o t h e f a c t t h a t
t h e s a m p l e w a s r e s t i n g o n at h i n , w e t p i e c e o f c l o t h o n
t h e t o p o f a s t a i n l e s s s t e e l t r a y d u r i n g s t e a m i n g . T h e c l o t h
w a s t o p r e v e n t t h e b r e a d f r o m a d h e r i n g t o t h e t r a y , a
c o m m o n p r a c t i c e i n i n d u s t r i a l s t e a m b r e a d p r o d u c t i o n .
S i n c e t h e c l o t h w a s a b l e t o a b s o r b m o r e w a t e r , i t p r o -
d u c e d a h i g h m o i s t u r e g r a d i e n t b e t w e e n t h e c l o t h a n d t h e
b o t t o m o f t h e s t e a m e d b r e a d , t h u s c a u s i n g h i g h m o i s t u r e
c o n t e n t s a t t h e b o t t o m .
3 . 2 N u m e r i c a l r e s u l t s
F o r w a r d E u l e r m e t h o d w a s i m p l e m e n t e d u s i n g M a t l a b ,
a n d t h e m o d e l w a s s i m u l a t e d f o r a p e r i o d o f 2 0 m i n .
F i g u r e 3 s h o w s s o m e s n a p - s h o t s o f t h e t e m p e r a t u r e p r o -
f i l e a t t h e s t e a m i n g t i m e s o f 0 , 1 , 2 , 5 , 1 0 a n d 2 0 m i n . T h e
g r a d u a l c h a n g e i n t e m p e r a t u r e a f t e r 5 m i n a c c u r a t e l y
d e p i c t e d a n d m a t c h e d t h e c h a r a c t e r i s t i c s o f t h e e x p e r i -
m e n t a l r e s u l t s o b t a i n e d .
3 . 3 T e m p e r a t u r e p r o f i l e s
F i g u r e 4 s h o w s t h a t a t a l l m e a s u r e m e n t p o i n t s d u r i n g t h e
s t e a m i n g p r o c e s s , t h e t e m p e r a t u r e e v e n t u a l l y r e a c h e d t h e
h e a t i n g m e d i u m t e m p e r a t u r e o f 1 0 0 ° C . A l l l o c a t i o n s i n
40
41
42
43
44
45
46
47
0 2 4 6 8 10 12 14 16 18 20
Steaming time, minSteaming time, min
Mo
istu
re c
on
ten
t, %
Mo
istu
re c
on
ten
t, % Point 2
Point 3
Point 4
Point 5
Bottom
Centre
Surface
F i g u r e 2 M o i s t u r e p r o f i l e s o f s t e a m e d b r e a d a t d i f f e r e n t m e a s u r e m e n t p o i n t s
V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d 6 1 7
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-
0z, cm
x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 0t
90
80
Te
mp
era
ture
,°C
70
60
50
40
0 z, cm x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 1 mint
90
80
Te
mp
era
ture
,°C
70
60
50
40
0z, cm
x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 2 mint
90
80
Te
mp
era
ture
,°C
70
60
50
40
0 z, cm x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 5 mint
90
80
Te
mp
era
ture
,°C
70
60
50
40
0 z, cm x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 10 mint
90
80
Te
mp
era
ture
,°C
70
60
50
40
0 z, cm x, cm –5 1
23
45
0
5
100
Temperature profile of cross-section of mantou during steaming at = 20 mint
90
80
Te
mp
era
ture
,°C
70
60
50
40
F i g u r e 3 S n a p - s h o t o f t h e t e m p e r a t u r e p r o f i l e t h r o u g h s t e a m i n g a t t i m e s 0 , 1 , 2 , 5 a n d 2 0 m i n
6 1 8 V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
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-
t h e b r e a d s a m p l e s h a d a n i n i t i a l t e m p e r a t u r e o f ~ 4 2 ° C . I t
w a s a l s o o b s e r v e d t h a t t h e t e m p e r a t u r e r i s e a t t h e c e n t r e
o f t h e s a m p l e w a s s l o w e s t d u e t o i t s l o n g e s t d i s t a n c e
a w a y f r o m t h e s u r f a c e . T h e t e m p e r a t u r e r i s e a t a p o i n t
o f m e a s u r e m e n t b e c a m e g r e a t e r a s i t s d i s t a n c e f r o m t h e
s u r f a c e o f t h e b r e a d d e c r e a s e d .
T h e i n i t i a l l o w e r t e m p e r a t u r e f o r t h e s u r r o u n d i n g ( i . e .
l e s s t h a n 1 0 0 ° C ) w a s d u e t o t h e o p e n i n g a n d c l o s i n g o f
t h e s t e a m e r l i d p r i o r t o t h e s t e a m i n g p r o c e s s , r e s u l t i n g i n
a l o s s o f s t e a m a n d a d i p i n t h e t e m p e r a t u r e . F o r s i m p l i -
c i t y i n t h e m o d e l l i n g , t h e s u r r o u n d i n g t e m p e r a t u r e w a s
t a k e n t o b e 1 0 0 ° C a t a l l t i m e s . T h e r a p i d h e a t t r a n s f e r
t h r o u g h c o n v e c t i o n o f s t e a m f r o m t h e b o i l i n g w a t e r a t t h e
b o t t o m r e s e r v o i r t o t h e o t h e r p a r t s o f t h e s t e a m e r j u s t i f i e s
s u c h a n a s s u m p t i o n .
3 . 4 O p t i m i z a t i o n o f v a l u e sλ
T h e o pt i mi z e d λ va l u e s wh i c h re s u lt e d i n t he l o w es t R M S Ev a l ue b e t w ee n t h e mo d e ll e d a n d e xp e ri m e nt a l v a lu e s a re
s h ow n i n Ta b le 1 . S i n ce t he t e m p er a tu re p r o fi l e s a t th o s e
p o i nt s d ir e ct l y u nd e r an d o n th e s u rf a ce w e re o b s e rv ed t o
b e a l mo st t h e s a m e fo r e ve r y e xp er i m e nt , t he s e t e m p er a -
t u re p r o f il e s a t a l l ti m e s o f th e s t e am i ng p r o c es s w e re
t a ke n t o b e t h e sa m e i n t hi s w o rk ( i . e. “s u rf a c e” m e as u r e -
m e nt p o i nt ) . T he e ff e c ti v e th e rm a l c o nd uc t i vi t y (λ) val ue s
d e te r mi n e d i n t h is s t u dy w e re i n t h e r an g e o f 0 .7 2 5–0 .8 5 5
W m−1
° C−1
( T ab l e 1 ), w h ic h w er e c l o se t o th e v a l ue s
r e po r t ed i n t h e l i te r a tu r e f o r b ak e d b re a d , e .g . 0 . 7 2
W m−1 ° C −1 f o r w hi t e b r e ad a f t e r 8 m i n o f b ak i n g [ 18 ] .
3 . 5 V e r i f i c a t i o n o f m o d e l u s i n g o p t i m i z e dλ v a l u e s
T h e o b t a i n e d m o d e l w a s v e r i f i e d w i t h t h e e x p e r i m e n t a l
t e m p e r a t u r e p r o f i l e s a t t h e i n t e r n a l f i v e p o i n t s o f m e a -
s u r e m e n t d u r i n g t h e s t e a m i n g . T h e v e r i f i c a t i o n s
p r o d u c e d l o w R M S E a n d h i g h c o e f f i c i e n t o f d e t e r m i n a t i o n
(R 2) v a l u e s b e t w e e n t h e t w o s e t s o f d a t a u s i n g t h e
o p t i m i z e d λ v a l u e s , a s l i s t e d i n T a b l e 1 . F i g u r e 5 s h o w st h e c o m p a r i s o n b e t w e e n t h e m o d e l l e d r e s u l t s a n d t h e
e x p e r i m e n t a l r e s u l t s . B a s e d o n t h e s m a l l R M S E v a l u e s
a n d h i g h R 2 v a l u e s , t h e m o d e l v e r i f i c a t i o n r e s u l t s
s u g g e s t t h a t t h e m o d e l i s a c c e p t a b l e . T h e m o d e l h a s a
g o o d p e r f o r m a n c e a n d c o u l d b e u s e d t o r e p r o d u c e
T a b l e 1 O p t i m i z e d λ v a l u e s a t f i v e d i f f e r e n t l o c a t i o n s i n t h es t e a m e d b r e a d w i t h t h e c o r r e s p o n d i n g R M S E a n d R
2v a l u e s
M e a s u r e m e n t p o i n t s λ R M S E R2
S u r f a c e 0 . 7 4 0 1 . 6 7 6 0 . 9 5 3
C e n t r e 0 . 8 3 5 1 . 4 7 8 0 . 9 9 7
P o i n t s 2 & 3 0 . 8 1 0 1 . 6 4 0 0 . 9 8 7
P o i n t s 4 & 5 0 . 8 5 5 2 . 9 6 7 0 . 9 8 0
B o t t o m 0 . 7 2 5 2 . 1 3 9 0 . 9 1 2
0
20
40
60
80
100
120
0 4 8 12 16 20 24 28
Steaming time, minSteaming time, min
Te
mp
era
ture
, °C
Te
mp
era
ture
, °C
Surroundings
Bottom
Points 2 & 3
Points 4 & 5
Centre
Directly under surface
Direct on surface
F i g u r e 4 E x p e r i m e n t a l r e s u l t s o f t e m p e r a t u r e p r o f i l e s i n t h e s t e a m e d b r e a d d u r i n g s t e a m i n g . E a c h t e m p e r a t u r e p r o f i l e i s a c u m u l a t i v e
r e p r e s e n t a t i o n o f t h r e e o r m o r e p r o f i l e s o f t h e s a m e p o i n t i n t h r e e o r m o r e d i f f e r e n t e x p e r i m e n t s
V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d 6 1 9
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( a )( b )
100 5 15
Time, min
20 25 30
100
90
80
70
60
50
40
Te
mp
era
ture
, °C
Temperature profile of model and experiment (surface), correlation coefficient = 0.95308
Model
Experiment
100 5 15
Time, min
20 25 30
100
90
80
70
60
50
40
Te
mp
era
ture
, °C
Model
Experiment
Temperature profile of model and experiment (centre), correlation coefficient = 0.99702
( c )
Temperature profile of model and experiment (points 2 & 3), correlation coefficient = 0.98662
100 5 15
Time, min
20 25 30 100 5 15
Time, min
20 25 30
100 5 15
Time, min
20 25 30
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, °C
Model
Experiment
( d )
( e )
Temperature profile of model and experiment (points 4 & 5), correlation coefficient = 0.97993
Temperature profile of model and experiment (bottom), correlation coefficient = 0.91165
100
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Model
Experiment
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F i g u r e 5 V e r i f i c a t i o n s o f t h e d e v e l o p e d m o d e l u s i n g e x p e r i m e n t a l d a t a o f t e m p e r a t u r e p r o f i l e s t a k e n a t ( a ) t h e s u r f a c e , ( b ) t h e c e n t r e ,
( c ) p o i n t s 2 & 3 , ( d ) p o i n t s 4 & 5 a n d ( e ) t h e b o t t o m o f t h e b r e a d
6 2 0 V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
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t e m p e r a t u r e p r o f i l e s i n t h e s t e a m e d b r e a d d u r i n g s t e a m -
i n g p r o c e s s .
3 . 6 V a l i d a t i o n o f m o d e l
T h e m od e l w as v a l i da t e d w it h t h e e xp e ri m e nt a l t em p er a -
t u re p r of i l es a t t he f i ve p o i nt s o f t em p er a tu r e m ea s u re me n t
w i th t w o a d d it i on a l s e ts o f i n d ep en d e nt e x p er i me n t al
r u ns . T h e v a li d at i on s a l s o p ro d uc e d l o w R MS E a n d
h i g h R2
v a l ue s b e tw e en t h e t w o s e ts o f d a t a u s in g t h e
o p ti m i ze d λ v a l ue s , wh i c h a r e l is t e d i n T a b l e 2 . F i g ur e 6s h ow s t h e v a l id at i o n r e su l ts o f t h e o b t ai n e d mo d e l
u s i ng t h e i n d ep en d e nt e x p er i m e nt a l d a t a . A g o o d ag r e e-
m e nt b e t w ee n t h e m od e l l ed v a l ue s a n d e x p er i me n ta l
r e su l t s i s e vi d e nt i n F i g ur e 6 . T o ge t h er w i th t h e l o w
R M S E v al u e s a nd h i g h R2 v a l ue s s h o wn i n T a b le 2 , i t
c o n fi rm s t h a t t h e m o de l h a s a g o o d q ua l it y a n d c a n b e
u s e d to p r e d i ct t e mp e r at u r e p ro f il e s a n d t hu s e n e rg y c o n-
s u mp t i on i n t h e s t e am e d b re a d d u r in g s t ea m in g .
F u r th e rm o re , t h e m o d el m a y a i d t o o p ti m i zi n g /m in i m i zi ng
t h e s t ea m in g t i me t h a t a s su r e s a s a t is f ac t or y p r o d uc t,
w h i ch e na b l es t h e mi n i mi z at i on o f e ne r g y c o n s um p ti o n
b y t h e s t e a m i n g p r o c e s s .
Temperature profile of model and experiment (surface), correlation coefficient = 0.96378 Temperature profile of model and experiment (centre), correlation coefficient = 0.99716
100 5 15
Time, min
20 25
100
90
80
70
60
50
40
Te
mp
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ture
,°C
Model
Experiment
100 5 15
Time, min
20 25
100
90
80
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60
50
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Te
mp
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ture
,°C
Model
Experiment
( a ) ( b )
Temperature profile of model and experiment (points 2 & 3), correlation coefficient = 0.98704
100 5 15
Time, min
20 25
100
90
80
70
60
50
40
Te
mp
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ture
,°C
Model
Experiment
( c )
Temperature profile of model and experiment (points 4 & 5), correlation coefficient = 0.9795
100 5 15
Time, min
20 25
100
90
80
70
60
50
40
Te
mp
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ture
,°C
Model
Experiment
( d )
F i g u r e 6 V a l i d a t i o n s o f t h e d e v e l o p e d m o d e l u s i n g i n d e p e n d e n t e x p e r i m e n t a l d a t a o f t e m p e r a t u r e p r o f i l e s t a k e n a t ( a ) t h e s u r f a c e , ( b ) t h e
c e n t r e , ( c ) p o i n t s 2 & 3 , ( d ) p o i n t s 4 & 5 a n d ( e ) t h e b o t t o m o f t h e s t e a m e d b r e a d
T a b l e 2 V a l i d a t i o n s o f t h e d e v e l o p e d m o d e l u s i n g i n d e p e n d e n t
e x p e r i m e n t a l d a t a w i t h t h e c o r r e s p o n d i n g R M S E a n d R2
v a l u e s
M e a s u r e m e n t p o i n t s R M S E ( v a l i d a t i o n s ) R2 ( v a l i d a t i o n s )
S u r f a c e 2 . 0 3 7 0 . 9 6 4
C e n t r e 1 . 3 9 1 0 . 9 9 7
P o i n t s 2 & 3 1 . 9 7 0 0 . 9 8 7
P o i n t s 4 & 5 3 . 5 4 5 0 . 9 8 0
B o t t o m 2 . 5 5 1 0 . 9 3 4
V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d 6 2 1
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4 C o n c l u s i o n s
A t hr e e -d i men s io n al p ar t i al d i ffe r en t ia l eq u at i on h e at t ra n s-
f er m o d e l fo r t he s t e am in g p r oc e ss o f s t ea m e d br e ad h a s
b ee n d ev e lo pe d a nd n u me r ic al l y so l ve d b y em p lo y in g t h e
F or w ar d E u le r m et h o d i n Ca r te si a n c oo rd i na t e s. A de q ua t el y
l o w R MS E a nd h i g h R2 v al u es w e r e o bt ai n e d fo r b ot h
v e ri fi c at i on a nd v a li da t i on da t as e ts t h at w e re i n de pe n d en t l y
g e n e r a t e d t h r o u g h e x p e r i m e n t s . T h i s i n d i c a t e s t h e g o o d
q ua l i ty o f th e mo d e l. T h e r es u l ts d em on s tr at e d th a t th e
t em p er a tu re p r of i l es i n s t e am e d b re a d d ur in g s te am i ng c a n
b e sa t i sfa c to r i ly m o d e ll ed a n d pr e di ct ed b y c on s id er i ng o nl y
h e a t t r a n s f e r t h r o u g h o p t i m i z e d e f f e c t i v e t h e r m a l c o n d u c t i v -
i ty (λ) va l u es . Mo is t ur e c on t e nt s t h ro u gh o ut t h e st ea m e d
b r ea d i n cr ea s e d p rog r e ss iv el y w i th s t e am i ng t i m e , al b ei t
v ar y in g in a n a rr o w ra ng e , wh ic h i nd i ca te d t ha t wa t e r d i ff u-
s i o n o c c u r r e d f r o m t h e o u t s i d e t o w a r d s t h e i n s i d e o f t h e
s t ea me d b re a d to i t s ce n tr e . F u tu re w o rk s sh o ul d b e ai m ed
t o s t u d y t h e p r o c e s s o f s i m u l t a n e o u s h e a t t r a n s f e r a n d m a s s
t r an sf e r d ur in g t h e st e am in g p r oc e ss t o f ur t h er e v al u at e i f
t he c o n tr i bu t io n f ro m t h e m as s t ra n sf e r i s s i gni f ic a n t or n o t
t o t h e qu a li ty o f a c o up l e d mo d el .
A c k n o w l e d g e m e n t s : F i n a n c i a l s u p p o r t s f r o m S i n g a p o r e
M i n i s t r y o f E d u c a t i o n t h r o u g h A c a d e m i c R e s e a r c h F u n d
T i e r 1 g r a n t R - 1 4 3 - 0 0 0 - 4 0 4 - 1 1 2 a n d t h e N a t i o n a l
U n i v e r s i t y o f S i n g a p o r e ( S u z h o u ) R e s e a r c h I n s t i t u t e
u n d e r t h e g r a n t n u m b e r N U S R I 2 0 1 1 - 0 0 7 a r e a c k n o w l -
e d g e d . T h e f i r s t a u t h o r i s g r a t e f u l t o t h e f i n a n c i a l s u p p o r t
f r o m t h e D i r e c t o r a t e G e n e r a l o f I n d o n e s i a n H i g h e r
E d u c a t i o n i n s p o n s o r i n g h e r P h D s t u d y .
R e f e r e n c e s
1 . H u a n g S , B e t k e r S , Q u a i l K , M o s s R . A n o p t i m i z e d p r o c e s s i n g
p r o c e d u r e b y r e s p o n s e s u r f a c e m e t h o d o l o g y ( R S M ) f o r
n o r t h e r n - s t y l e C h i n e s e s t e a m e d b r e a d . J C e r e a l S c i
1 9 9 3 ; 1 8 : 8 9 1 0 2 .–
2 . C a r v a l h o M G , M a r t i n s N . M a t h e m a t i c a l m o d e l i n g o f h e a t
a n d m a s s t r a n s f e r i n a f o r c e d c o n v e c t i o n b a k i n g o v e n . I n :
V o l i n t i n e B G , e d i t o r . A I C h E s y m p o s i u m s e r i e s - h e a t t r a n s f e r .
S a n D i e g o , C A , 1 9 9 2 : 2 0 5 1 1 .–
3 . S i m p s o n R , A b a k a r o v A . T h e r m a l f o o d p r o c e s s i n g
o p t i m i z a t i o n : s i n g l e a n d m u l t i - o b j e c t i v e o p t i m i z a t i o n c a s e
s t u d i e s . I n : A h m e d J , R a h m a n M S , e d i t o r s . H a n d b o o k
o f f o o d p r o c e s s d e s i g n . O x f o r d : W i l e y - B l a c k w e l l ,
2 0 1 2 : 1 6 7 8 9 .–
4 . P a u l u s K O . C o o k i n g k i n e t i c s : m o d e l s a n d k n o w l e d g e . I n :
Z e n t h e n P , e d i t o r . T h e r m a l p r o c e s s i n g a n d q u a l i t y o f f o o d s .
L o n d o n : E l s e v i e r A p p l i e d S c i e n c e , 1 9 8 4 : 3 0 4 1 2 .–
5 . S a b l a n i S S , M a r c o t t e M , B a i k O D , C a s t a i g n e F . M o d e l i n g o f
s i m u l t a n e o u s h e a t a n d w a t e r t r a n s p o r t i n t h e b a k i n g p r o c e s s .
L e b e n s m W i s s T e c h n o l 1 9 9 8 ; 3 1 : 2 0 1 9 .–
6 . T h e r d t h a i N , Z h o u W , A d a m c z a k T . T w o - d i m e n s i o n a l C F D
m o d e l l i n g a n d s i m u l a t i o n o f a n i n d u s t r i a l c o n t i n u o u s b r e a d
b a k i n g o v e n . J F o o d E n g 2 0 0 7 ; 6 0 : 2 1 1 1 7 .–
7 . W o n g S Y , Z h o u W , H u a J S . C F D m o d e l i n g o f a n i n d u s t r i a l c o n -
t i n u o u s b r e a d - b a k i n g p r o c e s s i n v o l v i n g U - m o v e m e n t . J F o o d
E n g 2 0 0 7 ; 7 8 : 8 8 8 9 6 .–
8 . Z h o u W . B ak in g p ro c es s : ma t he m at i ca l m od e li n g a nd
a n al y s is . In : F ar i d M M, e d i t or . Ma t he m at i ca l m od e li n g of f o od
p r o c e s s i n g . B o c a R a t o n , F L : C R C P r e s s , T a y l o r & F r a n c i s G r o u p ,
2 0 10: 35 7–3 72 ) .
9 . B a i k O D , M a r c o t t e M , S a b l a n i S S , C a s t a i g n e F . T h e r m a l a n d
p h y s i c a l p r o p e r t i e s o f b a k e r y p r o d u c t s . C r i t R e v F o o d S c i N u t r
2 0 0 1 ; 4 1 : 3 2 1 5 2 .–
1 0 . M a r c o t t e M . H e a t a n d m a s s t r a n s f e r d u r i n g b a k i n g . I n :
Y a n n i o t i s S , S u n d e n B , e d i t o r s . H e a t t r a n s f e r i n f o o d
p r o c e s s i n g . S o u t h a m p t o n a n d B o s t o n , M A : W I T P r e s s ,
2 0 0 7 .
1 1 . Z u n i g a R , L e - B a i l A . A s s e s s m e n t o f t h e r m a l c o n d u c t i v i t y a s a
f u n c t i o n o f p o r o s i t y i n b r e a d d o u g h d u r i n g p r o v i n g . F o o d
B i o p r o d u c t s P r o c e s s 2 0 0 9 ; 8 7 : 1 7 2 2 .–
1 2 . H o u G G , P o p p e r L . C h i n e s e s t e a m e d b r e a d . I n : P o p p e r L , S c h ä f e r W ,
F r e u n d W , e d i t o r s . F u t u r e o f f l o u r : a c o m p e n d i u m o f f l o u r i m p r o v e -
m e n t . G e r m a n y : M ü h l e n ch e m i e , 2 0 0 6 .
1 3 . F e y i s s a A H , G e r n a e y K V , A d l e r - N i s s e n J . U n c e r t a i n t y a n d
s e n s i t i v i t y a n a l y s i s : m a t h e m a t i c a l m o d e l o f c o u p l e d h e a t a n d
m a s s t r a n s f e r f o r a c o n t a c t b a k i n g p r o c e s s . J F o o d E n g
2 0 1 1 ; 1 0 9 : 2 8 1 9 0 .–
1 4 . S a k i n - Y i l m a z e r M , K e m e r l i T , I s l e r o g l u H , O z d e s t a n O ,
G u v e n G , U r e n A , e t a l . B a k i n g k i n e t i c s o f m u f f i n s i n c o n v e c t i o n
a n d s t e a m a s s i s t e d h y b r i d o v e n s . J F o o d E n g 2 0 1 3 ; 1 1 9 :
4 8 3 9 .–
Temperature profile of model and experiment (bottom), correlation coefficient = 0.93423
100 5 15
Time, min
20 25
100
90
80
70
60
50
40
Te
mp
era
ture
,°C
Model
Experiment
( e )
F i g u r e 6 ( c o n t i n u e d )
6 2 2 V . K . A n a n i n g s i h e t a l . : H e a t T r a n s f e r d u r i n g S t e a m i n g o f B r e a d
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1 5 . A O A C . I n : C u n n i f f P , e d i t o r . O f f i c i a l m e t h o d s o f a n a l y s i s o f
A O A C i n t e r n a t i o n a l , 6 0 t h e d . M a r y l a n d : A O A C I n t e r n a t i o n a l ,
1 9 9 6 .
1 6 . H a m d a m i N , M o n t e a u J - Y , L e B a i l A . M o i s t u r e d i f f u s i v i t y a n d
w a t e r a c t i v i t y o f f r o z e n p a r t b a k e d b r e a d . I n t J F o o d S c i T e c h n o l
2 0 0 3 ; 4 1 : 3 3 4 4 .–
1 7 . Z a n o n i B , P e r i C , G i a n o t t i R . D e t e r m i n a t i o n o f t h e t h e r m a l