doc vs internet + libraryrepository.unika.ac.id/15903/2/unicheck steaming the...u, % heat transfer...

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92.01% Originality 7.99% Similarity 175 Sources Doc vs Internet + Library Web sources: 145 sources found 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% Heat Transfer during S... Uploaded: 09/14/2018 Checked: 09/14/2018 Similarity Similarity from a chosen source Possible character replacement abc Citation References

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  • 92.01% Originality 7.99% Similarity 175 Sources

    Doc vs Internet + Library

    Web sources: 145 sources found

    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%

    Heat Transfer duringS...

    Uploaded: 09/14/2018

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    Similarity from a chosen source

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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/

  • 35. https://www.swmich.edu/webed/syllabi/201420/201420-1496-syllabus.doc 0.15%36. https://en.wikipedia.org/wiki/Compassion_fatigue 0.15%37. http://www.povray.org/documentation/3.7.0/r3_4.html 0.15%38. https://www.childwelfare.gov/pubPDFs/braindevtrauma.pdf 0.15%39. http://www.futureacademy.org.uk/files/menu_items/other/2_icc_2876_4078_fullText_0_2400.pdf 0.15%40. https://searchworks.stanford.edu/?f%5Bbuilding_facet%5D%5B%5D=Marine+Biology+(Miller)&pa… 0.15%41. http://www.aurora-schools.org/userfiles/140/Classes/1203/A%20Brief%20History%20of%20the%… 0.15%42. http://www.kyrene.org/cms/lib2/AZ01001083/Centricity/Domain/971/2013-2014%20Tips%20and%… 0.15%43. http://meetings.aps.org/Meeting/MAR08/SessionIndex3/%3FSessionEventID%3D76699/?VirtualS… 0.15%44. http://www.who.int/patientsafety/events/04/4_Timmons.pdf 0.15%45. https://www.suse.com/documentation/sled-12/singlehtml/book_sle_tuning/book_sle_tuning.html 0.15%46. https://www.slideshare.net/lecressini13/g8-healthq4lmcigarettes 0.15%47. http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter3.pdf 0.15%48. https://pubchem.ncbi.nlm.nih.gov/rest/pug_view/data/compound/1118/JSON/?response_type=dis… 0.15%49. http://cul.colgate.edu/content/new-acquisitions-may-2017 0.15%50. https://searchworks.stanford.edu/?per_page=100&q=%22Mathematics+Textbooks.%22&search_… 0.15%51. https://www3.nd.edu/~lawlib/innopac/acqspring11.html 0.15%52. http://research.gold.ac.uk/view/year/2009.type.html 0.15%53. https://es.slideshare.net/jaimeblancodeblas/hbitos-de-compra-offline-y-online-del-consumidor-esp… 0.15%54. https://vdocuments.site/documents/quimica-analitica-baeza-teoria-y-problemas-2005-5707bb4745… 0.15%55. https://moodle.capilanou.ca/mod/book/tool/print/index.php?id=328667 0.15%56. http://povray.org/documentation/current/r3_4.html 0.15%57. https://patents.google.com/patent/US6204248B1/en 0.15%58. https://www.treasury.gov/press-center/press-releases/Documents/TBAC%20Discussion%20Char… 0.15%59. https://viisaselama.fi/lahteet/kuinka-elaa-kuolematta 0.15%60. http://duqueteaches.blogspot.com/2009/12/earth-space-review.html 0.15%61. https://en.wikibooks.org/wiki/Microsoft_Office/Create_a_basic_two_table_database_with_reports 0.15%62. http://norient.com/posts/page/3 0.15%63. https://assets.kpmg.com/content/dam/kpmg/es/pdf/2017/06/la-realidad-de-consumidores-online.pdf 0.15%64. https://atpw.files.wordpress.com/2013/03/i-geotek.pdf 0.15%65. http://news.nhk-book.co.jp/archives/5467 0.15%66. https://www.kidsnewtocanada.ca/mental-health/developmental-disability 0.15%67. https://www.airbnb.ca/s/Niverville--NY 0.15%68. https://digitum.um.es/jspui/bitstream/10201/4413/3/DiazMolins.pdf.txt 0.15%69. https://cul.colgate.edu/content/new-acquisitions-july2017 0.15%70. http://web.mit.edu/povray_v3.7.0a/share/doc/povray-3.7/html/r3_4.html 0.15%71. https://www.slideshare.net/nandakishore58555941/numerical-methods-for-engineers-solution-man… 0.15%72. http://msvanwoerkom.weebly.com/uploads/3/6/7/5/3675744/a_brief_history_of_the_united_states… 0.15%73. https://en.wikibooks.org/wiki/Microsoft_Office/MLA_format 0.15%74. http://duqueteaches.blogspot.com/2009_12_01_archive.html 0.15%75. http://duqueteaches.blogspot.com 0.15%76. http://teacher.pas.rochester.edu/phy121/LectureNotes/Chapter18/Chapter18.html 0.15%77. http://wardamericanrevolution.weebly.com/uploads/1/4/9/1/14911572/unit_2_lesson_1_5e.pdf 0.15%78. https://wikivisually.com/wiki/Mongoloid 0.15%79. http://www.pi-schools.gr/special_education_new/ftp/books/a_gymnasiou/18_arial/a_maths_arial_1… 0.15%80. https://searchworks.stanford.edu/?f%5Btopic_facet%5D%5B%5D=Chemical+engineering&per_pa… 0.15%

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    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 -

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    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 .

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    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 -

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    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 .

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    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 ).

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    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 .

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    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 :

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    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

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    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

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    .

    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 .

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    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

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    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.

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    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 :

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    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 .

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    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 :

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    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 ) :

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    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 ) .

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    ΔΔt 0:5 h x

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    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

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    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

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    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

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    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 .

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    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 .

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    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

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    c o n t e n t s a t t h e b o t t o m .

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    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

    100

    90

    80

    70

    60

    50

    40

    Te

    mp

    era

    ture

    , °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

    90

    80

    70

    60

    50

    40

    Te

    mp

    era

    ture

    , °C

    Model

    Experiment

    100

    90

    80

    70

    60

    50

    40

    Te

    mp

    era

    ture

    , °C

    Model

    Experiment

    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

    era

    ture

    ,°C

    Model

    Experiment

    100 5 15

    Time, min

    20 25

    100

    90

    80

    70

    60

    50

    40

    Te

    mp

    era

    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

    era

    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

    era

    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 .–

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    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

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    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 :

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    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 ,

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    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

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    Model

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    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