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Dede

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‫‪Archive of SID‬‬ ‫ﻣﺠﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬

‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬
‫2*‬

‫ﻣﺤﺴﻦ دﻟﻮي1 ، ﻧﺎﺻﺮ ﻫﻤﺪﻣﯽ‬

‫1-ﮐﺎرﺷﻨﺎس ارﺷﺪ ﮔﺮوه ﻋﻠﻮم و ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﺻﻔﻬﺎن‬ ‫2- اﺳﺘﺎدﯾﺎر ﮔﺮوه ﻋﻠﻮم و ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﺻﻔﻬﺎن‬ ‫* ﻣﺴﺌﻮل ﻣﮑﺎﺗﺒﻪ: ‪E mail: hamdami@cc.iut.ac.ir‬‬

‫ﺗﺎرﯾﺦ ﭘﺬﯾﺮش: 92/8/98‬

‫ﺗﺎرﯾﺦ درﯾﺎﻓﺖ: 12/01/88‬

‫ﭘﺮوﻓﯿﻞ دﻣﺎ و ﻏﻠﻈﺖ رﻃﻮﺑﺖ ﻃﯽ ﻣﺮﺣﻠﻪ ﻧﻤﮏ ﭘﺎﺷﯽ، ﺑﻪ دﻟﯿﻞ اﺛﺮ آﻧﻬـﺎ ﺑـﺮ ﻓﻌﺎﻟﯿـﺖ ﻣﯿﮑﺮوﺑـﯽ و آﻧﺰﯾﻤـﯽ ﻧﻘـﺶ ﻣﻬﻤـﯽ را در‬ ‫ﮐﯿﻔﯿﺖ ﭘﻨﯿﺮ ﺑﺎزي ﻣﯽ ﮐﻨﻨﺪ. در اﯾﻦ ﺗﺤﻘﯿﻖ ﯾﮏ ﻣﺪل ﯾـﮏ ﺑﻌـﺪي ﺑـﺮاي ﺗﻮﺻـﯿﻒ اﻧﺘﻘـﺎل ﺣـﺮارت در ﭘﻨﯿـﺮ ﻓﺮاﭘـﺎﻻﯾﺶ ﺷـﺪه ﺑـﺎ‬ ‫اﺳﺘﻔﺎده از ﺣﻞ ﻋﺪدي ﻗﺎﻧﻮن دوم ﻓﻮرﯾﻪ ﺑﺎ روش ﺗﻔﺎﺿﻞ ﻣﺤﺪود ) ﻣﺒﻨﺎئ ﺷﻤﺎي ﮐﺮاﻧﮏ ﻧﯿﮑﻠﺴﻮن( ﺑﻌﻨـﻮان ﺗـﺎﺑﻌﯽ از ﻋﻮاﻣـﻞ‬ ‫دروﻧﯽ )دﻣﺎ و ﺗﺮﮐﯿﺐ ﺷﯿﻤﯿﺎﺋﯽ ﭘﻨﯿﺮ در ﻫﺮ ﻧﻘﻄـﻪ در داﺧـﻞ ﭘﻨﯿـﺮ( و ﻋﻮاﻣـﻞ ﺑﯿﺮوﻧـﯽ )دﻣـﺎ و ﺳـﺮﻋﺖ ﺣﺮﮐـﺖ ﻫـﻮاي ﻣﺤـﯿﻂ‬ ‫ﻧﮕﻬﺪاري( ﺗﻮﺳﻌﻪ داده ﺷﺪ. ﻧﺘﺎﯾﺞ ﻣﻘﺎﯾﺴﻪ ﭘﺮوﻓﯿﻞ ﻫﺎي دﻣﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺑﺎ ﻧﺮم اﻓﺰار ‪ MATLAB‬ﺑﺎ داده ﻫـﺎي اﻧـﺪازه‬ ‫ﮔﯿﺮي ﺷﺪه ، ﻧﺸﺎن داد ﮐﻪ ﻫﻤﺒﺴﺘﮕﯽ ﺑﺎﻻﯾﯽ ﺑﯿﻦ ﻣﻘﺎدﯾﺮ ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣﺪل و ﻣﻘﺎدﯾﺮ آزﻣﺎﯾﺸﯽ وﺟﻮد دارد )ﺑـﯿﺶ از‬ ‫99 درﺻﺪ(.‬ ‫واژه ﻫﺎي ﮐﻠﯿﺪي: اﻧﺘﻘﺎل ﺣﺮارت، ﭘﻨﯿﺮ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه، ﺗﻔﺎﺿﻞ ﻣﺤﺪود، ﻣﺪل ﺳﺎزي‬

‫ﭼﮑﯿﺪه‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫۶۴ دﻟﻮي و ﻫﻤﺪﻣﯽ‬

‫.‪Numerical Heat Transfer Modeling in Ultrafilterated White Cheese‬‬
‫*2‪M Dalvi1 and N Hamdami‬‬ ‫0102 ,11 ‪Received: January‬‬ ‫0102 ,02 ‪Accepted: November‬‬ ‫‪MSc, Isfahan University of technology, Iran‬‬ ‫2‬ ‫,‪Assistant Professor, Department of Food Science and Technology, Isfahan University of Technology‬‬ ‫‪Isfahan, Iran‬‬ ‫*‬ ‫‪Corresponding author: E mail: hamdami@cc.iut.ac.ir‬‬
‫1‬

‫‪Abstract‬‬ ‫‪Temperature profile and moisture concentration during the cheese salting process play an important‬‬ ‫,‪role in cheese quality since the microbial and enzyme activities, are affected by them. In this work‬‬ ‫‪a one dimensional heat transfer model was developed in the ultrafilterated cheese by using the‬‬ ‫‪numerical solution of the Fourier second law with finite difference method (Crank- Nicholson‬‬ ‫‪scheme) as a function of internal (cheese chemical composition at any point) and external variables‬‬ ‫‪(temperature and air velocity of storage). The comparison of the experimental and predicted‬‬ ‫‪temperature values using MATLAB showed a good agreement between the model and the‬‬ ‫.)99 > 2‪experimental data (R‬‬
‫‪Keywords: Heat transfer, Ultrafilterated cheese, Finite difference, Modeling‬‬

‫دﻣﺎ و ﺗﺮﮐﯿﺐ ﺷﯿﻤﯿﺎﯾﯽ، و ﺗﻮﺳﻌﻪ رواﺑـﻂ رﯾﺎﺿـﯽ ﺑـﺮاي‬ ‫ﺗﻮﺻﯿﻒ آﻧﻬﺎ ﻣﯽﺗﻮان دﻗﺖ ﻣﺪل ﻣﻮرد اﺳﺘﻔﺎده را اﻓﺰاﯾﺶ‬ ‫داد)اﯾﺮوداﯾﺎراج 2002 و ﻧﯿﮑﻮﻻي و ﻫﻤﮑﺎران 1002(. ﻣﺪل‬ ‫ﻫﺎي ﺑﮑﺎر رﻓﺘﻪ در ﻣﻮاد ﻏﺬاﯾﯽ، ﺑﻪ دو ﮔﺮوه ﻋﻤﺪه ﺗﻘـﺴﯿﻢ‬ ‫ﻣﯽ ﺷﻮﻧﺪ: 1- ﻣﺪل ﻫﺎي ﺑﻨﯿﺎدي1: ﻣﺪل ﻫـﺎي ﺗﺌﻮرﯾـﮏ2 ﯾـﺎ‬ ‫ﻣﺪل ﻫﺎي ﻋﻤﻮﻣﯽ ﻧﺎم دﯾﮕﺮ اﯾﻦ ﮔﻮﻧﻪ ﻣﺪل ﻫﺎﺳﺖ. اﯾﻦ ﻧﻮع‬ ‫ﻣﺪل ﻫﺎ از ﻧﻈﺮﯾﻪ ﻫـﺎ وﺗﺌـﻮري ﻫـﺎي ﻣﻮﺟـﻮد اﺳـﺘﻨﺒﺎط و‬ ‫اﺳﺘﻨﺘﺎج ﻣﯽ ﺷﻮﻧﺪ. در اﯾﻦ ﻧﻮع ﻣﺪل ﻫﺎ از ﮐﻞ ﺑﻪ ﺟﺰء ﭘـﯽ‬ ‫ﺑﺮده ﻣﯽ ﺷﻮد3 و ﻣﺎﻫﯿﺖ آن ﺗﺒﺪﯾﻞ ﺗﺌﻮري ﻫﺎ و ﻣﻔﺎﻫﯿﻢ ﺑﻪ‬ ‫ﺑﺮدن اﻃﻼﻋﺎت داده ﻫﺎي اﻧﺪازه ﮔﯿﺮي ﺷﺪه اﺳﺖ. داده ﻫﺎ‬ ‫ﺗﻨﻬﺎ ﺑﺮاي ﮐﺎﻟﯿﺒﺮه ﮐﺮدن و ﻣﻌﺘﺒﺮ ﺳﺎزي ﻣﺪل اﺳﺘﻔﺎده ﻣﯽ‬ ‫ﺷـﻮﻧﺪ. 2- ﻣـﺪل ﻫـﺎي ﺗﺠﺮﺑـﯽ4: در ﻓﺮآﯾﻨـﺪ ﻫـﺎي ﻏـﺬاﯾﯽ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻫﻤﯿــﺸﻪ ﭘــﯿﺶ زﻣﯿﻨــﻪ ي ﻣﻨﺎﺳــﺐ ﻋﻠﻤــﯽ در ﺧــﺼﻮص‬ ‫ﻓﺮآﯾﻨﺪي ﮐﻪ ﺑﺎﯾﺪ ﻣﺪل ﺳﺎزي ﺷﻮد، وﺟﻮد ﻧـﺪارد. در اﯾـﻦ‬
‫١‬ ‫٢‬

‫ﺷﻨﺎﺧﺖ ﺟـﺎﻣﻊ از ﭘﺮوﻓﯿـﻞ ﻫـﺎي دﻣـﺎ و رﻃﻮﺑـﺖ ﻃـﯽ‬

‫ﻣﻘﺪﻣﻪ‬

‫ﻧﮕﻬﺪاري، در داﺧﻞ ﭘﻨﯿﺮ داراي اﻫﻤﯿﺖ ﻓﺮاواﻧﯽ اﺳﺖ، زﯾﺮا‬ ‫دﻣــﺎ و ﻏﻠﻈــﺖ رﻃﻮﺑــﺖ در داﺧــﻞ ﭘﻨﯿــﺮ ﺑــﺮ ﺑــﺴﯿﺎري از‬

‫ﺧــﺼﻮﺻﯿﺎت و وﯾﮋﮔــﯽ ﻫــﺎي ﮐﯿﻔــﯽ آن از ﺟﻤﻠــﻪ ﺑــﺎر‬ ‫ﻣﯿﮑﺮوﺑﯽ، ارزش ﻏﺬاﯾﯽ، ﺑﺎﻓـﺖ ، ‪ ، a w‬ﻓﻌﺎﻟﯿـﺖ آﻧﺰﯾﻤﻬـﺎ و‬ ‫ﺷﺪت ﮔﻠﯿﮑـﻮﻟﯿﺰ ، ﻟﯿﭙـﻮﻟﯿﺰ و ﭘﺮوﺗﺌـﻮﻟﯿﺰ و ﻧﻬﺎﯾﺘـﺎ ﺧـﻮاص‬ ‫ارﮔﺎﻧﻮﻟﭙﺘﯿﮑﯽ ﻣﺤﺼﻮل ﻧﻬﺎﯾﯽ ﻣﻮﺛﺮ ﻣﯽ ﺑﺎﺷـﻨﺪ ) ﻧﯿﮑـﻮﻻي‬ ‫و ﻫﻤﮑﺎران 1002 و ﭘﺎﺟﻮﻧﮏ و ﻫﻤﮑـﺎران3002(. اﻣـﺮوزه‬ ‫ﻣﺪل ﺳﺎزي ﺑﻪ ﻋﻨﻮان ﯾـﮏ روش ﻣـﻮﺛﺮ ﺑـﺮاي ﺷـﻨﺎﺧﺖ و‬ ‫ﺗﻮﺻﯿﻒ ﭘﺪﯾﺪه ﻫـﺎي ﻣـﺸﺎﻫﺪه ﺷـﺪه وﭘـﯿﺶ ﺑﯿﻨـﯽ آن ﻫـﺎ‬ ‫ﺗﺤﺖ ﺷﺮاﯾﻂ ﻓﺮﺿﯽ ﺑﮑﺎر ﻣﯽ رود. دﻗﺖ ﭘﯿﺶ ﺑﯿﻨـﯽ ﻣـﺪل‬ ‫راﺑﻄﻪ ﻣﺴﺘﻘﯿﻤﯽ ﺑﺎ دﻗﺖ ﭘﺎراﻣﺘﺮ ﻫـﺎي ﻣـﻮرد اﺳـﺘﻔﺎده در‬ ‫ﻣﺪل دارد ﮐـﻪ از ﻣﻬـﻢ ﺗـﺮﯾﻦ ﭘـﺎراﻣﺘﺮ ﻫـﺎ در ﻣـﺪل ﻫـﺎي‬ ‫ﺗﻮﺻﯿﻒ ﮐﻨﻨﺪه اﻧﺘﻘﺎل ﺣﺮارت ﻣﯽ ﺗـﻮان ﺑـﻪ ﺧـﺼﻮﺻﯿﺎت‬ ‫ﺣﺮارﺗﯽ ﻣﺜﻞ ﮔﺮﻣﺎي وﯾﮋه، ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ، ﻧﻔﻮذ ﺣﺮارﺗﯽ،‬ ‫آﻧﺘﺎﻟﭙﯽ و ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت ﺳﻄﺤﯽ اﺷﺎره ﻧﻤـﻮد. ﺑـﺎ‬ ‫ﺗﻌﯿﯿﻦ ﭼﮕﻮﻧﮕﯽ ﺗﻐﯿﯿﺮ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺬﮐﻮر ﺑﻌﻨﻮان ﺗﺎﺑﻌﯽ از‬ ‫‪www.SID.ir‬‬

‫ﻓﺮﻣﻮل ﻫﺎ و رواﺑـﻂ رﯾﺎﺿـﯽ و ﻣﺤﺎﺳـﺒﺎﺗﯽ، ﺑـﺪون ﺑﮑـﺎر‬

‫‪Fundamental‬‬ ‫‪Theoretical‬‬ ‫٣‬ ‫‪Deduction‬‬ ‫۴‬ ‫‪Empirical‬‬

‫‪Archive of SID‬‬ ‫٧۴‬ ‫ﻣﺪل ﻣﺬﮐﻮر ﻣﯽ ﺗﻮاﻧﺪ ﺑﺮاي ﺷﻨﺎﺧﺖ ﺑﻬﺘﺮ ﻣﮑﺎﻧﯿﺴﻢ اﻧﺘﻘـﺎل‬ ‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬ ‫ﺻﻮرت، اﺳﺘﻔﺎده از داده ﻫﺎ ﺑـﺮاي ﺷـﺮح ﻓﺮآﯾﻨـﺪ و اراﺋـﻪ‬

‫ﺣﺮارت در داﺧﻞ ﭘﻨﯿﺮ و ﺗﺎﯾﯿﺪ ﻣﻘﺪﻣﺎﺗﯽ ﻣـﺪل ﻫـﺎي اﻧﺘﻘـﺎل‬ ‫ﺣﺮارت دو ﺑﻌﺪي و ﯾﺎ ﺳـﻪ ﺑﻌـﺪي در داﺧـﻞ ﭘﻨﯿـﺮ، ﻣـﻮرد‬ ‫اﺳﺘﻔﺎده ﻗﺮار ﮔﯿﺮد.‬ ‫ﻣﻮاد و روش ﻫﺎ‬ ‫ﺗﻬﯿﻪ ﻧﻤﻮﻧﻪ ﻫﺎي ﭘﻨﯿﺮ و ﺗﺠﺰﯾﻪ ﺗﻘﺮﯾﺒﯽ آﻧﻬﺎ‬ ‫ﻧﻤﻮﻧ ـﻪ ﻫ ـﺎي ﭘﻨﯿ ـﺮ ﻓﺮاﭘ ـﺎﻻﯾﺶ ﺷ ـﺪه ﺑﮑ ـﺎر رﻓﺘ ـﻪ در اﯾ ـﻦ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ﭘﮋوﻫﺶ از ﺧﻂ ﺗﻮﻟﯿﺪ ﮐﺎرﺧﺎﻧﻪ ﭘﮕﺎه اﺻﻔﻬﺎن ﺑﻌﺪ از ﻓﺮاﯾﻨﺪ‬ ‫ﻧﻤﮏ ﭘﺎﺷﯽ ﺧﺸﮏ ﺗﻬﯿﻪ ﮔﺮدﯾﺪ. ﺑﺮاي ﺗﻌﯿﯿﻦ ﻣﯿﺰان ﭼﺮﺑـﯽ،‬ ‫رﻃﻮﺑﺖ، ﭘﺮوﺗﺌﯿﻦ و ﺧﺎﮐﺴﺘﺮ ﻧﻤﻮﻧﻪ ﻫﺎي ﭘﻨﯿﺮ ﺑﻪ ﺗﺮﺗﯿﺐ از‬ ‫روش ژرﺑــﺮ، ﺧــﺸﮏ ﮐــﺮدن ﺑــﺎ آون، ﮐﻠــﺪال و ﮐــﻮره‬ ‫اﻟﮑﺘﺮﯾﮑﯽ اﺳﺘﻔﺎده ﺷﺪ ﻧﺘﺎﯾﺞ ﺗﺠﺰﯾﻪ ﺷﯿﻤﺎﯾﯽ ﻧﻤﻮﻧـﻪ ﻫـﺎ در‬ ‫ﺟﺪول1 آورده ﺷﺪه اﺳﺖ )اﺳﺘﺎﻧﺪارد ﻣﻠـﯽ اﯾـﺮان 2831و‬ ‫ﺣﺴﯿﻨﯽ 9631(. ﻫﺮ ﯾﮏ از آزﻣﺎﯾـﺸﺎت ﻓـﻮق ﺣـﺪاﻗﻞ در 3‬ ‫ﺗﮑﺮار اﻧﺠﺎم ﺷﺪ ﮐﻪ ﻧﺘـﺎﯾﺞ ﺑـﻪ ﺻـﻮرت ﻣﯿـﺎﻧﮕﯿﻦ ﮔـﺰارش‬ ‫ﺷﺪه اﺳﺖ.‬ ‫ﺗﻌﯿﯿﻦ ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﭘﻨﯿﺮ‬ ‫دﻗﺖ ﭘﯿﺶ ﺑﯿﻨﯽ ﻣﺪل، راﺑﻄـﻪ ﻣـﺴﺘﻘﯿﻤﯽ ﺑـﺎ دﻗـﺖ ﭘـﺎراﻣﺘﺮ‬ ‫ﻫﺎي ﻣﻮرد اﺳﺘﻔﺎده در ﻣﺪل دارد ﮐﻪ ﻣﻬـﻢ ﺗـﺮﯾﻦ ﭘـﺎراﻣﺘﺮ‬ ‫ﻫﺎ در ﻣﺪل ﻫﺎي اﻧﺘﻘﺎل ﺣﺮارت ﻋﺒﺎرﺗﻨﺪ از: ﮔﺮﻣـﺎي وﯾﮋه ،‬ ‫ﻫــﺪاﯾﺖ ﺣﺮارﺗــﯽ، داﻧــﺴﯿﺘﻪ و ﺿــﺮﯾﺐ اﻧﺘﻘــﺎل ﺣــﺮارت‬ ‫ﺳﻄﺤﯽ.‬

‫ﻣﺪﻟﯽ ﻣﻨﺎﺳﺐ اﻣﮑﺎن ﭘﺬﯾﺮ اﺳﺖ وﺣﺘﯽ ﻣﺎ را ﺑﻪ ﺳﻤﺖ اراﺋﻪ‬ ‫ﻓﺮﻣﻮل و ﭘﺸﻨﻬﺎداﺗﯽ درﺑـﺎره ﻣﮑﺎﻧﯿـﺴﻢ دﺧﯿـﻞ در ﻓﺮآﯾﻨـﺪ‬ ‫ﻫﺪاﯾﺖ ﻣﯽ ﮐﻨﺪ. ﺑﺎ اﺳﺘﻔﺎده از اﯾﻦ ﻧﻮع ﻣﺪل، ﺑﺪون اﯾـﻦ ﮐـﻪ‬ ‫ﺑﻪ ﻣﮑﺎﻧﯿﺴﻢ واﻗﻌﯽ اﺷﺎره اي ﺷﻮد ﻣﯽ ﺗـﻮان ورودي ﻫـﺎ‬ ‫را ﺑﻪ ﺧﺮوﺟﯽ ﺗﺒﺪﯾﻞ ﮐﺮد. ﺑﻪ ﻋﺒـﺎرت دﯾﮕـﺮ، در اﯾـﻦ ﻧـﻮع‬ ‫ﻣـﺪل از ﺟ ـﺰء ﺑ ـﻪ ﮐـﻞ ﭘ ـﯽ ﺑ ـﺮده ﻣـﯽ ﺷ ـﻮد )ﻧﯿﮑ ـﻮﻻي و‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ ـ ـ ـ‬ ‫ـ‬ ‫ﻫﻤﮑﺎران 1002 (. ﺑﺮرﺳﯽ ﻣﻨﺎﺑﻊ ﻧﺸﺎن ﻣﯽ دﻫـﺪ ﮐـﻪ ﻣـﺪل‬ ‫ﻫﺎي رﯾﺎﺿﯽ ﮔﻮﻧﺎﮔﻮﻧﯽ ﺑﺮ روي اﻧﺘﻘﺎل ﺟﺮم و ﺣﺮارت و‬ ‫ﻋﻤﻠﯿﺎت آب ﻧﻤﮏ ﮔﺬاري در اﻧﻮاع ﭘﻨﯿﺮ اﻧﺠـﺎم ﺷـﺪه اﺳـﺖ‬ ‫روﺑﯿﺎﻟﻮ 4991 ( ، ﭘﻨﯿﺮ ﮐﻮارﺗﯿﻮﻟﻮ6 )ﻟﻮﻧﺎ و ﺑﺮﺳﺎن 7891(،‬ ‫6991( و ﭘﻨﯿ ـﺮ اﻣﺎﻧﺘ ـﺎل9 )ﭘﺎﺟﻮﻧ ـﮏ و ﻫﻤﮑ ـﺎران 3002(‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﮐﻪ از آن ﺟﻤﻠـﻪ ﻣـﯽ ﺗـﻮان ﺑـﻪ : ﭘﻨﯿـﺮ ﻓﯿﻨﺒـﻮ5 )زورﯾـﻼ و‬

‫ﭘﻨﯿﺮ روﻣﺎﻧﻮ7 )ﮔﯿﻨﻪ و ﻓﺎﮐﺲ 3891(، ﭘﻨﯿـﺮ ﻓـﺖ8 )ﺗﻮرﻫـﺎن‬ ‫اﺷﺎره ﮐﺮد. ﺑﺎ وﺟﻮد اﯾﻨﮑﻪ ﭘﻨﯿـﺮ ﺳـﻔﯿﺪ ﻓﺮاﭘـﺎﻻﯾﺶ ﺷـﺪه‬ ‫ﺑﻌﻨﻮان ﻋﻤﺪه ﺗﺮﯾﻦ ﭘﻨﯿﺮ ﺻﻨﻌﺘﯽ ﺗﻮﻟﯿﺪي در داﺧﻞ ﮐـﺸﻮر‬ ‫ﻣﯽ ﺑﺎﺷﺪ، اﻣـﺎ ﻣﻄﺎﻟﻌـﻪ ﺟـﺎﻣﻊ ﻣﻨﺘـﺸﺮ ﺷـﺪه اي ﺑـﺮ روي‬ ‫ﺗﻐﯿﯿـﺮات اﯾﺠـﺎد ﺷـﺪه ﻃـﯽ ﻣﺮاﺣـﻞ ﭘـﺲ از ﻧﻤـﮏ ﭘﺎﺷـﯽ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬

‫)رﺳــــﯿﺪﮔﯽ( ﭘﻨﯿﺮﺳـــ ـﻔﯿﺪ ﺗﻮﻟﯿــــﺪ ﺷـــ ـﺪه ﺑـــ ـﺮوش‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫اوﻟﺘﺮاﻓﯿﻠﺘﺮاﺳــﯿﻮن و ﭘﺪﯾــﺪه ﻫــﺎي درﮔﯿــﺮ در آن )اﻧﺘﻘــﺎل‬ ‫ﺣﺮارت و ﺟﺮم( وﺟﻮد ﻧﺪارد. ﻟﺬا، ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ درك ﻧﺎﻗﺺ‬ ‫از ﻧﺤــﻮه ﺗﻐﯿﯿــﺮات رخ داده ﭘــﺲ از ﻧﻤــﮏ ﭘﺎﺷــﯽ ﭘﻨﯿــﺮ‬ ‫ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه ، ﮐﻨﺘﺮل ﻣﻨﺎﺳﺐ ﺑﺮ ﺗﻮﻟﯿﺪ وﺗﻀﻤﯿﻦ ﮐﯿﻔﯿﺖ‬ ‫اﯾﻦ ﻧﻮع ﭘﻨﯿﺮ ﻧﻤﯽ ﺗﻮان اﻋﻤﺎل ﻧﻤﻮد. در اﯾﻦ ﺗﺤﻘﯿـﻖ ﺑـﺮاي‬ ‫ﭘﺎﺳﺦ ﺑﻪ ﺑﺨﺸﯽ از ﻧﯿﺎز ﻣﺬﮐﻮر ﺑﻪ ﻣﻄﺎﻟﻌﻪ اﻧﺘﻘـﺎل ﺣـﺮارت‬ ‫ﺑﻌﻨﻮان ﯾﮑﯽ از ﭘﺪﯾﺪه ﻫﺎي اﺻﻠﯽ در ﭘﻨﯿـﺮ ﺳـﻔﯿﺪ ﺗﻮﻟﯿـﺪي‬ ‫ﺑ ـﺮوش اوﻟﺘﺮاﻓﯿﻠﺘﺮاﺳ ـﯿﻮن ﭘﺮداﺧﺘــﻪ ﺷ ـﺪه اﺳ ـﺖ. ﻫــﺪف‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺗﺤﻘﯿﻖ ﺣﺎﺿﺮ، ﻣﻄﺎﻟﻌﻪ اﻧﺘﻘﺎل ﺣـﺮارت ﺗـﮏ ﺑﻌـﺪي ﭘـﺲ از‬ ‫ﻣﺮﺣﻠﻪ ﻧﻤﮏ ﭘﺎﺷﯽ ﭘﻨﯿﺮ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه ﺑﺎ اﺳﺘﻔﺎده از ﻣﺪل‬ ‫ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣـﺮارت در ﺣﺎﻟـﺖ ﻧﺎﭘﺎﯾـﺎ ﻣـﯽ ﺑﺎﺷـﺪ‬

‫۵‬ ‫۶‬

‫‪Fynbo‬‬ ‫‪Cuartiolo‬‬ ‫٧‬ ‫‪Romano‬‬ ‫٨‬ ‫‪Feta‬‬ ‫٩‬ ‫‪Emmental‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬
‫*‬
‫∗∗∗‬

‫٨۴ دﻟﻮي و ﻫﻤﺪﻣﯽ‬

‫ﺟﺪول 1: درﺻﺪ ﺗﺮﮐﯿﺒﺎت ﺷﯿﻤﯿﺎﯾﯽ ﻧﻤﻮﻧﻪ ﭘﻨﯿﺮ ﻓﺮا ﭘﺎﻻﯾﺶ ﺷﺪه‬
‫ﺧﺎﮐﺴﺘﺮ )%(‬ ‫11 /0 +98 /3‬
‫∗∗‬

‫ﻻﮐﺘﻮز )%(‬ ‫85/4‬

‫ﭘﺮوﺗﺌﯿﻦ )%(‬

‫ﭼﺮﺑﯽ )%(‬ ‫01 + 0/71‬

‫رﻃﻮﺑﺖ )%(‬ ‫13 / + 14 /36‬

‫40 / + 21 /11‬

‫* اﻋﺪاد، ﻣﯿﺎﻧﮕﯿﻦ + ‪ SD‬ﻣﯽ ﺑﺎﺷﻨﺪ‬

‫ﻻﮐﺘﻮز )001 –رﻃﻮﺑﺖ – ﭘﺮوﺗﺌﯿﻦ – ﭼﺮﺑﯽ - ﺧﺎﮐﺴﺘﺮ(‬

‫** 83/6× )درﺻﺪ ﻧﯿﺘﺮوژن(‬

‫***‬

‫ﻧﻤﻮﻧﻪ ﺑﻪ دﻣﺎي ﻣـﻮرد ﻧﻈـﺮ در داﺧـﻞ اﻧﮑﻮﺑـﺎﺗﻮر، ﺟﺮﯾـﺎن‬ ‫ﺑﺮق ﺑﺎ ﺷﺪت ﺟﺮﯾﺎن ﻣﺸﺨﺼﯽ ﮐﻪ ﺗﻮﺳﻂ ﻣﻮﻟﺘﯽ ﻣﺘـﺮ ﺑـﺎ‬ ‫دﻗﺖ1/0± ﺗﻌﯿﯿﻦ ﻣﯽ ﮔﺮدﯾﺪ، از داﺧﻞ ﻣـﺎده ﻏـﺬاﯾﯽ ﻋﺒـﻮر‬ ‫داده ﺷﺪه و اﻓﺰاﯾﺶ دﻣﺎ ﺗﻮﺳﻂ ﺗﺮﻣﻮﮐﻮﭘﻞ ﺗﻌﺒﯿﻪ ﺷﺪه در‬ ‫داﺧﻞ ﭘﺮوب اﻧﺪازه ﮔﯿﺮي و در ﻓﻮاﺻﻞ زﻣـﺎﻧﯽ ﯾـﮏ ﺛﺎﻧﯿـﻪ‬ ‫ﺗﻮﺳﻂ دﯾﺘﺎ ﻻﮔﺮ ﺛﺒـﺖ ﺷـﺪ. ﻣﯿـﺰان ﺷـﺪت ﺟﺮﯾـﺎن ﻣـﻮرد‬ ‫اﺳﺘﻔﺎده ﺑﻪ ﻧﺤﻮي اﻧﺘﺨﺎب ﮔﺮدﯾﺪ ﮐـﻪ ﺑﺘﻮاﻧـﺪ ﯾـﮏ اﻓـﺰاﯾﺶ‬ ‫دﻣـﺎي 01 درﺟـﻪ ﺳـﺎﻧﺘﯿﮕﺮادي در ﻣـﺪت 01 ﺛﺎﻧﯿـﻪ اﯾﺠـﺎد‬ ‫ـ‬ ‫ﻧﻤﺎﯾﺪ. ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ ﻣﺎده، از ﺷﯿﺐ ﺑﺨﺶ ﺧﻄـﯽ ﻧﻤـﻮدار‬ ‫دﻣــﺎ – ﻟﮕــﺎرﯾﺘﻢ زﻣــﺎن ﺑــﺮآورد ﮔﺮدﯾــﺪ. آزﻣــﺎﯾﺶ در‬ ‫ﻣﺤﺪوده دﻣـﺎﯾﯽ 1 ﺗـﺎ 32 درﺟـﻪ ﺳـﺎﻧﺘﯿﮕﺮاد و در ﻫﻔـﺖ‬ ‫ﺗﮑﺮار ﺻﻮرت ﮔﺮﻓﺖ و ﻧﺘﺎﯾﺞ ﺑـﻪ ﺻـﻮرت ﻣﯿـﺎﻧﮕﯿﻦ ﻫﻔـﺖ‬ ‫ﺗﮑﺮار ﺑﺮاي ﻧﻤﻮﻧﻪ ﮔﺰارش ﮔﺮدﯾﺪ. از ﮔﻠﯿﺴﯿﺮﯾﻦ و آب )ژل‬ ‫آﮔﺎر ﻧﯿﻢ درﺻﺪ( ﮐـﻪ در دﻣﺎﻫـﺎي ﻣﺘﻔـﺎوت داراي ﻫـﺪاﯾﺖ‬ ‫ﺣﺮارﺗﯽ ﻣﺸﺨﺼﯽ ﻫﺴﺘﻨﺪ ﺑـﺮاي ﮐـﺎﻟﯿﺒﺮه ﻧﻤـﻮدن ﭘـﺮوب‬ ‫اﺳﺘﻔﺎده ﺷﺪ )ﻫﻤﺪﻣﯽ و ﻫﻤﮑﺎران 3002(.‬ ‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ ﭘﻨﯿﺮ ﺑﺎ اﺳـﺘﻔﺎده از ﻣـﺪل ﻣـﻮازي ﻧﯿـﺰ ﺑـﺮ‬ ‫آورد ﮔﺮدﯾﺪ در اﯾﻦ ﻣﺪل اﺟﺰاء ﻣﺨﺘﻠﻒ ﻣـﺎده ﻏـﺬاﯾﯽ ﺑـﻪ‬ ‫ﺻﻮرت ﻣﻘﺎوﻣﺖ ﻫﺎي ﻣﻮازي و در ﺟﻬﺖ اﻧﺘﻘﺎل ﺣـﺮارت‬ ‫در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﯽ ﺷﻮﻧﺪ )ﻣﻌﺎدﻟﻪ 2 و 3(. اﯾﻦ ﻣﺪل، ﻫﺪاﯾﺖ‬ ‫ﺣﺮارﺗﯽ ﻣﺎده را ﮐﻤﯽ ﺑﯿﺸﺘﺮ از ﻣﻘﺪار واﻗﻌﯽ آن ﺑﺮآورد‬ ‫ﻣﯽ ﻧﻤﺎﯾﺪ‬
‫‪k = ∑ k i vi‬‬
‫1= ‪i‬‬ ‫‪N‬‬

‫ﮔﺮﻣﺎي وﯾﮋه ﻧﻤﻮﻧﻪ ﻫﺎي ﭘﻨﯿـﺮ در ﻣﺤـﺪوده دﻣـﺎﯾﯽ 05 -‬

‫ﮔﺮﻣﺎي وﯾﮋه:‬

‫ﺗﺎ 04 درﺟـﻪ ﺳـﺎﻧﺘﯿﮕﺮاد ﺑـﺎ ﺳـﺮﻋﺖ ﮔﺮﻣـﺎﯾﺶ 2 درﺟـﻪ‬ ‫ﺳﺎﻧﺘﯿﮕﺮاد در دﻗﯿﻘﻪ، در 3 ﺗﮑﺮار ﺑﺎ اﺳـﺘﻔﺎده از ﮐـﺎﻟﺮﯾﻤﺘﺮ‬ ‫اﺳ ـﮑﻨﯽ ﺗﻔﺮﻗ ـﯽ01 ﻣ ـﺪل 0004 ‪ Mettler TA‬ﺳ ـﺎﺧﺖ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺳﻮﺋﯿﺲ اﻧﺪازه ﮔﯿﺮي ﮔﺮدﯾﺪ‬ ‫ﮔﺮﻣ ـﺎي وﯾ ـﮋه را ﻣ ـﯽ ﺗ ـﻮان ﺑ ـﻪ ﺑ ـﺎ اﺳ ـﺘﻔﺎده از ﺗﺮﮐﯿ ـﺐ‬ ‫ـ‬ ‫ـ ـ ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺷــﯿﻤﯿﺎﯾﯽ ﻣــﺎده ﻏــﺬاﯾﯽ ﻧﯿــﺰ ﺑﺪﺳــﺖ آورد راﺑﻄــﻪ ]1[‬ ‫واﺑﺴﺘﮕﯽ ﮔﺮﻣﺎي وﯾﮋه ﺑﻪ ﺗﺮﮐﯿﺐ ﺷﯿﻤﯿﺎﯾﯽ ﻣﺎده را ﻧـﺸﺎن‬ ‫ﻣﯿﺪﻫﺪ‬
‫‪C p = 1.424mc + 1.549m p + 1.675m f + 0.837 ma + 4.187 mm‬‬

‫]1[‬ ‫‪ c ، f ، p ،m‬و ‪ a‬ﺑ ـﻪ ﺗﺮﺗﯿ ـﺐ ﻣﻌــﺮف رﻃﻮﺑ ـﺖ، ﭘــﺮوﺗﺌﯿﻦ،‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﭼﺮﺑﯽ، ﮐﺮﺑﻮﻫﯿﺪرات و ﺧﺎﮐﺴﺘﺮ ﻣﻮاد ﻣﯽ ﺑﺎﺷﻨﺪ )رﺣﻤﺎن‬ ‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ :‬ ‫5991(.‬ ‫ﮐﻪ در آن، ‪ m‬ﮐﺴﺮ وزﻧﯽ ﻫﺮ ﯾـﮏ از اﺟـﺰاء و اﻧﺪﯾـﺴﻬﺎي‬

‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ ﭘﻨﯿﺮ ﺑﺎ اﺳﺘﻔﺎده از ﭘﺮوب ﺣﺮارﺗـﯽ اﻧـﺪازه‬ ‫ﮔﯿﺮي ﺷﺪ. ﭘﺮوب ﻣﻮرد اﺳـﺘﻔﺎده ﻋﺒـﺎرت از ﯾـﮏ ﺳـﻮزن‬ ‫ﺑﺎ ﻗﻄﺮ1ﻣﯿﻠﯿﻤﺘﺮ و ﻃﻮل64 ﻣﯿﻠﯿﻤﺘﺮ ﺑـﻮد ﮐـﻪ ﯾـﮏ‬
‫11‬

‫ﺗﺰرﯾﻖ‬

‫ﺳﯿﻢ ﮐﻨﺴﺘﺎﻧﺘﺎن )ﺑﺮاي ﺗﻮﻟﯿـﺪ ﺣـﺮارت( و ﯾـﮏ ﺗﺮﻣﻮﮐﻮﭘـﻞ‬ ‫ﻧﻮع ‪) K‬ﺑﺮاي ﺗﻌﯿﯿﻦ دﻣﺎ( در داﺧﻞ آن ﺗﻌﺒﯿـﻪ ﺷـﺪه اﺳـﺖ.‬ ‫ﺑﺮاي ﺟﻠﻮﮔﯿﺮي ازﺗﺒﺎدل رﻃﻮﺑﺖ ﭘﻨﯿﺮ ﺑﺎ ﻣﺤﯿﻂ اﻃـﺮاف در‬ ‫ﺣﯿﻦ آزﻣﺎﯾﺶ در داﺧﻞ اﻧﮑﻮﺑﺎﺗﻮر، ﭘﻮﺷﺶ ﭘﻠـﯽ اﺗﯿﻠﻨـﯽ در‬ ‫اﻃﺮاف ﻧﻤﻮﻧﻪ ﭘﻨﯿـﺮ ﻗـﺮار ﮔﺮﻓـﺖ. ﭘـﺲ از رﺳـﯿﺪن دﻣـﺎي‬
‫٠١‬ ‫١١‬

‫]2[‬ ‫]3[‬

‫‪xi / ρ i‬‬ ‫= ‪vi‬‬ ‫) ‪∑ (xi / ρi‬‬

‫‪Differential scanning calorimetery‬‬ ‫‪Hypodermic needle‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫٩۴‬ ‫اول، ﯾﮏ ﻗﻄﻌـﻪ آﻟﻮﻣﯿﻨـﻮم ﺑـﻪ وزن 04/64 ﮔـﺮم و اﺑﻌـﺎد‬ ‫ﺳﻄﺢ آن ﯾﮏ ﺳﻮراخ ﺑﻪ ﻋﻤﻖ 5 ﻣﯿﻠﯿﻤﺘﺮ اﯾﺠﺎد ﺷﺪه ﺑـﻮد،‬ ‫ﻣﻮرد اﺳﺘﻔﺎده ﻗـﺮار ﮔﺮﻓـﺖ. ﭘـﺲ از ﻗـﺮار ﮔـﺮﻓﺘﻦ ﻗﻄﻌـﻪ‬ ‫ﻣﺬﮐﻮر در ﯾﮏ ﭼﺎرﭼﻮب از ﺟﻨﺲ ﭘﻠـﯽ اﺳـﺘﯿﺮن ﺑـﻪ اﺑﻌـﺎد‬ ‫01×52×52 ﺳﺎﻧﺘﯿﻤﺘﺮ، دو ﻋﺪد ﺗﺮﻣﻮﮐﻮﭘـﻞ از ﻧـﻮع ‪ K‬در‬ ‫ﺳﻄﺢ و ﻣﺮﮐﺰ ﻗﻄﻌﻪ ﮐﺎر ﮔﺬاﺷﺘﻪ ﺷﺪه و ﺳـﭙﺲ ﺗﻐﯿﯿـﺮات‬ ‫دﻣﺎ در ﻧﻘﺎط ﻣـﺬﮐﻮر در ﻃـﯽ ﮔـﺮم ﮐـﺮدن ﺑـﺎ اﺳـﺘﻔﺎده از‬ ‫ﻫﻮاي ﮔﺮم در دﻣﺎي ‪ 50 °C‬در داﺧﻞ ﺧﺸﮏ ﮐﻦ ﺑﻮﺳـﯿﻠﻪ‬ ‫دﯾﺘﺎ ﻻﮔﺮ ﺛﺒﺖ ﮔﺮدﯾﺪ ﺷﮑﻞ )1(.‬ ‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬ ‫در رواﺑﻂ ﺑﺎﻻ ‪ kBiB‬و ‪ k‬ﺑﻪ ﺗﺮﺗﯿﺐ ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ اﺟﺰاء‬ ‫وﻫﺪاﯾﺖ ﺣﺮارﺗﯽ ﭘﻨﯿﺮ ﻣﯽ ﺑﺎﺷﺪ و ‪ vBiB‬ﮐﺴﺮ ﺣﺠﻤﯽ‬ ‫اﺟﺰاي ﺷﯿﻤﯿﺎﯾﯽ ﭘﻨﯿﺮاﺳﺖ و ‪ xBiB‬و ‪ ρBiB‬ﺑﻪ ﺗﺮﺗﯿﺐ ﮐﺴﺮ‬ ‫ﺟﺮﻣﯽ و داﻧﺴﯿﺘﻪ اﺟﺰاء ﻣﯽ ﺑﺎﺷﻨﺪ.‬ ‫اﻧﺪازه ﮔﯿﺮي ﺣﺠﻢ ﭘﻨﯿﺮ ﺑﺎ اﺳﺘﻔﺎده از ﺳﻨﺠﺶ ﻣﯿﺰان ﻣـﺎﯾﻊ‬ ‫)آب( ﺟﺎﺑﺠﺎ ﺷـﺪه در اﺛـﺮ ﻏﻮﻃـﻪ وري ﻧﻤﻮﻧـﻪ در داﺧـﻞ‬ ‫ﺣﺠﻢ ﻣﺸﺨﺼﯽ از ﻣﺎﯾﻊ اﻧﺠﺎم ﺷﺪ. ﺑﺮاي ﺗﻌﯿﯿﻦ ﺣﺠﻢ ﭘﻨﯿﺮ‬ ‫ﺑﺎ اﺳﺘﻔﺎده از ﭘﯿﮑﻨﻮﻣﺘﺮ از راﺑﻄﻪ زﯾﺮ اﺳﺘﻔﺎده ﮔﺮدﯾﺪ:‬ ‫داﻧﺴﯿﺘﻪ :‬

‫8/0× 5× 5 ﺳــﺎﻧﺘﯿﻤﺘﺮ ﮐــﻪ در ﻓﺎﺻــﻠﻪ 4/0 ﻣﯿﻠﯿﻤﺘــﺮي از‬

‫ﻗﻄﻌﻪ آﻟﻮﻣﯿﻨﯿﻮم‬

‫ﭘﻠﯽ اﺳﺘﯿﺮن‬

‫=‪V‬‬

‫‪(W‬‬

‫‪pf‬‬

‫) ‪− Wp ) − (Wpfs − Wps‬‬ ‫‪ρf‬‬

‫]4[‬

‫ﮐﻪ در آن ‪ Wpfs ،Wps ،Wpf ،Wp ،V‬و ‪ ρf‬ﺑﻪ ﺗﺮﺗﯿـﺐ ﺣﺠـﻢ‬ ‫ﭘﻨﯿﺮ )ﺳﺎﻧﺘﯿﻤﺘﺮ ﻣﮑﻌﺐ(، ﺟﺮم ﭘﯿﮑﻨﻮﻣﺘﺮ ﺧﺎﻟﯽ )ﮔﺮم(، ﺟـﺮم‬ ‫ﭘﯿﮑﻨﻮﻣﺘﺮ ﭘﺮ ﺷﺪه ﺑﺎ ﺳﯿﺎل )ﮔﺮم(، ﺟﺮم ﭘﯿﮑﻨـﻮﻣﺘﺮ و ﭘﻨﯿـﺮ‬ ‫)ﮔ ـﺮم(، ﺟــﺮم ﭘﯿﮑﻨ ـﻮﻣﺘﺮ ﺣــﺎوي ﭘﻨﯿ ـﺮو ﺳــﯿﺎل )ﮔــﺮم( و‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫داﻧـﺴﯿﺘﻪ ﺳـﯿﺎل )ﮔـﺮم ﺑـﺮ ﺳـﺎﻧﺘﯿﻤﺘﺮ ﻣﮑﻌـﺐ( ﻣـﯽ ﺑﺎﺷـﻨﺪ‬ ‫ـ‬ ‫)ﻣﺤﺴﻨﯿﻦ 0891(. اﺳﺘﻔﺎده از آب ﺑﻪ ﻋﻨـﻮان ﺳـﯿﺎل داراي‬ ‫ﻣﻌﺎﯾﺐ ﻣﺨﺘﻠﻔﯽ اﺳﺖ ﮐﻪ از ﻣﻬﻢ ﺗـﺮﯾﻦ آﻧﻬـﺎ ﺟـﺬب آب در‬ ‫ﻓﻮق ﺑﺪﻟﯿﻞ ﮐﻮﺗﺎه ﺑـﻮدن ﻣـﺪت زﻣـﺎن ﻏﻮﻃـﻪ وري در آب‬ ‫ﺧﻄﺎي ﻗﺎﺑﻞ ﺗﻮﺟﻬﯽ در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﺳﯿﺎﻻت دﯾﮕﺮ ﻣـﺸﺎﻫﺪه‬ ‫ﻧﺸﺪ‬ ‫از ﻧﻈﺮ ﺗﺌﻮري، اﮔﺮ ﺗﺮﮐﯿﺐ ﻣﺎده ﻏﺬاﯾﯽ ﻣﻌﻠﻮم ﺑﺎﺷﺪ‬ ‫داﻧﺴﯿﺘﻪ ﻣﺎده ﻏﺬاﯾﯽ را ﻣﯽ ﺗﻮان ﺑﺮ اﺳﺎس راﺑﻄﻪ زﯾﺮ‬ ‫ﺗﺨﻤﯿﻦ زد‬ ‫=‪ρ‬‬ ‫‪ρi‬‬ ‫ﮐﻪ در راﺑﻄﻪ ‪ xBiB‬ﮐﺴﺮ وزﻧﯽ اﺟﺰاء ﺗﺸﮑﯿﻞ دﻫﻨﺪه ﭘﻨﯿﺮ و‬ ‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ :‬ ‫‪ ρBiB‬داﻧﺴﯿﺘﻪ اﺟﺰاء ﻣﯽ ﺑﺎﺷﺪ.‬ ‫1‬ ‫‪xi‬‬ ‫]5[‬ ‫ﺣﯿﻦ ﻏﻮﻃﻪ وري ﺗﻮﺳﻂ ﻧﻤﻮﻧﻪ ﻣﯽ ﺑﺎﺷﺪ وﻟـﯽ در ﺗﺤﻘﯿـﻖ‬

‫‪5 cm‬‬

‫‪25 cm‬‬

‫ﺷﮑﻞ 1- ﻧﻤﺎي روﺑﺮوي ﭼﺎرﭼﻮب ﭘﻠﯽ اﺳﺘﺎﯾﺮﻧﯽ ﺑﺮاي‬

‫ﺗﻌﯿﯿﻦ ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ‬

‫ﺿـﺮﯾﺐ اﻧﺘﻘـﺎل ﺣـﺮارت در ﺳـﻄﺢ ﺑـﺎ اﺳـﺘﻔﺎده از ﺷـﯿﺐ‬ ‫ﺑﺨـﺶ ﺧﻄـﯽ ﻧﻤـﻮدار زﻣـﺎن ﻧـﺴﺒﺖ ﺑـﻪ ) ‪،ln (T∞ -Tal‬‬ ‫ﺑﻮﺳﯿﻠﻪ ﻣﻌﺎدﻟﻪ زﯾﺮ ﺑﺮآورد ﮔﺮدﯾﺪ:‬ ‫=‪h‬‬ ‫‪M al Cp al‬‬ ‫‪Sm‬‬ ‫]6[‬

‫ﮔﺮﻣﺎي وﯾﮋه آﻟﻮﻣﯿﻨﯿﻮم و ‪ S‬و ‪ m‬ﺑﻪ ﺗﺮﺗﯿﺐ ﺳﻄﺢ و ﺷﯿﺐ‬

‫ﮐﻪ در راﺑﻄﻪ ﺑﺎﻻ ‪ ، Mal‬ﺟﺮم ﻗﻄﻌﻪ آﻟﻮﻣﯿﻨﻮﻣﯽ ، ‪، Cpal‬‬
‫ﻧﻤﻮدار ) ‪ ln (T∞ -Tal‬ﻧﺴﺒﺖ ﺑﻪ زﻣﺎن ﻣﯽ ﺑﺎﺷﻨﺪ‬ ‫)ﻫﻤﺪﻣﯽ و ﻫﻤﮑﺎران 4002(.‬

‫52‬

‫‪10 cm‬‬

‫‪cm‬‬

‫∑‬

‫ﺑﺮاي ﺗﻌﯿﯿﻦ ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ ﺑﺎ اﺳﺘﻔﺎده از‬ ‫اﻋﺪاد ﺑﺪون ﺑﻌﺪ ، از راﺑﻄﻪ ﺗﺠﺮﺑﯽ زﯾﺮ ﮐﻪ در ﻣﻮرد ﺗﺒﺎدل‬ ‫ﺣﺮارت ﻣـﺎﺑﯿﻦ ﯾـﮏ ﺳـﯿﺎل در ﺣـﯿﻦ ﺟﺮﯾـﺎن از روي ﯾـﮏ‬

‫ﺑﺮاي ﺗﻌﯿـﯿﻦ ﺿـﺮﯾﺐ اﻧﺘﻘـﺎل ﺣـﺮارت در ﺳـﻄﺢ، از روش‬

‫اﻧﺪازه ﮔﯿﺮي دﻣﺎ در ﺣﺎﻟﺖ ﮔﺬرا و روش اﻋﺪاد ﺑﺪون ﺑﻌـﺪ‬ ‫اﺳﺘﻔﺎده ﮔﺮدﯾﺪ و ﻧﺘﺎﯾﺞ ﺑـﺎ ﻫـﻢ ﻣﻘﺎﯾـﺴﻪ ﮔﺮدﯾـﺪ. در روش‬ ‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫در راﺑﻄــﻪ ﺑــﺎﻻ ‪ R‬ﺛﺎﺑــﺖ ﮔﺎزﻫــﺎ، ‪ T‬درﺟــﻪ ﺣــﺮارت، ‪µ‬‬ ‫ﺑﺎﺷﻨﺪ)ﮐﺎرﺳﻮن 6002(.‬ ‫1- ﻣﺪل ﺳﺎزي‬ ‫ﺗﻮﺳﻌﻪ ﻣﺪل‬ ‫ﺗﻮﺳﻌﻪ ﻣﺪل رﯾﺎﺿﯽ ﺑﺮاي ﺗﻮﺻﯿﻒ اﻧﺘﻘﺎل ﺣﺮارت در ﯾﮏ‬ ‫ﻣﺎده ﺟﺎﻣﺪ ﻣﯽ ﺗﻮاﻧﺪ ﺑﺎ اﺳﺘﻔﺎده از ﺣﻞ ﻋﺪدي ﻗـﺎﻧﻮن دوم‬ ‫ﻓﻮرﯾﻪ ﺻﻮرت ﭘﺬﯾﺮد. در ﺑـﯿﻦ روش ﻫـﺎي ﻋـﺪدي، روش‬ ‫ﺑﻪ دﻟﯿﻞ ﺳﺎدﮔﯽ و ﻗﺎﺑﻠﯿﺖ ﺗﻮﺳﻌﻪ آن ﺑﻪ‬
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‫٠۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬ ‫ﺻﻔﺤﻪ ﻣﺮﺑﻊ ﺷﮑﻞ و در ﺳﺮﻋﺖ ﻫﺎي ﭘﺎﯾﯿﻦ ﺻـﺎدق اﺳـﺖ‬

‫وﯾﺴﮑﻮزﯾﺘﻪ، ‪ ρ‬داﻧـﺴﯿﺘﻪ و‪ Dm‬ﺿـﺮﯾﺐ دﯾﻔﻮزﯾـﻮن ﻣـﯽ‬

‫اﺳﺘﻔﺎده ﮔﺮدﯾﺪ ) ﮐﺎرﺳﻮن، 6002( :‬ ‫]7[‬

‫3 / 1 ‪Nu = 0.665 Re1 / 2 Pr‬‬

‫ﺟﺮﯾﺎن ﻫﻮا ﯾﮑﯽ از ﭘﺎراﻣﺘﺮﻫﺎي ﻣﻮﺛﺮ در اﻧﺘﻘﺎل ﺣﺮارت‬ ‫ﺑﻮده و داراي ﻣﺸﺨﺼﻪ ي ﺳﺮﻋﺖ و ﺟﻬﺖ ﻣﯽ ﺑﺎﺷﺪ ،‬ ‫اﯾﻦ ﭘﺎراﻣﺘﺮ ﻧﻘﺶ ﻣﻬﻤﯽ در ﻣﯿﺰان ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت‬ ‫دارد ﺑﺎ اﻓﺰاﯾﺶ ﺳﺮﻋﺖ ﻫﻮا ﻣﻘﺪار ﻋﺪد رﯾﻨﻮﻟﺪز اﻓﺰاﯾﺶ‬ ‫ﯾﺎﻓﺘﻪ ﮐﻪ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﻌﺎدﻟﻪ )7( ﻣﻘﺪار ﻋﺪد ﻧﺎﺳﻠﺖ و در‬ ‫ﻧﺘﯿﺠﻪ ﻣﻘﺪار ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ ﺗﻐﯿﯿﺮ ﻣﯽ‬ ‫ﮐﻨﺪ و در ﻧﺘﯿﺠﻪ ﺳﺮﻋﺖ ﮔﺮﻣﺎﯾﺶ ﺑﯿﺸﺘﺮ ﻣﯽ ﺷﻮد ﺑﺮاي‬ ‫اﺳﺘﻔﺎده‬
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‫ﺗﻔﺎﺿﻞ ﻣﺤﺪود‬

‫ﻣﺪل ﻫﺎي دو ﺑﻌﺪي و ﺳﻪ ﺑﻌـﺪي ﮐـﺎرﺑﺮد ﮔـﺴﺘﺮده ﺗـﺮي‬ ‫دارد. ﻣﺮاﺣﻞ اﺻﻠﯽ ﻣﺪل ﺳﺎزي ﺑﺎ اﯾﻦ روش ﻋﺒﺎرﺗﻨﺪ از :‬ ‫1- ﻣﺶ ﺑﻨﺪي ، ﺳﯿـﺴﺘﻢ ﻣـﻮرد ﻣﻄﺎﻟﻌـﻪ )ﺟـﺴﻢ ﻣـﻮرد‬ ‫ﻧﻈﺮ( را ﺑﻪ ﮔﺮه ﻫﺎ و اﻟﻤﺎن ﻫﺎﯾﯽ ﺗﻘـﺴﯿﻢ ﻣـﯽ ﻧﻤـﺎﯾﯿﻢ.‬ ‫اﯾﻦ ﮐﺎر ﺑﺎ ﺗﻘﺴﯿﻢ ﮐﺮدن ﺟـﺴﻢ ﻣـﻮرد ﻧﻈـﺮ ﺑـﻪ ﭼﻨـﺪ‬ ‫ﻧﺎﺣﯿﻪ ﮐﻮﭼﮑﺘﺮ و ﻣﺸﺨﺺ ﮐﺮدن ﯾﮏ ﻧﻘﻄﻪ ﺑﻪ ﻋﻨـﻮان‬ ‫ﻣﺮﮐﺰ ﻫﺮ ﻧﺎﺣﯿﻪ ﺻﻮرت ﻣﯽ ﮔﯿـﺮد. ﻧﻘﻄـﻪ ﻣﺮﺟـﻊ را‬ ‫ﻣﻌﻤﻮﻻً ﮔﺮه 61 و ﻣﺠﻤﻮﻋﻪ ﻧﻘـﺎط را ﺷـﺒﮑﻪ ﮔـﺮه ﻣـﯽ‬
‫51‬

‫ﮔﺸﺖ در ﻣﺮﺣﻠﻪ ﺑﻌﺪ ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﻫﻮا در‬

‫ﺗﻌﯿﯿﻦ ﺳﺮﻋﺖ ﺣﺮﮐﺖ ﻫﻮا از ﯾﮏ اﻧﻪ ﻣﻮﻣﺘﺮ‬

‫درﺟﻪ ﺣﺮارت 05 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد ﺑﺮاي ﺗﻌﯿﯿﻦ ﻋﺪد‬ ‫ﭘﺮاﻧﺘﻞ ﺗﻌﯿﯿﻦ ﮔﺮدﯾﺪ ) اﯾﻨﮑﺮوﭘﺮا و دوﯾﺖ 6991 (.و ﺑﺮاي‬ ‫ﺑﺪﺳﺖ آوردن ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺟﺮم از راﺑﻄﻪ ﺷﯿﻠﺘﻮن -‬ ‫اﺳﺘﻔﺎده ﮔﺸﺖ:‬
‫3/2‬

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‫ﮐﻮﻟﺒﻮرن‬

‫ﻧﺎﻣﻨﺪ. اﯾﻦ ﻣﺮﺣﻠﻪ ﺣﺴﺎﺳﺘﺮﯾﻦ ﻣﺮﺣﻠﻪ در ﻣﺪل ﺳﺎزي‬ ‫ﺑﺎ روش ﺗﻔﺎﺿﻞ ﻣﺤﺪود ﻣﯽ ﺑﺎﺷﺪ .‬ ‫2- ﻗﺪم ﺑﻌﺪي ﺟﺎﯾﮕﺰﯾﻨﯽ ﻣﻌـﺎدﻻت ﺣـﺎﮐﻢ ﺑـﺮ ﮔـﺮه ﻫـﺎي‬ ‫داﺧﻠﯽ و ﺧﺎرﺟﯽ ﺑﺎ ﻣﻌﺎدﻻت ﺗﻘﺮﯾﺒﯽ ﺗﻔﺎﺿﻞ ﻣﺤـﺪود‬ ‫ﻣﯽ ﺑﺎﺷﺪ. دو روش ﮐﻠـﯽ ﮐـﻪ ﺑـﺮاي اﯾﺠـﺎد ﻣﻌـﺎدﻻت‬ ‫ﺗﻔﺎﺿﻞ ﻣﺤﺪود در اﯾﻦ ﺣﺎﻟﺖ ﺑﮑﺎر ﻣﯽ روﻧﺪ ﻋﺒﺎرﺗﻨـﺪ‬ ‫ﺳﺮي ﺗﯿﻠﻮر .‬ ‫3- ﺗﻮﺳﻌﻪ ﯾﮏ ﺳﯿﺴﺘﻢ ﻣﻌﺎدﻻت ﺟﺒﺮي ﺑﺮاي ﮔﺮه ﻫـﺎي‬ ‫داﺧﻠﯽ و ﺧﺎرﺟﯽ‬ ‫4- ﺣﻞ ﻣﻌﺎدﻻت ﺟﺒﺮي ﮔﺮه ﻫﺎ ﺑﺎ ﺷﻤﺎي ﻋﺪدي‬
‫81‬

‫‪M p  Sc ‬‬ ‫‪h‬‬ ‫]8[‬ ‫‪= Cp air  ‬‬ ‫‪M water  Pr ‬‬ ‫‪km‬‬ ‫در راﺑﻄﻪ ﺑﺎﻻ‪ Cp‬ﮔﺮﻣﺎي وﯾﮋه ﻫﻮا در دﻣﺎي اﻧﺪازه ﮔﯿﺮي،‬ ‫‪ Mair‬و ‪ Mwater‬ﺑـﻪ ﺗﺮﺗﯿـﺐ ﺟـﺮم ﻣﻠﮑـﻮﻟﯽ ﻫـﻮا وآب، ‪km‬‬ ‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺟـﺮم، ‪ P‬ﻓـﺸﺎر ﻫـﻮا، ‪ Sc‬و ‪ Pr‬ﺑـﻪ ﺗﺮﺗﯿـﺐ‬ ‫اﻋﺪاد ﺑﺪون ﺑﻌﺪ اﺷﻤﯿﺖ وﭘﺮاﻧﺘﻞ ﻣﯽ ﺑﺎﺷﺪ ﮐﻪ ﺑـﻪ ﺻـﻮرت‬ ‫زﯾﺮ ﺗﻌﺮﯾﻒ ﻣﯽ ﺷﻮﻧﺪ:‬ ‫=‪P‬‬ ‫= ‪Sc‬‬ ‫‪ρRT‬‬ ‫‪M air‬‬ ‫‪µ‬‬ ‫‪µ‬‬ ‫=‬ ‫‪ρDm M air Dwm‬‬ ‫‪Cpµ‬‬ ‫‪k‬‬ ‫]9[‬ ‫]01[‬ ‫]11[‬

‫از 1( روش ﮐﻨﺘـ ـﺮل ﺣﺠﻤـ ـﯽ71 و 2( روش ﺑـ ـﺴﻂ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬

‫= ‪Pr‬‬
‫‪Finite Difference‬‬ ‫‪Meshing‬‬ ‫۶١‬ ‫‪Nodal point‬‬ ‫٧١‬ ‫‪Control volume approach‬‬ ‫٨١‬ ‫‪Tailor series expansion‬‬
‫۵١‬ ‫۴١‬

‫٢١‬ ‫٣١‬

‫‪Anemometer‬‬ ‫‪Chilton – Colburn‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫١۵‬ ‫)4991( ﻣﻘﺪار اﯾﻦ ﺣﺮارت ﻧﺎﭼﯿﺰ و ﺑﯿﻦ 10/0 – 520/0‬ ‫وات ﺑﺮ ﮐﯿﻠﻮﮔﺮم ﻣﯽ ﺑﺎﺷﺪ.‬ ‫ﺳﯿﺴﺘﻢ ﻣﻌﺎدﻻت‬ ‫ﺳﯿﺴﺘﻢ ﻣﻌﺎدﻻت ﻣﻮرد اﺳـﺘﻔﺎده ﺑـﺮاي ﺗﻮﺻـﯿﻒ اﻧﺘﻘـﺎل‬ ‫ﺣ ـﺮارت در داﺧ ـﻞ ﭘﻨﯿ ـﺮ و ﻣ ـﺎﺑﯿﻦ ﭘﻨﯿ ـﺮ و ﻫ ـﻮاي اﻃ ـﺮاف‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻋﺒﺎرﺗﺴﺖ از :‬ ‫1. ﻣﻌﺎدﻟﻪ اﺻﻠﯽ‬ ‫‪∂ρCpT‬‬ ‫‪ ∂T ‬‬ ‫‪= ∇ k‬‬ ‫‪‬‬ ‫‪∂t‬‬ ‫‪ ∂x ‬‬ ‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬ ‫روش ﺗﻔﺎﺿﻞ ﻣﺤـﺪود ﺑـﻪ ﺳـﻪ دﺳـﺘﻪ ﻋﻤـﺪه ﺻـﺮﯾﺢ91 ،‬ ‫روش ﺻﺮﯾﺢ، ﻣﺸﺘﻘﺎت ﻣﮑﺎﻧﯽ را در ﻫﺮ ﮔﺎم زﻣـﺎﻧﯽ22 ﺑـﺎ‬ ‫اﺳﺘﻔﺎده از ﻣﻘﺎدﯾﺮ ﻣﻌﻠﻮم در ﮔﺎم زﻣﺎﻧﯽ ﻗﺒﻞ ﺑﻪ ﺗﻘﺮﯾﺐ ﻣﯽ‬ ‫رﺳ ـﺎﻧﻨﺪ در ﺣﺎﻟﯿﮑ ـﻪ در روش ﺿ ـﻤﻨﯽ ﺑ ـﺮاي ﺑ ـﻪ ﺗﻘﺮﯾ ـﺐ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫رﺳﺎﻧﺪن از ﻣﻘﺎدﯾﺮ ﻣﺠﻬﻮل ﻫﻤﺎن ﮔﺎم زﻣﺎﻧﯽ اﺳﺘﻔﺎده ﻣـﯽ‬ ‫ﺷﻮد. در روش ﮐﺮاﻧـﮏ ﻧﯿﮑﻠـﺴﻮن ﻧﯿـﺰ ﺑـﺮاي ﺑـﻪ ﺗﻘﺮﯾـﺐ‬ ‫رﺳ ـﺎﻧﺪن از ﻣﻘ ـﺎدﯾﺮ ﻣﻌﻠ ـﻮم ﮔ ـﺎم زﻣ ـﺎﻧﯽ ﻗﺒ ـﻞ و ﻣﻘ ـﺎدﯾﺮ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻣﺠﻬﻮل ﻫﻤﺎن ﮔﺎم زﻣﺎﻧﯽ ﺑﻪ ﺻﻮرت ﻫﻤﺰﻣﺎن اﺳﺘﻔﺎده ﻣﯽ‬ ‫ﺷـــﻮد. روش اﺧﯿـــﺮ از دﻗـــﺖ ﺑﯿـــﺸﺘﺮي ﺑﺮﺧـــﻮردار‬ ‫اﺳـــﺖ)اﯾﻨﮑﺮوﭘـــﺮا و دوﯾـــﺖ 6991، اُزﯾـــﺴﯿﮏ 5891 و‬ ‫2. ﺷﺮاﯾﻂ ﻣﺮزي‬ ‫ﺑﺮاي ﺗﻮﺳﻌﻪ ﻣﺪل در ﺣﺎﻟﺖ ﺗﮏ ﺑﻌﺪي ﻓـﺮض ﺷـﺪه اﺳـﺖ‬ ‫ﮐﻪ ﺑﻪ ﻣﺤﺾ ﻗﺮار ﮔـﺮﻓﺘﻦ ﭘﻨﯿـﺮ در ﻣﻌـﺮض ﻫـﻮا، اﻧﺘﻘـﺎل‬ ‫ﺣﺮارت در ﺳﻄﺢ ﭘﻨﯿﺮ رخ ﻣﯽ دﻫﺪ. ﺷﺪت اﻧﺘﻘـﺎل ﺣـﺮارت‬ ‫در ﺳﻄﺢ ﺗﻮﺳﻂ ﮔﺮادﯾﺎن دﻣﺎﯾﯽ ﻣﺎﺑﯿﻦ دﻣﺎي ﺳﻄﺢ ﭘﻨﯿﺮ و‬ ‫دﻣﺎي ﻫﻮا و ﺿﺮﯾﺐ ﺗﺒﺎدل ﺣﺮارت در ﺳﻄﺢ ﮐﻨﺘـﺮل ﻣـﯽ‬ ‫ﮔﺮدد. ﺑﺪﻧﺒﺎل ﺗﻐﯿﯿﺮ دﻣﺎ در ﺳﻄﺢ، اﻧﺘﻘﺎل ﺣﺮارت در داﺧﻞ‬ ‫ﭘﻨﯿﺮ ﻓﺮض ﻣﯽ ﺷﻮد ﮐﻪ ﻓﻘﻂ ﺑﺎ ﻣﮑﺎﻧﺴﯿﻢ ﻫﺪاﯾﺖ اﻧﺠﺎم ﻣﯽ‬ ‫ﺷﻮد.‬ ‫– ﺗﻐﯿﯿﺮ ﺣﺠﻢ ﭘﻨﯿﺮ ﻃﯽ اﻧﺘﻘﺎل ﺣﺮارت ﻗﺎﺑﻞ ﺻـﺮف ﻧﻈـﺮ‬ ‫ﮐﺮدن اﺳﺖ.‬ ‫– ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ ﺛﺎﺑﺖ و ﯾﮑﻨﻮاﺧـﺖ در‬ ‫ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪه اﺳﺖ.‬ ‫– در ﺣﯿﻦ ﮔﺮم ﮐﺮدن ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﭘﻨﯿـﺮ ﺑـﻪ‬ ‫ﺟﺰ ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ، ﺛﺎﺑﺖ ﻓﺮض ﺷﺪه اﺳﺖ.‬ ‫– از ﺣــﺮارت ﺗﻮﻟﯿــﺪي ﭘﻨﯿــﺮ ﮐــﻪ ﻣﺮﺑــﻮط ﺑــﻪ ﻓﻌﺎﻟﯿــﺖ‬ ‫ﻣﯿﮑﺮوارﮔﺎﻧﯿﺴﻢ ﻫﺎ و ﻓﺮاﯾﻨﺪ ﺗﺨﻤﯿﺮ ﻣـﯽ ﺑﺎﺷـﺪ ﺻـﺮف‬ ‫ﻧﻈ ـﺮ ﻣــﯽ ﺷ ـﻮد زﯾــﺮا ﺑ ـﺮ اﺳــﺎس ﺗﺤﻘﯿﻘ ـﺎت ﺑﻨــﺎﭼﯿﻮ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻓﺮﺿﯿﺎت ﻣﺪل‬ ‫اُزﯾﺴﯿﮏ 4991(.‬

‫ﺿ ـﻤﻨﯽ02 و ﮐﺮاﻧ ـﮏ ﻧﯿﮑﻠ ـﺴﻮن 12 ﺗﻘ ـﺴﯿﻢ ﻣ ـﯽ ﺷ ـﻮد. در‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬

‫]21[‬

‫,0= ‪At x‬‬

‫‪∂T‬‬ ‫0=‬ ‫‪∂x‬‬

‫]31[‬

‫ﻣﻌﺎدﻟﻪ ﻓﻮق ﺑﺪﻟﯿﻞ وﺟﻮد ﻋﺎﯾﻖ ﺣﺮارﺗﯽ )ﭘﻠﯽ اﺳـﺘﯿﺮن( در‬ ‫اﻧﺘﻬﺎي ﺟﺴﻢ ﺣﺎﺻﻞ ﻣﯽ ﺷﻮد. اﻧﺘﻘـﺎل ﺣـﺮارت در ﺳـﻄﺢ‬ ‫ﺧﺎرﺟﯽ ﭘﻨﯿﺮ در اﺛﺮ ﺟﺮﯾﺎن ﻫﻤﺮﻓﺘﯽ، ﺗﺒﺨﯿـﺮ و ﺗﺸﻌـﺸﻊ‬ ‫ﻣﯽ ﺑﺎﺷﺪ اﮔﺮ ﭼﻪ ﺑﺎ اﺳﺘﻔﺎده از ﭘﻮﺷﺶ ﭘﻠﯽ اﺗﯿﻠﻨﯽ ﻧﺎزﮐﯽ‬ ‫ﮐﻪ در ﺳﻄﺢ ﭘﻨﯿﺮ ﻗﺮار ﮔﺮﻓﺖ از اﻧﺘﻘﺎل ﺣـﺮارت ﺑـﻪ ﺷـﮑﻞ‬ ‫ﺗﺒﺨﯿﺮ ﺟﻠﻮﮔﯿﺮي ﺑﻌﻤﻞ آﻣﺪ و ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ آﻧﮑﻪ دﻣﺎي ﺳﻄﺢ‬ ‫اﻓﺰاﯾﺶ ﻗﺎﺑـﻞ ﺗـﻮﺟﻬﯽ ﻧﻤـﯽ ﮐﻨـﺪ ﺑﻨـﺎﺑﺮاﯾﻦ از اﺛـﺮ اﻧﺘﻘـﺎل‬ ‫ﺣﺮارت ﺑﻪ ﺷﮑﻞ ﺗﺸﻌﺸﻊ ﻧﯿﺰ ﺻﺮف ﻧﻈﺮ ﮔﺮدﯾﺪ در ﻧﺘﯿﺠﻪ‬ ‫ﺷﺮاﯾﻂ ﻣﺮزي در ﺳﻄﺢ ﺑﻪ ﺻﻮرت زﯾﺮ ﺧﻮاﻫﺪ ﺑﻮد:‬ ‫‪∂T‬‬ ‫‪At x = L, − k‬‬ ‫]41[ ) ∞‪= h (TS − T‬‬ ‫‪∂x‬‬ ‫3. ﺷﺮط اوﻟﯿﻪ‬ ‫‪T = Ti‬‬

‫]51[‬

‫ﺑ ـﻪ ﻣﻨﻈﻮرآﻧﮑــﻪ ﻣــﺪل ﺗﻔﺎﺿ ـﻞ ﻋــﺪدي از دﻗــﺖ ﺑــﺎﻻﺗﺮي‬ ‫ـ‬ ‫ـ‬ ‫ﺑﺮﺧـﻮردار ﺑﺎﺷـﺪ، واﺑـﺴﺘﮕﯽ دﻣـﺎﺋﯽ ﻫـﺪاﯾﺖ ﺣﺮارﺗـﯽ در‬ ‫ـ‬ ‫ﻣﻌﺎدﻻت در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪ. واﺑﺴﺘﮕﯽ ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ ﺑـﻪ‬

‫٩١‬ ‫٠٢‬

‫‪Explicit‬‬ ‫‪Implicit‬‬ ‫١٢‬ ‫‪Crank Nicholson‬‬ ‫٢٢‬ ‫‪Time step‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫ﺷﺪ. ﭘﺎراﻣﺘﺮﻫﺎ و ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣـﻮﻓﯿﺰﯾﮑﯽ ﺑﮑـﺎر ﮔﺮﻓﺘـﻪ‬ ‫ﺷﺪه در ﻣﺪل در ﺟﺪول )2 و 3 ( آورده ﺷﺪه اﺳﺖ.‬ ‫ﺗﺎﯾﯿﺪ ﻣﺪل‬ ‫ﺗﺎﺋﯿﺪ ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه در دو ﻣﺮﺣﻠﻪ ﺻﻮرت ﮔﺮﻓﺖ:‬ ‫اﻟﻒ( ﺗﺎﺋﯿﺪ رﯾﺎﺿـﯽ )ﺗﺎﯾﯿـﺪ اوﻟﯿـﻪ(: ﺗﺎﯾﯿـﺪ اوﻟﯿـﻪ ﻣﻌـﺎدﻻت‬ ‫ﺑﻮﺳﯿﻠﻪ ﻣﻘﺎﯾﺴﻪ ﻧﺘﺎﯾﺞ ﺣﺎﺻﻠﻪ از روش ﺗﻔﺎﺿﻞ ﻣﺤﺪود ﺑـﺎ‬ ‫ﻧﺘﺎﯾﺞ ﺣﺎﺻﻠﻪ از ﺣﻞ ﺗﺤﻠﯿﻠﯽ ﮔﺮﻣﺎﯾﺶ ﺗﮏ ﺑﻌﺪي ﻗﺎﻟﺐ‬ ‫ﭘﻨﯿﺮي ﺑﺎ ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣـﻮﻓﯿﺰﯾﮑﯽ ﺛﺎﺑـﺖ ﺑـﺎ اﺳـﺘﻔﺎده از‬ ‫ﺟﺮﯾﺎن ﻫﻤﺮﻓﺖ اﺟﺒﺎري ﻫﻮاي ﮔﺮم اﻧﺠﺎم ﺷﺪ.‬ ‫٢۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬ ‫دﻣﺎ را ﻣﯽ ﺗﻮان ﺑﻪ ﺷﮑﻞ ﻣﯿـﺎﻧﮕﯿﻦ ﺣـﺴﺎﺑﯽ و ﯾـﺎ ﻣﯿـﺎﻧﮕﯿﻦ‬ ‫ﺗﻮاﻓﻘﯽ ﺗﻌﯿﯿﻦ ﻧﻤﻮد، ﮐﻪ‬ ‫دﻗﺖ ﺑﺮآورد روش ﻣﯿﺎﻧﮕﯿﻦ ﺗـﻮاﻓﻘﯽ ﺑـﺎﻻﺗﺮﻣﯽ ﺑﺎﺷـﺪ. در‬

‫ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه از ﻣﯿﺎﻧﮕﯿﻦ ﺗﻮاﻓﻘﯽ اﺳﺘﻔﺎده ﮔﺮدﯾﺪ.‬
‫‪ 2 × k(T (i +1,n +1)) × k(T (i , n +1)) ‬‬ ‫‪k=‬‬ ‫‪‬‬ ‫‪ k(T (i +1,n +1)) × k(T (i , n +1)) ‬‬ ‫‪‬‬ ‫‪‬‬

‫]61[‬

‫ﻣﻌﺎدﻻت اﺻﻠﯽ اﻧﺘﻘﺎل ﺣﺮارت ﺑﺎ اﻋﻤـﺎل ﺷـﺮاﯾﻂ اوﻟﯿـﻪ و‬ ‫ﻣﺮزي ﺑـﻪ ﻃـﻮر ﻋـﺪدي و ﺑـﺎ اﺳـﺘﻔﺎده از روش ﺗﻔﺎﺿـﻞ‬ ‫ﻣﺤﺪود ﺑﺮ ﻣﺒﻨﺎئ ﺷﻤﺎي ﮐﺮاﻧﮏ ﻧﯿﮑﻮﻟﺴﻮن- ﻣﺮﮐﺰي ﺣﻞ‬ ‫ﮔﺮدﯾﺪﻧﺪ. در اﯾﻦ ﻣﻄﺎﻟﻌﻪ ﯾﮏ ﺑﻌﺪي، ﻃـﻮل ﻧﻤﻮﻧـﻪ ﭘﻨﯿـﺮ )5‬ ‫ﺳﺎﻧﺘﯿﻤﺘﺮ( ﺑﻪ 01 ﮔـﺮه ﺗﻘـﺴﯿﻢ ﮔﺮدﯾـﺪ )ﺷـﮑﻞ 2(. ﺑﺮﻧﺎﻣـﻪ‬ ‫ﻧﻮﯾﺴﯽ ﺑـﺮ روي ﻧـﺮم اﻓـﺰار 1.5.6 ‪ MATLAB‬اﻧﺠـﺎم‬

‫ﻃﻮل )ﻣﺘﺮ(‬ ‫‪ l‬ﺳﻄﺢ‬

‫ﺷﻤﺎره ﮔﺮه‬
‫‪N‬‬

‫‪5 cm‬‬
‫1+‪i‬‬

‫‪5 cm‬‬

‫ﭘﻨﯿﺮ‬

‫‪x‬‬

‫‪i‬‬

‫ﺷﮑﻞ 2- ﻣﺶ ﺑﻨﺪي و ﺷﺒﮑﻪ ﮔﺮه ﻫﺎ ﺑﺮاي ﭘﻨﯿﺮ در ﺣﺎﻟﺖ ﺗﮏ ﺑﻌﺪي‬
‫ﮐﻒ‬
‫0‬ ‫1‬

‫1-‪i‬‬

‫ﺟﺪول 2: ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﭘﻨﯿﺮ در ﻣﺤﺪوده ي دﻣﺎﯾﯽ 0 – 32 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد‬ ‫)اﻧﺪازه ﮔﯿﺮي ﺷﺪه و داده ﻫﺎي ﺣﺎﺻﻞ از ﻣﺪل( .‬
‫ﮔﺮﻣﺎي وﯾﮋه‬ ‫)‪(J/kgK‬‬ ‫72/0 +0543‬ ‫8023‬ ‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ‬ ‫)‪(W/mK‬‬ ‫91/0+44/0‬ ‫764/0‬ ‫داﻧﺴﯿﺘﻪ‬ ‫)3‪(kg/m‬‬ ‫52/0 +0501‬ ‫9/9501‬ ‫ﺧﺼﻮﺻﯿﺎت‬ ‫ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ‬ ‫اﻧﺪازه ﮔﯿﺮي‬ ‫ﻣﺪل‬

‫ﺟﺪول 3: ﭘﺎراﻣﺘﺮﻫﺎ و ﺷﺮاﯾﻂ ﺑﮑﺎر رﻓﺘﻪ ﺑﻪ ﻋﻨﻮان ورودي ﻣﺪل ﺑﺮاي ﭘﯿﺶ ﺑﯿﻨﯽ دﻣﺎ ﻃﯽ ﺣﺮارت دﻫﯽ‬
‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت‬ ‫در ﺳﻄﺢ‬ ‫) ‪( W/m2 K‬‬ ‫42‬ ‫ﻣﺪت زﻣﺎن ﺣﺮارت‬ ‫دﻫﯽ ) ﺛﺎﻧﯿﻪ (‬ ‫00001‬ ‫درﺟﻪ ﺣﺮارت ﻣﺤﯿﻂ‬ ‫) ﺳﺎﻧﺘﯿﮕﺮاد(‬ ‫04‬ ‫دﻣﺎي اوﻟﯿﻪ‬ ‫ﮔﺎم زﻣﺎﻧﯽ‬ ‫) ﺛﺎﻧﯿﻪ (‬ ‫01‬

‫)ﺳﺎﻧﺘﯿﮕﺮاد(‬ ‫5‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫٣۵‬ ‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬

‫دﺳﺘﮕﺎه ﮐﺎﺗﺮ، ﺑﺮﯾﺪه ﺷﺪه و درﭼﺎرﭼﻮب ﭘﻠـﯽ اﺳـﺘﺎﯾﺮﻧﯽ‬ ‫ﻗﺮار ﮔﺮﻓﺖ ﺷﮑﻞ )3(. ﺳﭙﺲ دو ﻋﺪد ﺗﺮﻣﻮﮐﻮﭘـﻞ ﻧـﻮع ‪،K‬‬ ‫ﺑﻪ ﺗﺮﺗﯿﺐ در ﺳـﻄﺢ و در ﻣﺮﮐـﺰ ﭘﻨﯿـﺮ ﻗـﺮار داده ﺷـﺪه و‬ ‫ﺑﺮاي ﺟﻠﻮﮔﯿﺮي ازاﻧﺘﻘﺎل ﺟـﺮم در ﺣـﯿﻦ اﻧﺠـﺎم آزﻣـﺎﯾﺶ،‬ ‫ﭘﻮﺷﺶ ﭘﻠﯽ اﺗﯿﻠﻨﯽ در ﺳﻄﺢ ﭘﻨﯿﺮ ﻗﺮار ﮔﺮﻓﺖ. ﻧﻤﻮﻧﻪ آﻣﺎده‬ ‫ﺷﺪه ﭘﺲ از رﺳﯿﺪن ﺑﻪ دﻣـﺎي اوﻟﯿـﻪ ﯾﮑﻨﻮاﺧـﺖ در داﺧـﻞ‬ ‫ﻗﺮار ﮔﺮﻓﺘﻪ و ﺗﻐﯿﯿﺮات دﻣﺎي ﻧﻤﻮﻧﻪ ﺗﻮﺳﻂ دﯾﺘﺎ ﻻﮔﺮ ﻣﺪل‬ ‫2‪ DL‬ﺳﺎﺧﺖ اﻧﮕﻠﺴﺘﺎن در ﻓﻮاﺻﻞ زﻣﺎﻧﯽ ده ﺛﺎﻧﯿﻪ ﺑﺮاي‬ ‫ﻣﺪت3 ﺳﺎﻋﺖ ﺛﺒﺖ ﮔﺮدﯾﺪ.‬ ‫2- ﻧﺘﺎﯾﺞ و ﺑﺤﺚ‬ ‫ﻧﺘــﺎﯾﺞ ﻣﺮﺑــﻮط ﺑــﻪ ﺗﺠﺰﯾــﻪ ي ﺗﻘﺮﯾﺒــﯽ و ﺧــﻮاص‬ ‫ـ‬ ‫ـ‬ ‫ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ )ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ، ﮔﺮﻣـﺎي وﯾـﮋه و داﻧـﺴﯿﺘﻪ(‬ ‫ﻧﻤﻮﻧﻪ ﻫﺎي ﭘﻨﯿﺮ ﻣـﻮرد اﺳـﺘﻔﺎده در ﺟـﺪاول 1 و 2 ﻧـﺸﺎن‬ ‫داده ﺷﺪه اﺳﺖ. ﻫﻤﺎﻧﮕﻮﻧﻪ ﮐﻪ ﻣﺸﺎﻫﺪه ﻣـﯽ ﺷـﻮد ﻣﻘـﺎدﯾﺮ‬ ‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ، ﮔﺮﻣﺎي وﯾﮋه و داﻧﺴﯿﺘﻪ ﻧﻤﻮﻧﻪ ي ﭘﻨﯿﺮ در‬ ‫ﻣﺤﺪوده دﻣﺎﯾﯽ 0-32 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد ﺑﻪ ﺗﺮﺗﯿـﺐ ﺑﺮاﺑـﺮ‬ ‫ﺑﺎ 44/0 وات ﺑﺮ ﻣﺘﺮ ﺳﺎﻧﺘﯿﮕﺮاد، 0543 ژول ﺑﺮ ﮐﯿﻠـﻮﮔﺮم‬ ‫درﺟﻪ ﮐﻠﻮﯾﻦ، و 0501 ﮐﯿﻠﻮﮔﺮم ﺑﺮ ﻣﺘﺮ ﻣﮑﻌﺐ ﻣﯽ ﺑﺎﺷـﻨﺪ.‬ ‫در ﺟـﺪول 2 ﻣﻘ ـﺎدﯾﺮ ﻫ ـﺪاﯾﺖ ﺣﺮارﺗـﯽ ، ﮔﺮﻣ ـﺎي وﯾ ـﮋه و‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫داﻧﺴﯿﺘﻪ ﺑﺮآورد ﺷﺪه ﺗﻮﺳـﻂ ﻣـﺪل ﻫـﺎ ﻧﯿـﺰ آورده ﺷـﺪه‬ ‫اﺳﺖ.‬ ‫ﻧﮑﺘﻪ ﻗﺎﺑﻞ ﺗﻮﺟـﻪ، ﺑـﺎﻻ ﺑـﻮدن ﻫـﺪاﯾﺖ ﺣﺮارﺗـﯽ ﭘﻨﯿـﺮ‬ ‫ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه در ﻣﻘﺎﯾﺴﻪ ﺑﺎ دﯾﮕﺮ ﭘﻨﯿﺮ ﻫﺎ ﻣﯽ ﺑﺎﺷﺪ، ﮐـﻪ‬ ‫ﺑﻪ ﻣﯿﺰان ﺑﺎﻻي رﻃﻮﺑﺖ اﯾﻦ ﻧﻮع ﭘﻨﯿﺮ ﻣﺮﺑـﻮط ﻣـﯽ ﺷـﻮد.‬ ‫ﯾﮑﯽ از ﻋﻮاﻣﻞ ﻣﻮﺛﺮ در ﺑﺎﻻ ﺑﻮدن ﻣﯿﺰان رﻃﻮﺑـﺖ در اﯾـﻦ‬ ‫ﭘﻨﯿﺮﺣﻔﻆ و ﺑﺎﻗﯽ ﻣﺎﻧﺪن ﭘﺮوﺗﺌﯿﻦ ﻫﺎي آب ﭘﻨﯿﺮ و ﻇﺮﻓﯿـﺖ‬ ‫و ﻫﻤﮑﺎران 9991 و اِل ﺳﻮدا و ﻋﺒﺪاﻟﺴﻼم2002(.‬ ‫ﻧﮕﻬﺪاري آب42 ﺑﺎﻻي اﯾﻦ ﭘﺮوﺗﺌﯿﻨﻬﺎ ﻣﯽ ﺑﺎﺷﺪ )ﻋﺒﺪاﻟـﺴﻼم‬ ‫ﺳﺮدﺧﺎﻧﻪ، در ﻣﻌﺮض ﺟﺮﯾﺎن ﻫﻮاي ﮔﺮم ﺑـﺎ دﻣـﺎي ﺛﺎﺑـﺖ‬

‫ﺣﻞ ﺗﺤﻠﯿﻠﯽ ﺗﻮزﯾﻊ دﻣﺎ ﺑﺮاي دﯾﻮار ﺗﺨﺘﯽ ﺑﻪ ﺿﺨﺎﻣﺖ ‪2L‬‬ ‫)‪ L‬ﻃــﻮل ﻣﺸﺨــﺼﻪ دﯾــﻮار ﻣــﯽ ﺑﺎﺷــﺪ و از راﺑﻄــﻪ‬ ‫‪ L = V‬ﺑﺪﺳﺖ ﻣﯽ آﯾﺪ ﮐﻪ ‪ V‬ﺣﺠﻢ و ‪ A‬ﺳﻄﺢ دﯾـﻮار‬ ‫‪A‬‬ ‫ﺗﺨﺖ ﻣﯽ ﺑﺎﺷﺪ ( ﮐﻪ ﺑﻪ ﺻﻮرت ﻧﺎﮔﻬﺎﻧﯽ در ﺳـﯿﺎﻟﯽ ﻓـﺮو‬ ‫ﺑﺮده ﺷﻮد و ﻋﺮض و ﻃﻮل دﯾﻮار در‬ ‫ﻣﻘﺎﯾـﺴﻪ ﺑـﺎ ﺿـﺨﺎﻣﺖ ﮐﻮﭼـﮏ ﻣـﯽ ﺑﺎﺷـﺪ از راﺑﻄـﻪ ذﯾـﻞ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ﺑﺪﺳﺖ ﻣﯽ آﯾﺪ ) ﻧﯿﮑﻮﻻي و ﻫﻤﮑﺎران 1002(:‬
‫= ‪θ‬‬

‫‪∑ 2ς‬‬
‫1= ‪n‬‬

‫∞‬

‫) ‪4 sin(ς n‬‬ ‫‪x‬‬ ‫2‬ ‫]71[ ) ‪exp(ς n F 0) cos(ς n‬‬ ‫‪L‬‬ ‫) ‪n + sin( 2ς n‬‬

‫ﺗﻮزﯾﻊ دﻣﺎ ﺑﺮاي ﯾﮏ دﯾﻮار ﺗﺨﺖ در ﺣﺎﻟﺖ ﮔﺬرا ﺗﺎﺑﻊ ﻋﻤﻮﻣﯽ از ‪،L‬‬ ‫0‪ F‬و ‪ Bi‬ﻣ ـﯽ ﺑﺎﺷ ـﺪ ﮐ ـﻪ 0‪ F‬و ‪ Bi‬ﺑ ـﻪ ﺻ ـﻮرت زﯾ ـﺮ ﺗﻌﺮﯾ ـﻒ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ﻣﯿﺸﻮﻧﺪ:‬ ‫= ‪Bi‬‬ ‫‪hL‬‬ ‫‪k‬‬ ‫‪kt‬‬ ‫2‪ρCpL‬‬

‫]81[‬ ‫]91[‬

‫= 0‪F‬‬

‫ﮐﻪ در راﺑﻄﻪ ﺑﺎﻻ 0‪ F‬و ‪ θ‬اﻋﺪاد ﺑﺪون ﺑﻌﺪ زﻣﺎن و دﻣﺎ ﻣﯽ‬ ‫ﺑﺎﺷﻨﺪ و ﻣﻘﺎدﯾﺮ ﮔﺴﺴﺘﻪ )ﻣﻘﺎدﯾﺮ وﯾﮋه(32 ‪ ζn‬رﯾـﺸﻪ ﻫـﺎي‬ ‫ﻣﺜﺒﺖ ﻣﻌﺎدﻟﻪ اﻧﺪ .‬ ‫‪ζ n tan(ζ n ) = Bi‬‬

‫]02[‬

‫ب( ﺗﺎﯾﯿﺪ ﻧﻬﺎﯾﯽ ﻣﺪل: ﺗﺎﺋﯿﺪ ﻓﺮﺿﯿﺎت ﻣﺪل ﺑﻮﺳﯿﻠﻪ ﻣﻘﺎﯾـﺴﻪ‬ ‫ﭘﺮوﻓﯿﻠﻬﺎي دﻣﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣـﺪل ﺑـﺎ ﻣﻘـﺎدﯾﺮ‬ ‫اﻧﺪازه ﮔﯿﺮي ﺷـﺪه ﺗﻮﺳـﻂ ﺗﺮﻣﻮﮐﻮﭘـﻞ در ﮔﺮﻣـﺎﯾﺶ ﺗـﮏ‬ ‫ﺑﻌﺪي و ﺳﻪ ﺑﻌﺪي ﭘﻨﯿﺮ ﺑﺎ ﺟﺎﺑﺠﺎﺋﯽ اﺟﺒـﺎري ﻫـﻮاي ﮔـﺮم‬ ‫اﻧﺠﺎم ﺷﺪ.‬ ‫ﺑﺮاي اﻧﺪازه ﮔﯿﺮي دﻣﺎ در ﺣﺎﻟﺖ ﮔﺮﻣﺎﯾﺶ ﺗﮏ ﺑﻌﺪي، اﺑﺘـﺪا‬ ‫ﻧﻤﻮﻧـﻪ ﭘﻨﯿـﺮي ﺑـﻪ اﺑﻌـﺎد 5×5×5 ﺳـﺎﻧﺘﯿﻤﺘﺮ ﺗﻮﺳـﻂ ﯾـﮏ‬

‫۴٢‬

‫‪Water Holding Capacity‬‬

‫٣٢‬

‫‪Eigenvalue‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫ﻣــﺸﺎﻫﺪات ﻣــﺸﺎﺑﻬﯽ ﺗﻮﺳــﻂ ﮐﺎرﺳــﻮن )6002( و‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﮐﻨﺪﺟﻮﯾﺎن )6991( ﮔﺰارش ﺷﺪه اﺳﺖ.‬ ‫ﺷﮑﻞ4 ﻣﻘﺎﯾﺴﻪ ﺑﯿﻦ دﻣﺎﻫﺎي ﭘـﯿﺶ ﺑﯿﻨـﯽ ﺷـﺪه ﺗﻮﺳـﻂ‬ ‫ﺣﻞ ﺗﺤﻠﯿﻠﯽ ﺑﺎ ﻧﺘﺎﯾﺞ ﺣﺎﺻـﻞ از ﻣـﺪل ﻋـﺪدي ﺗﻮﺳـﻌﻪ داده‬ ‫ﺷﺪه اﺳﺖ.‬ ‫در ﻣﺮﮐـﺰ و ﺳ ـﻄﺢ ﯾـﮏ ﻗﺎﻟ ـﺐ ﭘﻨﯿ ـﺮ ﻣﮑﻌـﺐ ﺷ ـﮑﻞ ﺑ ـﺎ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﺛﺎﺑـﺖ ﻃـﯽ ﺣـﺮارت دﻫـﯽ ﺗـﮏ‬ ‫ﺑﻌﺪي ﺑﺎ ﺟﺮﯾﺎن اﺟﺒﺎري ﻫﻮاي ﮔﺮم ﺑﻤﺪت ﺳﻪ ﺳـﺎﻋﺖ در‬ ‫دﻣﺎي 04 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد را ﻧﺸﺎن ﻣﯽ دﻫﺪ.‬ ‫۴۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬ ‫ﺟﺪول4، ﻣﻘﺎدﯾﺮ ﺿـﺮاﯾﺐ اﻧﺘﻘـﺎل ﺣـﺮارت و ﺟـﺮم در‬

‫ﺳﻄﺢ در دﻣﺎي ‪ 40°C‬و ﺳﺮﻋﺖ 4/1 ﻣﺘﺮ ﺑﺮ ﺛﺎﻧﯿﻪ ﺑﺎ‬

‫اﺳﺘﻔﺎده از دو روش ﻣﺘﻔـﺎوت )اﻧـﺪازه ﮔﯿـﺮي دﻣـﺎ در‬ ‫ﺣﺎﻟﺖ ﻧﺎﭘﺎﯾﺎ و روش اﻋﺪاد ﺑﺪون ﺑﻌﺪ( را ﻧﺸﺎن ﻣﯽ دﻫﺪ.‬ ‫ﻣﻘﺪار ﻋﺪد رﯾﻨﻮﻟﺪز و ﻋﺪد ﭘﺮاﻧﺘﻞ ﺑﻪ ﺗﺮﺗﯿـﺐ ﺑﺮاﺑـﺮ ﺑـﺎ‬ ‫0083 و 7/0 ﺗﻌﯿﯿﻦ ﮔﺮدﯾـﺪ. ﻫﻤـﺎﻧﻄﻮر ﮐـﻪ ﻣـﺸﺎﻫﺪه ﻣـﯽ‬ ‫ﺷﻮد، ﻣﻘﺪار ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ اﻧﺪازه ﮔﯿﺮي‬ ‫ﺷﺪه ﻧﺴﺒﺖ ﺑﻪ ﻣﻘﺪار ﺑـﺮآورد ﺷـﺪه ﺑـﺎ اﺳـﺘﻔﺎده از روش‬ ‫اﻋﺪاد ﺑﺪون ﺑﻌﺪ، ﺑﺰرﮔﺘﺮ ﻣـﯽ ﺑﺎﺷـﺪ. ﺗﻔـﺎوت ﻣـﺬﮐﻮر ﻣـﯽ‬ ‫ﺗﻮاﻧـﺪ ﺑـﻪ ﺷـﺪت اﻏﺘـﺸﺎش ﺟﺮﯾـﺎن ﻫـﻮا در اﺛـﺮ ﻧﻮﺳـﺎن‬ ‫ـ‬ ‫ـ‬ ‫ﺳﺮﻋﺖ در داﺧﻞ ﻣﺤﻔﻈﻪ ي ﺣﺮارت دﻫﯽ ﻣﺮﺗﺒﻂ ﺑﺎﺷﺪ.‬

‫ﭘﻨﯿﺮ‬

‫ﭘﻠﯽ اﺳﺘﯿﺮن‬

‫‪5 cm‬‬

‫‪25 cm‬‬

‫ﺗﺮﻣﻮﮐﻮﭘﻞ‬

‫‪5 cm‬‬

‫52‬

‫‪10 cm‬‬

‫‪cm‬‬

‫ﺟﺮﯾﺎن ﻫﻮا‬

‫ﺷﮑﻞ 3 - ﻧﻤﺎي روﺑﺮو و ﺑﺮش ﻋﺮﺿﯽ ﭼﺎرﭼﻮب ﭘﻠﯽ اﺳﺘﺎﯾﺮﻧﯽ ﺑﺮاي ﻣﺪل ﯾﮏ ﺑﻌﺪي‬ ‫ﺟﺪول 4: ﺿﺮاﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت و ﺟﺮم در ﺳﻄﺢ در دﻣﺎي ‪ 40°C‬و ﺳﺮﻋﺖ 4/1 ﻣﺘﺮ ﺑﺮ ﺛﺎﻧﯿﻪ ﺑﺎ اﺳﺘﻔﺎده از دو روش ﻣﺘﻔﺎوت‬ ‫)‪hm (W/m2 °C‬‬ ‫47/52‬ ‫46/02‬ ‫)‪km (m/s‬‬ ‫7320/0‬ ‫0910/0‬ ‫)‪kg (s/m‬‬ ‫951000000/0‬ ‫821000000/0‬ ‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ‬ ‫روش دﻣﺎي ﮔﺬرا‬ ‫روش اﻋﺪاد ﺑﺪون ﺑﻌﺪ‬

‫ﺷﺪه و ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه ﻃﯽ‬ ‫ﮔﺮﻣﺎﯾﺶ ﺳﻪ ﺑﻌﺪي ﭘﻨﯿﺮ در دﻣﺎﻫﺎي ﻣﺘﻔﺎوت اﻧﺠﺎم ﮔﺮدﯾﺪ.‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺗﺸﺎﺑﻪ ﻧﺘﺎﯾﺞ ﻣﺮﺑﻮط ﺑﻪ دﻣﺎﻫﺎي ﻣﺘﻔﺎوت، ﻧﺘﺎﯾﺞ‬ ‫ﻣﻘﺎﯾﺴﻪ ﭘﺮوﻓﯿﻞ ﻫﺎي دﻣﺎﯾﯽ اﻧﺪازه ﮔﯿﺮي ﺷﺪه در دﻣـﺎي‬ ‫04 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد و داده ﻫﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷـﺪه ﺗﻮﺳـﻂ‬

‫اﻧﻄﺒﺎق ﮐﺎﻣﻞ ﻣﻮﺟﻮد ﻣﺎﺑﯿﻦ ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ از ﺣﻞ ﻋـﺪدي و‬ ‫ﺗﺤﻠﯿﻠﯽ، ﺑﯿﺎﻧﮕﺮ ﺻﺤﯿﺢ ﺑﻮدن ﺣﻞ ﺳﯿﺴﺘﻢ ﻣﻌﺎدﻻت و ﺗﺎﯾﯿﺪ‬ ‫اوﻟﯿﻪ ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه ﻣﯽ ﺑﺎﺷﺪ.‬ ‫ﺗﺎﯾﯿﺪ ﻧﻬﺎﯾﯽ ﻣﺪل ﺑﺎ ﻣﻘﺎﯾﺴﻪ ﭘﺮوﻓﯿﻠﻬﺎي دﻣﺎﯾﯽ اﻧﺪازه ﮔﯿﺮي‬ ‫‪www.SID.ir‬‬ ‫ﻫﻤﺎﻧﮕﻮﻧﻪ ﮐﻪ در ﺑﺨﺶ ﻣﻮاد و روﺷﻬﺎ ﺗﻮﺿـﯿﺢ داده ﺷـﺪ،‬

‫‪Archive of SID‬‬ ‫۵۵‬ ‫ﻫﻤﺎﻧﮕﻮﻧﻪ ﮐﻪ ﻣﺸﺎﻫﺪه ﻣﯽ ﺷﻮد، ﻫﻤﺒﺴﺘﮕﯽ ﺑـﺴﯿﺎر ﺧـﻮﺑﯽ‬ ‫ﻣﺎﺑﯿﻦ داده ﻫﺎي آزﻣﺎﯾﺸﯽ و ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه وﺟﻮد دارد.‬
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‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬ ‫ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه ﺑﺮ ﻣﺒﻨﺎي ورودي ﻫﺎي ﻣﻨـﺪرج در‬

‫ﺟﺪول 3 اراﯾﻪ ﺷﺪه اﺳﺖ. ﺷﮑﻞ ﻫﺎي 5 و 6 ﻣﻘﺎﯾﺴﻪ ﻧﺘﺎﯾﺞ‬ ‫ﺗﻐﯿﯿﺮات دﻣﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣـﺪل ﺗﻮﺳـﻌﻪ داده‬ ‫ﺷﺪه و ﻣﻘﺎدﯾﺮ دﻣﺎي اﻧﺪازه ﮔﯿﺮي ﺷﺪه در ﺳﻄﺢ و ﻣﺮﮐـﺰ‬ ‫ﭘﻨﯿ ـﺮ ﻃ ـﯽ ﺣ ـﺮارت دﻫ ـﯽ ﺗ ـﮏ ﺑﻌ ـﺪي در ‪ 40°C‬ﺑﻤ ـﺪت 3‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ ـ ـ‬ ‫ﺳﺎﻋﺖ را ﻧﺸﺎن ﻣﯽ دﻫـﺪ. ﻫﻤـﺎن ﻃـﻮر ﮐـﻪ ﻣـﺸﺎﻫﺪه ﻣـﯽ‬ ‫ﮔﺮدد اﻧﻄﺒﺎق ﺧـﻮﺑﯽ ﻣـﺎﺑﯿﻦ دﻣﺎﻫـﺎي ﭘـﯿﺶ ﺑﯿﻨـﯽ ﺷـﺪه و‬ ‫اﻧﺪازه ﮔﯿﺮي ﺷﺪه وﺟﻮد دارد. ﻫﻤﺎن ﻃﻮر ﮐﻪ ﻣﺸﺎﻫﺪه ﻣﯽ‬ ‫ﺷﻮد، دﻣﺎي ﺳﻄﺢ ﻧﻤﻮﻧﻪ ﺑﺪﻟﯿﻞ اﺛﺮ ﻫﻤﺮﻓﺘﯽ ﻫﻮا ﺳﺮﯾﻊ ﺗـﺮ‬ ‫از ﻣﺮﮐـﺰ ﻧﻤﻮﻧ ـﻪ اﻓ ـﺰاﯾﺶ ﯾﺎﻓﺘ ـﻪ اﺳ ـﺖ. ﺟ ـﺪول5 ﻣﻘﺎﯾ ـﺴﻪ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ﺿﺮﯾﺐ ﻫﻤﺒﺴﺘﮕﯽ و رﯾـﺸﻪ ﻣﯿـﺎﻧﮕﯿﻦ ﻣﺮﺑﻌـﺎت ﺧﻄـﺎ ﺑـﯿﻦ‬ ‫داده ﻫ ـﺎي ﺗﺠﺮﺑ ـﯽ و آزﻣﺎﯾ ـﺸﯽ ﺗﻮﺳ ـﻂ ﻣ ـﺪل ﻋ ـﺪدي را‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻧﺸﺎن ﻣﯽ دﻫﺪ.‬

‫ﺑ ـﺮاي ﺗﻌﯿ ـﯿﻦ ﻣ ـﻮﺛﺮﺗﺮﯾﻦ ﻣﺘﻐﯿ ـﺮ روي ﻣ ـﺪل از ﺷ ـﺎﺧﺺ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺣﺴﺎﺳﯿﺖ اﺳﺘﻔﺎده ﺷـﺪ ﮐـﻪ ﺑـﺎ ﺗﻐﯿﯿـﺮ 01 % در ﻫﺮﯾـﮏ از‬ ‫ﻣﺘﻐﯿﺮﻫــﺎ، )داﻧــﺴﯿﺘﻪ، ﮔﺮﻣــﺎي وﯾــﮋه، ﻫــﺪاﯾﺖ ﺣﺮارﺗــﯽ و‬ ‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ( و ﺑﺮرﺳـﯽ اﺛـﺮ آﻧﻬـﺎ در‬ ‫ﻣﻘﺎﯾﺴﻪ ﺑﺎﻫﻢ ﺑﺪﺳﺖ ﻣﯽ آﯾﺪ‬

‫ﺷﺎﺧﺺ ﺣﺴﺎﺳﯿﺖ ﻣﺪل‬

‫54‬
‫دﻣﺎ ) ﺳــﺎﻧﺘﯿﮕﺮاد (‬

‫ﻣﺮﮐﺰ - ﻣﺪل ﺗﺤﻠﯿﻠﯽ‬ ‫ﻣﺮﮐﺰ - ﻣﺪل ﻋﺪدي‬

‫ﺳﻄﺢ - ﻣﺪل ﺗﺤﻠﯿﻠﯽ‬ ‫ﺳﻄﺢ - ﻣﺪل ﻋﺪدي‬

‫04‬ ‫53‬ ‫03‬ ‫52‬ ‫02‬ ‫0‬ ‫0002‬ ‫0004‬ ‫0006‬
‫زﻣﺎن ) ﺛﺎﻧﯿـﻪ (‬

‫0008‬

‫00001‬

‫00021‬

‫ﺷﮑﻞ4 -ﻣﻘﺎﯾﺴﻪ ﺑﯿﻦ داده ﻫﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﺣﻞ ﺗﺤﻠﯿﻠﯽ ﺑﺎ ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ از ﻣﺪل ﻋﺪدي ﺗﻮﺳﻌﻪ داده ﺷﺪه‬

‫۵٢‬

‫‪Sensitivity Index‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫۶۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬

‫03‬ ‫52‬
‫ﺩﻣﺎ )ﺳﺎﻧﺘﻴﮕﺮﺍﺩ(‬

‫ﻣﺮﮐﺰ -ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه‬

‫ﻣﺮﮐﺰ - آزﻣﺎﯾﺸﯽ‬

‫02‬ ‫51‬ ‫01‬ ‫5‬ ‫0‬ ‫0‬ ‫0002‬ ‫0004‬
‫ﺯﻣﺎﻥ ) ﺛﺎﻧﻴﻪ(‬

‫0006‬

‫0008‬

‫ﺷﮑﻞ 5 - ﻣﻘﺎﯾﺴﻪ ﭘﺮوﻓﯿﻞ دﻣﺎي داده ﻫﺎي آزﻣﺎﯾﺸﯽ و داده ﻫﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣﺪل در ﻣﺮﮐﺰ ﻃﯽ ﺣﺮارت دﻫﯽ در 04‬ ‫درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد‬

‫ﺟﺪول 5 - ﻣﻘﺎﯾﺴﻪ ﺿﺮﯾﺐ ﻫﻤﺒﺴﺘﮕﯽ و رﯾﺸﻪ ﻣﯿﺎﻧﮕﯿﻦ ﻣﺮﺑﻌﺎت ﺧﻄﺎ ﺑﯿﻦ داده ﻫﺎي ﺗﺠﺮﺑﯽ و ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣﺪل ﻋﺪدي‬ ‫در ﺣﺎﻟﺖ ﯾﮏ ﺑﻌﺪي در دﻣﺎي 04 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد‬ ‫ﺿﺮﯾﺐ ﻫﻤﺒﺴﺘﮕﯽ‬ ‫6899/.‬ ‫999/0‬
‫ﺩﻣﺎﻱ ﭘﻴﺶ ﺑﻴﻨﻲ ﺷﺪﻩ - ﺳﻄﺢ‬ ‫ﺩﻣﺎﻱ ﺁﺯﻣﺎﻳﺸﻲ - ﺳﻄﺢ‬

‫رﯾﺸﻪ ﻣﯿﺎﻧﮕﯿﻦ ﻣﺮﺑﻌﺎت ﺧﻄﺎ‬ ‫316/0‬ ‫580/0‬

‫ﻣﺤﻞ ﻗﺮار ﮔﯿﺮي ﺗﺮﻣﻮﮐﻮﭘﻞ‬ ‫ﺳﻄﺢ‬ ‫ﻣﺮﮐﺰ‬

‫53‬ ‫03‬
‫ﺩﻣﺎ ) ﺳﺎ ﻧ ﺘﻴﮕﺮﺍﺩ(‬

‫52‬ ‫02‬ ‫51‬ ‫01‬ ‫5‬ ‫0‬ ‫0‬ ‫0001‬ ‫0002‬ ‫0003‬ ‫0004‬ ‫0005‬ ‫0006‬ ‫0007‬

‫ﺯﻣﺎﻥ ) ﺛﺎﻧﻴﻪ(‬

‫ﺷﮑﻞ 6 -ﻣﻘﺎﯾﺴﻪ ﭘﺮوﻓﯿﻞ داده ﻫﺎي آزﻣﺎﯾﺸﯽ و داده ﻫﺎي ﭘﯿﺶ ﺑﯿﻨﯽ ﺷﺪه ﺗﻮﺳﻂ ﻣﺪل در ﺳﻄﺢ ﻃﯽ ﺣﺮارت دﻫﯽ در 04 درﺟﻪ ﺳﺎﻧﺘﯿﮕﺮاد‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫ﺗﻐﯿﯿــﺮات دﻣــﺎ را در ﻧﻘــﺎط ﻣﺘﻔــﺎوت ﭘﻨﯿــﺮ ﻓﺮاﭘــﺎﻻﯾﺶ‬ ‫ﺷ ـﺪه ﻃ ـﯽ ﻣﺮاﺣ ـﻞ ﭘ ـﺲ از ﻧﻤ ـﮏ ﭘﺎﺷ ـﯽ ﺧ ـﺸﮏ، ﺗﻌﯿ ـﯿﻦ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ‬ ‫ﮐﺮد‬ ‫از اﯾ ـﻦ ﻣ ـﺪل ﻣ ـﯽ ﺗ ـﻮان ﺑ ـﺮاي ﺷ ـﻨﺎﺧﺖ ﺑﻬﺘ ـﺮ ﻣﮑﺎﻧﯿ ـﺴﻢ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ ـ‬ ‫اﻧﺘﻘـــﺎل ﺣـــﺮارت در داﺧـــﻞ ﭘﻨﯿـــﺮ و ﺗﺎﯾﯿـــﺪ ﻣﻘـــﺪﻣﺎﺗﯽ‬ ‫ﻣ ـﺪل ﻫ ـﺎي اﻧﺘﻘــﺎل ﺣ ـﺮارت دو ﺑﻌ ـﺪي و ﯾــﺎ ﺳ ـﻪ ﺑﻌــﺪي‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺳﻮد ﺑـﺮده و ﺗﻮﻟﯿـﺪ ﭘﻨﯿـﺮي ﺑـﺎ ﮐﯿﻔﯿـﺖ ﺑـﺎﻻ و ﯾﮑﻨﻮاﺧـﺖ،‬ ‫ﻧﻤﻮد.‬ ‫٧۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬ ‫ﺷـ ـﮑﻞ 7 اﺛـ ـﺮ ﺷـ ـﺎﺧﺺ ﺣـ ـﺴﺎﺳﯿﺖ را ﺑـ ـﺮ روي اﯾـ ـﻦ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻣﺘﻐﯿﺮ ﻫﺎ ﻧـﺸﺎن ﻣـﯽ دﻫـﺪ و ﻫﻤـﺎﻧﻄﻮر ﮐـﻪ ﻣـﺸﺎﻫﺪه ﻣـﯽ‬ ‫ﺷــﻮد دو ﻣﺘﻐﯿــﺮ داﻧــﺴﯿﺘﻪ و ﮔﺮﻣــﺎي وﯾــﮋه ﺑﯿــﺸﺘﺮﯾﻦ‬ ‫ﺗﺎﺛﯿﺮ را ﺑﺮ روي ﻣـﺪل ﻣـﯽ ﮔﺬارﻧـﺪ. ﻧﮑﺘـﻪ دﯾﮕـﺮي ﮐـﻪ از‬ ‫ﻧﻤــﻮدار ﻣﻌﻠــﻮم ﻣﯿــﺸﻮد ﺗــﺎﺛﯿﺮ اﯾــﻦ ﺷــﺎﺧﺺ ﻫــﺎ ﺑــﺮ‬ ‫ﺳـ ـﺮﻋﺖ اﻧﺘﻘـ ـﺎل ﺣـ ـﺮارت ﻣـ ـﯽ ﺑﺎﺷـ ـﺪ ﻫﻤـ ـﺎﻧﻄﻮر ﮐـ ـﻪ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻣـﯽ داﻧـﯿﻢ ﻧـﺴﺒﺖ ﻫ ـﺪاﯾﺖ ﺣﺮارﺗـﯽ ﺑـﻪ ﻇﺮﻓﯿـﺖ ﮔﺮﻣ ـﺎﯾﯽ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫)ﺣﺎﺻﻠﻀﺮب داﻧﺴﯿﺘﻪ در ﮔﺮﻣﺎي وﯾﮋه (‬ ‫ﺷـﻤﺎر ﻣـﯽ آﯾـﺪ و ﺿـﺮﯾﺐ ﻧﻔـﻮذ ﺣـﺮارت62 ﻧـﺎم دارد ﺑـﺎ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫وﯾــﮋه ﻣﻘــﺪار اﯾــﻦ ﺿــﺮﯾﺐ ﮐــﺎﻫﺶ ﯾﺎﻓﺘــﻪ و ﺳــﺮﻋﺖ‬ ‫ﺧﺎﺻــﯿﺖ ﻣﻬﻤــﯽ در ﺗﺠﺰﯾــﻪ و ﺗﺤﻠﯿــﻞ اﻧﺘﻘــﺎل ﮔﺮﻣــﺎ ﺑــﻪ‬

‫اﻓــﺰاﯾﺶ 01 درﺻــﺪي در ﻣﻘــﺎدﯾﺮ داﻧــﺴﯿﺘﻪ و ﮔﺮﻣــﺎي‬ ‫اﻧﺘﻘـﺎل ﺣـﺮارت ﮐـﺎﻫﺶ ﻣـﯽ ﯾﺎﺑـﺪ در ﺣﺎﻟﯿﮑـﻪ ﺑـﺎ اﻓـﺰاﯾﺶ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫01 درﺻـــﺪي در ﻣﻘـــﺪار ﻫـــﺪاﯾﺖ ﺣﺮارﺗـــﯽ ﺳـــﺮﻋﺖ‬ ‫اﻧﺘﻘـــﺎل ﺣـــﺮارت اﻓـــﺰاﯾﺶ ﻣـــﯽ ﺑﺎﺑـــﺪ از اﯾـــﻦ رو در‬ ‫ﻧﻤﻮدارﻫﺎي ﻓـﻮق ﻣﺤـﻞ ﻗـﺮار ﮔﯿـﺮي ﺧﻄـﻮط ﻧﻘﻄـﻪ ﭼـﯿﻦ‬ ‫و ﺧـــﻂ ﭼـــﯿﻦ ﻧـــﺴﺒﺖ ﺑـــﻪ ﺧـــﻂ ﺗـــﻮﭘﺮ در ﻣـــﻮرد‬ ‫ﺧﺼﻮﺻﯿﺎت ﺗﺮﻣﻮﻓﯿﺰﯾﮑﯽ ﻣﺨﺘﻠﻒ ﻓﺮق ﻣﯽ ﮐﻨﺪ.‬ ‫3- ﻧﺘﯿﺠﻪ ﮔﯿﺮي‬ ‫ﯾـﮏ ﻣ ـﺪل رﯾﺎﺿـﯽ ﺑ ـﺮاي ﺗﻮﺻ ـﯿﻒ اﻧﺘﻘـﺎل ﺣ ـﺮارت ﺗ ـﮏ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ ـ‬ ‫ﺑﻌــﺪي ﻃــﯽ ﮔﺮﻣﺨﺎﻧــﻪ ﮔــﺬاري و ﺳــﺮدﺧﺎﻧﻪ ﮔــﺬاري‬ ‫ـ‬ ‫ـ‬ ‫ﻧﻤﻮﻧــﻪ ﻫــﺎي ﭘﻨﯿــﺮ ﺑﻌــﺪ از ﻧﻤــﮏ ﭘﺎﺷــﯽ ﺧــﺸﮏ، ﺑــﺎ‬ ‫اﺳـــﺘﻔﺎده از ﺣـــﻞ ﻋـــﺪدي ﻗـــﺎﻧﻮن دوم ﻓﻮرﯾـــﻪ )روش‬ ‫ﺗﻔﺎﺿــﻞ ﻣﺤــﺪود ( ﺑــﺮروي ﻧــﺮم اﻓــﺰار ‪MATLAB‬‬ ‫ﺗﻮﺳـﻌﻪ داده ﺷـﺪ. ﺑـﺮاي ﺗﺎﯾﯿـﺪ ﻣـﺪل ﺗﻮﺳـﻌﻪ داده ﺷـﺪه،‬ ‫ﻧﺘــﺎﯾﺞ ﭘــﯿﺶ ﺑﯿﻨــﯽ ﺷــﺪه ﺗﻮﺳــﻂ ﻣــﺪل ﺑــﺎ داده ﻫــﺎي‬ ‫ﺗﺠﺮﺑــﯽ )ﭘﺮوﻓﯿــﻞ ﻫــﺎي دﻣــﺎ در ﺣــﯿﻦ اﻧﺒــﺎر ﮔــﺬاري(‬ ‫ﻣــﻮرد ﻣﻘﺎﯾــﺴﻪ ﻗــﺮار ﮔﺮﻓــﺖ. ﻫﻤﺒــﺴﺘﮕﯽ ﺧــﻮب ﻣــﺎﺑﯿﻦ‬ ‫ﭘﺮﻓﯿﻠﻬــﺎي دﻣــﺎي ﭘــﯿﺶ ﺑﯿﻨــﯽ ﺷــﺪه و اﻧــﺪازه ﮔﯿــﺮي‬ ‫ﺷﺪه، ﻧـﺸﺎن داد ﮐـﻪ ﻣـﺪل ﺗﻮﺳـﻌﻪ داده ﺷـﺪه ﻣـﯽ ﺗﻮاﻧـﺪ‬ ‫ﺑﻪ ﺧـﻮﺑﯽ ﺗﻐﯿﯿـﺮات دﻣـﺎ در ﻫـﺮ ﻧﻘﻄـﻪ در داﺧـﻞ ﭘﻨﯿـﺮ را‬ ‫ﭘـﯿﺶ ﺑﯿﻨـﯽ ﻧﻤﺎﯾـﺪ. ﺑـﺎ ﮐـﺎر ﺑـﺮد ﻣـﺪل ﻣـﺬﮐﻮر ﻣـﯽ ﺗـﻮان‬ ‫ـ‬ ‫ـ‬ ‫ـ‬
‫۶٢‬

‫‪Thermal Diffusivity‬‬

‫‪www.SID.ir‬‬

‫‪Archive of SID‬‬ ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل 9831‬ ‫٨۵ دﻟﻮي و ﻫﻤﺪﻣﯽ‬

‫03‬ ‫دﻣﺎ - ﺳﺎﻧﺘﯿﮕﺮاد‬ ‫دﻣﺎ - ﺳﺎﻧﺘﯿﮕﺮاد‬ ‫داﻧﺴﯿﺘﻪ‬ ‫0‬ ‫0005‬ ‫زﻣﺎن - ﺛﺎﻧﯿﻪ‬ ‫00001‬ ‫02‬ ‫01‬ ‫0‬ ‫03‬ ‫دﻣﺎ - ﺳﺎﻧﺘﯿﮕﺮاد‬ ‫02‬ ‫01‬ ‫0‬ ‫ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ‬ ‫0‬ ‫0005‬ ‫زﻣﺎن - ﺛﺎﻧﯿﻪ‬ ‫00001‬ ‫دﻣﺎ - ﺳﺎﻧﺘﯿﮕﺮاد‬

‫03‬ ‫02‬ ‫01‬ ‫0‬ ‫03‬ ‫02‬ ‫01‬ ‫0‬ ‫ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ‬ ‫0‬ ‫0005‬ ‫زﻣﺎن - ﺛﺎﻧﯿﻪ‬ ‫00001‬ ‫ﮔﺮﻣﺎي وﯾﮋه‬ ‫0‬ ‫0005‬ ‫زﻣﺎن - ﺛﺎﻧﯿﻪ‬ ‫00001‬

‫ﺷﮑﻞ 7 - اﺛﺮ ﺷﺎﺧﺺ ﺣﺴﺎﺳﯿﺖ ﺑﺮ روي ﻣﺘﻐﯿﺮﻫﺎي ﻣﺨﺘﻠﻒ ﻣﺪل ) ﺧﻄﻮط ﺗﻮﭘﺮ، ﺧﻂ ﭼﯿﻦ و ﻧﻘﻄﻪ ﭼﯿﻦ ﺑﻪ ﺗﺮﺗﯿﺐ ﻣﻘﺪار ﻣﺘﻐﯿﺮ و‬ ‫ﻣﻘﺪار ﻣﺘﻐﯿﺮ01 % + در ﻣﺮﮐﺰ ﺟﺴﻢ ﻣﯽ ﺑﺎﺷﻨﺪ(.‬

‫‪ : M‬ﺟﺮم ﻣﻠﮑﻮﻟﯽ، ﺟﺮم )ﮐﯿﻠﻮﮔﺮم(‬ ‫‪ : n‬ﮔﺎم زﻣﺎﻧﯽ ) ﺛﺎﻧﯿﻪ (‬ ‫‪ : P‬ﻓﺸﺎر ) ﭘﺎﺳﮑﺎل(‬ ‫‪ : R‬ﺛﺎﺑﺖ ﮔﺎزﻫﺎ 5138 )ژول ﺑﺮ ﮐﯿﻠﻮﮔﺮم ﻣﻮل ﮐﻠﻮﯾﻦ(‬ ‫‪ : S‬ﺳﻄﺢ )ﻣﺘﺮ ﻣﺮﺑﻊ(‬ ‫‪ : t‬زﻣﺎن )ﺛﺎﻧﯿﻪ(‬ ‫‪ : T‬دﻣﺎ در ﻫﺮ ﻟﺤﻈﻪ ) ﺳﺎﻧﺘﯿﮕﺮاد- ﮐﻠﻮﯾﻦ (‬ ‫‪ : vBiB‬ﮐﺴﺮ ﺣﺠﻤﯽ اﺟﺰاي ﺷﯿﻤﯿﺎﯾﯽ ﭘﻨﯿﺮ‬ ‫‪ : V‬ﺣﺠﻢ )ﺳﺎﻧﺘﯿﻤﺘﺮ ﻣﮑﻌﺐ(‬ ‫‪ : W‬ﺟﺮم )ﮔﺮم(‬ ‫‪ : xBiB‬ﮐﺴﺮ ﺟﺮﻣﯽ اﺟﺰاي ﺷﯿﻤﯿﺎﯾﯽ ﭘﻨﯿﺮ‬ ‫ﺣﺮوف ﯾﻮﻧﺎﻧﯽ :‬ ‫‪ : x‬ﻣﺨﺘﺼﺎت ﮐﺎرﺗﺰﯾﻦ ) ﻣﺘﺮ(‬

‫4- ﻋﻼﺋﻢ واﺧﺘﺼﺎرات‬ ‫‪ :Cp‬ﮔﺮﻣﺎي وﯾﮋه) ژول /ﮐﯿﻠﻮﮔﺮم ﮐﻠﻮﯾﻦ(‬ ‫‪ :Dm‬ﺿﺮﯾﺐ دﯾﻔﻮزﯾﻮن‬ ‫‪ : h‬ﻣﯿﺎﻧﮕﯿﻦ ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ )وات / ﻣﺘﺮ‬ ‫‪ : i‬ﺷﻤﺎره ﮔﺮه در ﺟﻬﺖ ‪x‬‬ ‫ﻣﺮﺑﻊ ﮐﻠﻮﯾﻦ(‬

‫‪ : k‬ﺿﺮﯾﺐ ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ )وات / ﻣﺘﺮ ﮐﻠﻮﯾﻦ (‬ ‫‪ : kBiB‬ﺿﺮﯾﺐ ﻫﺪاﯾﺖ ﺣﺮارﺗﯽ اﺟﺰاي ﭘﻨﯿﺮ )وات / ﻣﺘﺮ‬ ‫ﮐﻠﻮﯾﻦ (‬ ‫‪ : km‬ﻣﯿﺎﻧﮕﯿﻦ ﺿﺮﯾﺐ اﻧﺘﻘﺎل ﺟﺮم در ﺳﻄﺢ )ﻣﺘﺮ ﺑﺮ ﺛﺎﻧﯿﻪ(‬ ‫‪ : L‬ﻃﻮل ) ﻣﺘﺮ(‬ ‫‪ : m‬ﺷﯿﺐ ﺧﻂ رﮔﺮﺳﯿﻮن ﺑﺮاي اﻧﺪازه ﮔﯿﺮي ﺿﺮﯾﺐ‬
‫اﻧﺘﻘﺎل ﺣﺮارت در ﺳﻄﺢ )ﺛﺎﻧﯿﻪ(، ﮐﺴﺮ وزﻧﯽ ﻫﺮ ﯾﮏ از‬ ‫اﺟﺰاي ﺷﯿﻤﯿﺎﯾﯽ‬

‫‪ : ρ‬داﻧﺴﯿﺘﻪ )ﮐﯿﻠﻮﮔﺮم / ﻣﺘﺮ ﻣﮑﻌﺐ (‬

‫‪www.SID.ir‬‬

Archive of SID ۵٩ ‫ : ﮐﺮﺑﻮﻫﯿﺪرات‬c ‫ : اوﻟﯿﻪ‬i ‫ : ﺳﯿﺎل، ﭼﺮﺑﯽ‬f ‫ : ﭘﯿﮑﻨﻮﻣﺘﺮ، ﭘﺮوﺗﺌﯿﻦ‬p ‫ : ﺳﻄﺢ‬S ‫ : ﻫﻮا‬air ‫ : آﻟﻮﻣﯿﻨﯿﻮم‬al ‫ : آب‬water ‫ﻣﺪل ﺳﺎزي ﻋﺪدي اﻧﺘﻘﺎل ﺣﺮارت در ﭘﻨﯿﺮ ﺳﻔﯿﺪ ﻓﺮاﭘﺎﻻﯾﺶ ﺷﺪه‬ ( ‫ : داﻧﺴﯿﺘﻪ اﺟﺰاء )ﮐﯿﻠﻮﮔﺮم / ﻣﺘﺮ ﻣﮑﻌﺐ‬ρBiB

‫: دﻣﺎي ﺑﺪون ﺑﻌﺪ‬θ

(‫ : وﯾﺴﮑﻮزﯾﺘﻪ )ﭘﺎﺳﮑﺎل ﺛﺎﻧﯿﻪ‬µ ‫ : ﻣﻘﺎدﯾﺮ وﯾﮋه ﻣﻌﺎدﻟﻪ ﺑﺮاي دﯾﻮار ﺗﺨﺖ‬ζn ‫ : ﻋﺪد ﺑﯿﻮت‬Bi ‫ : ﻋﺪد ﻓﻮرﯾﻪ‬Fo ‫: ﻋﺪد ﻧﺎﺳﻠﺖ‬Nu ‫ : ﻋﺪد ﭘﺮاﻧﺘﻞ‬Pr ‫: ﻋﺪد رﯾﻨﻮﻟﺪز‬Re ‫ : ﻋﺪد اﺷﻤﯿﺖ‬Sc ‫زﯾﺮﻧﻮﯾﺲ ﻫﺎ‬ ‫ : ﺧﺎﮐﺴﺘﺮ‬a

‫ : رﻃﻮﺑﺖ‬m

‫ : اﺗﻤﺴﻔﺮ‬atm ‫∞: ﻣﺤﯿﻂ‬

: ‫5- ﻣﻨﺎﺑﻊ ﻣﻮرد اﺳﺘﻔﺎده‬ -(‫اﺳﺘﺎﻧﺪارد ﻣﻠﯽ اﯾﺮان 0802، 2831. ﺷﯿﺮ و ﻓﺮآورده ﻫﺎي آن - اﻧﺪازه ﮔﯿﺮي ﻣﻘﺪار ﻣﺎده ﺧﺸﮏ -ﭘﻨﯿﺮ ﺳﺮم- )روش ﻣﺮﺟـﻊ‬ .‫روش آزﻣﻮن، ﻣﻮﺳﺴﻪ اﺳﺘﺎﻧﺪارد و ﺗﺤﻘﯿﻘﺎت ﺻﻨﻌﺘﯽ اﯾﺮان‬ .159-193 ‫ﺣﺴﯿﻨﯽ، ز.، 9631. روﺷﻬﺎي ﻣﺘﺪاول در ﺗﺠﺰﯾﻪ ﻣﻮاد ﻏﺬاﯾﯽ. اﻧﺘﺸﺎرات داﻧﺸﮕﺎه ﺷﯿﺮاز. ﺻﻔﺤﻪي‬ Abd El-Salam, M. H., Alichanidis, E., & Zerfiridis, G. K. (1999). Domiati and Feta type cheeses. In P. F. Fox (Ed.). Cheese: chemistry, physics and microbiology (Vol. 2, pp. 301–335). Aspen Publ. Bennachio, D. (1994). D´etermination de la chaleur de fermentation del Emmental au cours de laffinage. RALIMENT, France, private communication. Carson, J. K., Willix, J., North, M. F. (2006). "Measurements of heat transfer coefficients within convection ovens. J Food Engineering, 72, 293-301. El Soda, M., & Abd El-Salam, M. H. (2002). Cheese matured in brine. In H. Roginski, et al. (Eds.). Encyclopedia of dairy science (Vol. 1, pp. 406–410). Guinee, T. P., Fox, P. F. (1983). "Sodium chloride and moisture chenges in Ramano-type cheese during salting." J Dairy Res, 50, 511-518. Hamdami, N., J. Monteau and A. Bail. 2003. Effective thermal conductivity of a high porosity model food at above and sub-freezing temperatures. Inte. J Refrigeration. 26: 809-816. Hamdami, N., Monteau, J.Y. & Le Bail, A. (2004). Transport properties of a high porosity model food at above and sub-freezing temperatures.part 1: thermophysical properties and water activity. J Food Engineering. 62, 373-383. Incropera, F. P., De Witt, D. P. (1996). Introduction to Heat Transfer, John Wiley & Sons, Inc., New York. Irudayaraj, J., 2002, Food Processing Operation Modeling. New York: Marcel Dekker, Inc. Kondjoyan, A., Daudin, J. D., Bimbenet, J. J. (1993). "Heat and mass transfer coefficients at the surface of elliptical cylinders placed in a turbulent air flow. J Food Engineering, 20, 339-367. www.SID.ir

Archive of SID 1389 ‫ﺟﻠﻪ ﭘﮋوﻫﺶﻫﺎي ﺻﻨﺎﯾﻊ ﻏﺬاﯾﯽ/ ﺟﻠﺪ 3/02 ﺷﻤﺎره 2/ ﺳﺎل‬ ‫٠۶ دﻟﻮي و ﻫﻤﺪﻣﯽ‬

Luna, J. A., Bressan, J. A. (1987). "Mass trasfer during ripening of Cuartiolo Argentino cheese. J Food Sci, 52(2), 308-311. Mohsenin, N. N. 1980. Thermal properties of foods and agricultural materials, CRC press, New York. Nicolaï, B. M., Verboven, P., Scheerlinck, N. (2001). "The modelling of heat and mass transfer." Food process modelling, L. M. M. Tijskens, Hertog, M. L. A. T. M., Nicoli, B. M., (Eds.), CRC Press, Boca Rayton. Özisik, M. N. (1985). Heat transfer - A basic approach, McGraw-Hill., Singapore. Özisik, M. N. (1994). Finite difference methods in heat transfer, CRC press, London. Pajonk, A. S., Saurel, R., Andrieu, J., Laurent, P., Blanc, D. (2003). "Heat transfer study and modeling during Emmental ripening. J Food Engineering, 57, 249-255. Rahman, M. S. 1995. Food properties handbook, CRC Press, Boca Raton Turhan, M. (1996). "Modelling of salt transfer in white cheese during short initial brining." Netherlands Milk and Dairy J, 50, 541-550. Zorrilla, S. E., Robialo, A. C. (1994). "Fynbo cheese NaCl and KCl changes during ripening." J Food Sci, 59(5), 972-975. Zorrilla, S. E., and Rubiolo, A. C. (1994). "Modeling Nacl and Kcl Movement in Fynbo Cheese During Salting. J Food Sci, 59(5), 976-980.

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