ﻣﺠﻠﻪ ﻋﻠﻮم و ﺻﻨﺎ ﻊﯾ ﻏﺬا ﯾﯽ ﯾا ﺮان

(1)

زا هدﺎﻔﺘﺳا ﺎﺑ دﺎﻤﺠﻧا ﺪﻨﯾآﺮﻓ ﯽﻃ رد ﺮﮔﺮﺒﻤﻫ يﺎﻣد تاﺮﯿﯿﻐﺗ ﯽﻨﯿﺑ ﺶﯿﭘ و ﻪﺴﯾﺎﻘﻣ ﻠﺘﺨﻣ شور ود

ﻒ

زﺎﺳ لﺪﻣ ي

دﺪﻋ ي

ﻮﻟد ﻦﺴﺤﻣ ي

نﺎﻬﻔﺻا ،1

ﯽﺋاراد ﺮﯿﻣا ﻧﺎﺧ ﻪﻣﺮﮔ

2ﯽ 

1 - دﺎﺘﺳا ﯾ ﺎﻨﺻ و مﻮﻠﻋ هوﺮﮔ رﺎ ﯾ

اﺬﻏ ﻊ ﯽﯾ زروﺎﺸﮐ هﺪﮑﺸﻧاد ، ي

ا ،مﺮﻬﺟ ،مﺮﻬﺟ هﺎﮕﺸﻧاد ، ﯾ

ناﺮ .

2 - ﯽﺳﺪﻨﻬﻣ هوﺮﮔ ،رﺎﯾدﺎﺘﺳا ﺎﻨﯿﺳ ﯽﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،نﺎﮐﺮﺴﯾﻮﺗ ﯽﻌﯿﺒﻃ ﻊﺑﺎﻨﻣ و ﯽﻨﻓ هﺪﮑﺸﻧاد ،ﯽﯾاﺬﻏ ﻊﯾﺎﻨﺻ و مﻮﻠﻋ

ناﺮﯾا ،ناﺪﻤﻫ ، .

تﺎﻋﻼﻃا ﻪﻟﺎﻘﻣ

ﮑﭼ

ﯿ هﺪ

رﺎﺗ ﯾ ﺦ ﺎﻫ ي ﻪﻟﺎﻘﻣ :

رﺎﺗ ﯾ ﺦ رد ﯾ ﺖﻓﺎ : 18 / 07 / 99

رﺎﺗ ﯾ ﺦ ﺬﭘ ﯾ شﺮ : 09 / 12 / 99

تﺎﻤﻠﮐ ﻠﮐ ﯿ ﺪ ي :

،دوﺪﺤﻣ ءاﺰﺟا

،تراﺮﺣ لﺎﻘﺘﻧا

،دﺎﻤﺠﻧا وﺪﺤﻣ ﻞﺿﺎﻔﺗ

،د

ﺮﮔﺮﺒﻤﻫ . DOI: 10.29252/fsct.18.06.28

لﻮﺌﺴﻣ

تﺎﺒﺗﺎﮑﻣ : [email protected]

فﺮﺼﻣ ﺮﭘ زا ﯽﮑﯾ ﺮﮔﺮﺒﻤﻫ ﺖﺳا نﺎﻬﺟ ﺮﺳاﺮﺳ رد ﯽﺘﺷﻮﮔ تﻻﻮﺼﺤﻣ ﻦﯾﺮﺗ

. لﻮﺼﺤﻣ ﻦﯾا يرﺎﮔﺪﻧﺎﻣ

زا ًﻻﻮﻤﻌﻣ ﻦﯾاﺮﺑﺎﻨﺑ و ﺖﺳا هﺎﺗﻮﮐ ًﺎﺘﺒﺴﻧ ﺪﻨﯾاﺮﻓ

ا ﺮﯿﺜﮑﺗ زا يﺮﯿﮔﻮﻠﺟ و ﯽﺑآ ﺖﯿﻟﺎﻌﻓ ﺶﻫﺎﮐ ياﺮﺑ دﺎﻤﺠﻧ

ﯽﻣ هدﺎﻔﺘﺳا ﻢﺴﯿﻧﺎﮔراوﺮﮑﯿﻣ دﻮﺷ

. شور ﯽﺣاﺮﻃ رد دﺎﻤﺠﻧا مﺎﮕﻨﻫ رد ﺎﻣد ﻖﯿﻗد ﯽﻨﯿﺑ ﺶﯿﭘ ﺶﯾﺎﻣﺮﺳ يﺎﻫ

،

ﯽﻣ ﻢﻬﻣ لﻮﺼﺤﻣ ﺖﯿﻔﯿﮐ ﺖﻓا زا يﺮﯿﮔﻮﻠﺟ و يزﺎﺳ ﻪﻨﯿﻬﺑ ﺪﺷﺎﺑ

. لﺪﻣ زا دﺎﻤﺠﻧا نﺎﻣز ﯽﻨﯿﺑ ﺶﯿﭘ يﺎﻫ

هدﺎﺳ ًﺎﺘﺒﺴﻧ ﯽﻠﯿﻠﺤﺗ تﻻدﺎﻌﻣ )

ﺮﺑ ﯽﻨﺘﺒﻣ تﺎﺿوﺮﻔﻣ يداﺪﻌﺗ (

شور ﺎﺗ ﻪﺘﻓﺮﮔ ﯽﻋﻮﻨﺘﻣ يدﺪﻋ ﻞﺣ يﺎﻫ

ﺖﺳا ﺮﯿﻐﺘﻣ ،ﺪﻧراد زﺎﯿﻧ هﺪﯿﭽﯿﭘ ﺮﺗﻮﯿﭙﻣﺎﮐ و يدﺎﯾز تﺎﺒﺳﺎﺤﻣ نﺎﻣز ﻪﺑ ﻪﮐ .

ﺖﺴﺨﻧ ،ﻖﯿﻘﺤﺗ ﻦﯾا رد

لﺪﻣ ﺎﺑ هﮋﯾو يﺎﻣﺮﮔ و ﯽﺗراﺮﺣ ﺖﯾاﺪﻫ ،ﺦﯾ ﺮﺴﮐ ﻪﻠﻤﺟ زا ،ﺮﮔﺮﺒﻤﻫ ﯽﺗراﺮﺣ تﺎﯿﺻﻮﺼﺧ ﯽﺿﺎﯾر يﺎﻫ

ﺑ ﺮﮔﺮﺒﻤﻫ دﺎﻤﺠﻧا ﺪﻨﯾاﺮﻓ ﺲﭙﺳ و ﺪﻧﺪﺷ ﻦﯿﯿﻌﺗ ﻒﻠﺘﺨﻣ يدﺪﻋ شور ود ﺎ

) ءاﺰﺟا و دوﺪﺤﻣ ﻞﺿﺎﻔﺗ

دوﺪﺤﻣ ( ﺪﺷ ﯽﺳرﺮﺑ .

هداد ﺎﺑ ﻞﺻﺎﺣ ﺞﯾﺎﺘﻧ لﺪﻣ ود ﺮﻫ ﻪﭼﺮﮔا ﻪﮐ ﺪﯾدﺮﮔ ﺺﺨﺸﻣ و ﻪﺴﯾﺎﻘﻣ ﯽﺑﺮﺠﺗ يﺎﻫ

ﯽﻣ ءاﺰﺟا لﺪﻣ ﺎﻣا ،ﺪﻨﻨﮐ ﯽﻨﯿﺑ ﺶﯿﭘ دﺎﻤﺠﻧا مﺎﮕﻨﻫ ار ﺮﮔﺮﺒﻤﻫ تراﺮﺣ ﻪﺟرد ﯽﻘﻄﻨﻣ رﻮﻃ ﻪﺑ ﺪﻨﻧاﻮﺗ

ﺖﺒﺴﻧ ﺎﻣد ﯽﻨﯿﺑ ﺶﯿﭘ رد يﺮﺘﺸﯿﺑ ﯽﯾﺎﻧاﻮﺗ زا دوﺪﺤﻣ ﺖﺳا رادرﻮﺧﺮﺑ دوﺪﺤﻣ ﻞﺿﺎﻔﺗ لﺪﻣ ﻪﺑ

. ﻦﯾا

ﻪﺘﺴﺑ زا هدﺎﻔﺘﺳا ﻪﮐ داد نﺎﺸﻧ ﻪﻌﻟﺎﻄﻣ يﺎﻫ

راﺰﻓا مﺮﻧ ﺪﻨﻧﺎﻣ CFD COMSOL

ﯽﻣ ناﻮﻨﻋ ﻪﺑ ﺪﻧاﻮﺗ

هدروآﺮﻓ دﺎﻤﺠﻧا نﺎﻣز ﻦﯿﻤﺨﺗ ياﺮﺑ ﯽﺒﺳﺎﻨﻣ ﻪﻨﯾﺰﮔ دﻮﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد ﯽﺘﺷﻮﮔ يﺎﻫ

.

ﻪﻠﺠﻣ مﻮﻠﻋ و ﺎﻨﺻ ﯾ ﻊ اﺬﻏ ﯽﯾ اﯾ ناﺮ

www.fsct.modares.ac.ir :ﻪﻠﺠﻣﺖﯾﺎﺳ

ﻪﻟﺎﻘﻣ ﻤﻠﻋ ﯽ ﺸﻫوﮋﭘ_ ﯽ

[ Downloaded from fsct.modares.ac.ir on 2023-10-11 ]

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1 - ﻪﻣﺪﻘﻣ

ﻮﮕﻟا ي فﺮﺼﻣ ﯽﯾاﺬﻏ داﻮﻣ ﺴﺑ

ﯿ رﺎ ي زا مدﺮﻣ نﺎﻬﺟ رد لﺎﺳ يﺎﻫ

ﺧا ﯿﺮ ﺎﺑ ﻪﺟﻮﺗ ﻪﺑ ﺪﻧور ﻐﺗ ﯿﯿ تاﺮ ﺷ ﯿ هﻮ ﮔﺪﻧز ﯽ و دﻮﺒﻤﮐ نﺎﻣز اﺮﺑ ي

ﻬﺗ ﯿﻪ ﺎﻫاﺬﻏ ي ﺘﻨﺳ ﯽ ﻪﺑ رﺪﺗ ﯾ ﺞ ﻐﺗ ﯿﯿ ﺮ هدﺮﮐ ﺖﺳا و ﺎﻤﺗ ﯾ ﻞ ﻪﺑ فﺮﺼﻣ

ﺎﻫاﺬﻏ ي ﻧ ﺪﻤﺠﻨﻣ ﯿ ﻪﻤ آ هدﺎﻣ ﯾ هدﺎﻣآ ﺎ ﺑﯿ ﺮﺘﺸ هﺪﺷ ﺖﺳا . ﺮﮔﺮﺒﻤﻫ زا

ﻪﻠﻤﺟ اﯾ ﻦ ﻪﮐ ﺖﺴﻫ ﺎﻫاﺬﻏ ﻪﺑ

ﻟد ﯿ ﻞ ﺖﻟﻮﻬﺳ ﺖﺨﭘ و

،فﺮﺼﻣ ﻢﻌﻃ

،بﻮﻠﻄﻣ ﻪﺘﺴﺑ يﺪﻨﺑ يﺎﻫ باﺬﺟ و

،عﻮﻨﺘﻣ ﻞﻣﺎﮐ ندﻮﺑ زا ﻈﻧ ﺮ داﻮﻣ

ﺬﻐﻣ ي و ﻢﻟﺎﺳ و ﺘﺷاﺪﻬﺑ ﯽ ندﻮﺑ رد ﻫرﻮﺸﮐ ﺎ ي نﺎﻬﺟ ﻪﺑ وﯾ هﮋ

ﺎﻫرﻮﺸﮐ ي ﺘﻌﻨﺻ ﯽ ﺎﺟ زا ﯾ هﺎﮕ هﮋﯾو يا رادرﻮﺧﺮﺑ ﺖﺳا هﺪﺷ

. ﺮﺑ

رﺎﻣآ سﺎﺳا ﺮﻣآ ﺮﻫ لﺎﺳ رد ﻂﺳﻮﺘﻣ رﻮﻃ ﻪﺑ ،

ﯾ ﺎﮑ ﯽﯾ 15 ﮐ ﯿ مﺮﮔﻮﻠ

فﺮﺼﻣ ﺮﮔﺮﺒﻤﻫ ﯽﻣ

ﺪﻨﮐ . ا رد ﯾ ﻪﻧاﺮﺳ فﺮﺼﻣ ﻪﭼ ﺮﮔا ،ناﺮ

هدروآﺮﻓ يﺎﻫ ﺴﺑ ﯽﺘﺷﻮﮔ ﯿ

ﺎﻫرﻮﺸﮐ زا ﺮﺘﻤﮐ رﺎ ي

ﻪﻌﺳﻮﺗ ﯾ ﺖﺳا ﻪﺘﻓﺎ

) 5/

1 ﮐ ﯿ ازا ﻪﺑ مﺮﮔﻮﻠ ي

ﺮﻔﻧ ﺮﻫ (،

ﻟد ﻪﺑ ﺎﻣا ﯿ ﻌﻤﺟ ندﻮﺑ ناﻮﺟ ﻞ ﯿ

،ﺖ

اﺰﻓا ﯾ ﻨﭽﻤﻫ و نﺎﻧز لﺎﻐﺘﺷا ﺶ ﯿ

ﮔدﺎﺳ و ﺖﻋﺮﺳ ﻦ ﯽ

ﻬﺗ ﯿ ا ﻪ ﯾ ﻦ

ا ،هدرواﺮﻓ ﯾ ﺑﻮﺧ ﻪﺑ لﻮﺼﺤﻣ ﻦ ﯽ

ﺎﺟ ي هﺮﻔﺳ رد ار شدﻮﺧ ﯽﻧاﺮﯾا

ﺎﻫ

ﭘ و ﺖﺳا هدﺮﮐ زﺎﺑ ﯿ

ﺶ ﯽﻨﯿﺑ ﺎﻫ ﮐﺎﺣ ﯽ اﺰﻓا زا ﯾ ا ﻢﻬﺳ ﺶ ﯾ لﻮﺼﺤﻣ ﻦ

داﻮﻣ ﺪﺒﺳ رد اﺬﻏ

ﯽﯾ ا ﯾ ﻧاﺮ ﯿ آ رد نﺎ ﯾ هﺪﻨ ﯽﻣ ﺪﺷﺎﺑ 1] .[ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ

ﺎﻣز رﺎﮔﺪﻧﺎﻣ ن ي ﺣاﺮﻃ ،لﻮﺼﺤﻣ ﻢﮐ ﯽ

ﯾ ﺳ ﮏ ﯿ ﺪﻣآرﺎﮐ دﺎﻤﺠﻧا ﻢﺘﺴ

ﺶﻫﺎﮐ ﺚﻋﺎﺑ ﺎﻬﻨﺗ ﻪﻧ ﻪﻨﯾﺰﻫ

يﺎﻫ اﺮﻓ ﯾ ﻮﺟ ﻪﻓﺮﺻ و ﺪﻨ ﯽﯾ

فﺮﺼﻣ رد

ژﺮﻧا ي ﯽﻣ دﻮﺷ

، ﻪﮑﻠﺑ ﯽﻣ ﺪﻧاﻮﺗ ﮐ دﻮﺒﻬﺑ رد ﯿﻔ

ﯿ ﻧ لﻮﺼﺤﻣ ﺖ ﯿ

ﺶﻘﻧ ﺰ

ﺮﺛﻮﻣ ي ﺪﺷﺎﺑ ﻪﺘﺷاد .

اﺮﺑﺎﻨﺑ ﯾ ﭘ ،ﻦ ﯿ ﺑ ﺶ ﯿﻨ ﯽ ﻗد ﯿ اﺬﻏ دﺎﻤﺠﻧا نﺎﻣز ﻖ

اﺮﺑ ي ﺖﺳد ﯽﺑﺎﯾ ﺣاﺮﻃ ﻪﺑ ﯽ ﺳ ﺐﺳﺎﻨﻣ ﯿ

ﺗ ﻢﺘﺴ ﺮﺒ ﯾ روﺮﺿ ﺪ ي ﺖﺳا .

دﺎﻤﺠﻧا شور زا هدﺎﻔﺘﺳا ﻪﭼ ﺮﮔا ﻪﺤﻔﺻ

1يا اﺮﺑ ي ا دﺎﻤﺠﻧا ﯾ ﻦ

لﻮﺼﺤﻣ ﺐﺳﺎﻨﻣ ﺮﺗ ﺮﻈﻧ ﻪﺑ ﯽﻣ ﺪﺳر ﻟو ، ﯽ ﺮﺜﮐا رد تﺎﺠﻧﺎﺧرﺎﮐ

اﯾ ناﺮ اﻮﻫ ﺎﺑ دﺎﻤﺠﻧا زا هدﺎﻔﺘﺳا ، ي

2دﺮﺳ لﻮﻤﻌﻣ ﺮﺗ ﺖﺳا . ﺖﻋﺮﺳ

ﻌﺗ و ﺎﻣﺮﮔ جوﺮﺧ ﯿﯿ

ﻓوﺮﭘ ﻦ ﯿ ﺎﻣد ﻞ ي اﺮﺑ لﻮﺼﺤﻣ ي

ﻌﺗ ﯿﯿ ﻣ ﻦ ﯿ ناﺰ

ژﺮﻧا فﺮﺼﻣ ي

ﻮﺼﺤﻣ نزو ﺖﻓا ، ﮐ و ل

ﯿﻔ ﯿ ﺎﻬﻧ ﺖ ﯽﯾ لﻮﺼﺤﻣ

ﻤﻫا هﺪﺷ ﺪﻤﺠﻨﻣ ﯿ

ﺖ ﻪﺘﺷاد ﭘ و ﯿ ﺶ ﺑﯿﻨ ﯽ ﻗد ﯿ داﻮﻣ دﺎﻤﺠﻧا نﺎﻣز ﻖ

اﺬﻏ ﯽﯾ اﺮﺑ ي زرا ﯾﺑﺎ ﯽ ﮐ ﯿﻔ ﯿ و ﺖ ﻪﺒﻨﺟ يﺎﻫ دﺎﺼﺘﻗا ي داﻮﻣ دﺎﻤﺠﻧا

اﺬﻏ ﯽﯾ ﻢﻬﻣ ﺮﻈﻧ ﻪﺑ ﯽﻣ ﺪﺳر 2] . [

اﺮﺑ ي ﻌﺗ ﯿﯿ ﻦ تﺪﻣ نﺎﻣز دﺎﻤﺠﻧا ود ﺮﻌﺗ ﯾ ﻒ ﺮﺑ سﺎﺳا ﻦﻤﺠﻧا

ﻦﯿﺑ ﯽﻠﻠﻤﻟا يزﺎﺳ ﺎﻣﺮﺳ رد

ﺖﺳد ﯽﻣ ﺪﺷﺎﺑ . ﺮﺑ ﺒﻃ ﻖ ﯾ ﮏ ﺮﻌﺗ ﯾ ﻒ

1. Plate freezer 2. Air blast freezer

تﺪﻣ دﺎﻤﺠﻧا زا ﻧﺎﻣز ﯽ ﻪﮐ ﻪﺟرد تراﺮﺣ ﺢﻄﺳ هدﺎﻣ اﺬﻏ ﯽﯾ ﻪﺑ ﻔﺻ ﺮ

ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ ﺳر ﯿ هﺪ ﺎﺗ ﺘﻗو ﯽ ﻪﮐ ﻪﺟرد تراﺮﺣ ﺰﮐﺮﻣ ﺗراﺮﺣ ﯽ

اﯾ ﻦ هدﺎﻣ ﻪﺑ 10 ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ ﺮﺘﻤﮐ زا ﺗراﺮﺣ ﻪﺟرد ﯽ

ﻪﮐ

لﺎﺘﺴﯾﺮﮐ يﺎﻫ ﻟوا ﯿﻪ ﯾ ﺦ رد اﯾ ﻦ ﺰﮐﺮﻣ ﮑﺸﺗ ﯿ ﻞ ﯽﻣ ﺪﻧﻮﺷ

، ﺪﺳﺮﺑ اﯾ ﻦ

نﺎﻣز مﻮﺳﻮﻣ ﻪﺑ تﺪﻣ نﺎﻣز ﻤﺳا دﺎﻤﺠﻧا

3ﯽ ﺖﺳا ﺒﺳﺎﻨﻣ ﺺﺧﺎﺷ و ﯽ

ﺳرﺮﺑ ﺖﻬﺟ ﯽ

ﮐ ﯿﻔ ﯿ ﺎﻬﻧ ﺖ ﯽﯾ ﺖﺳا لﻮﺼﺤﻣ .

ﻨﺑ ﺎ ﺮﺑ ﺮﻌﺗ ﯾ ﻒ دﯾ ﺮﮕ ﻪﮐ

تﺪﻣ نﺎﻣز دﺎﻤﺠﻧا

4ﺮﺛﻮﻣ ﻣﺎﻧ ﯿ هﺪ ﯽﻣ دﻮﺷ

، تﺪﻣ دﺎﻤﺠﻧا ترﺎﺒﻋ

ﺖﺳا زا تﺪﻣ ﻧﺎﻣز ﯽ ﻪﮐ مزﻻ ﺖﺳا ﻪﺟرد تراﺮﺣ هدﺎﻣ اﺬﻏ ﯽﯾ زا

ﯾ ﮏ ﻪﺟرد تراﺮﺣ ﻟوا ﯿﻪ ﺎﺗ ﯾ ﮏ ﻪﺟرد تراﺮﺣ زا صﺎﺧ ﭘﯿ ﺶ

ﻌﺗ ﯿﯿ ﻦ هﺪﺷ رد ﺰﮐﺮﻣ ﺗراﺮﺣ ﯽ اﯾ ﻦ هدﺎﻣ ﺶﻫﺎﮐ هداد دﻮﺷ ا ﯾ. ﻦ

اﺮﺑ ﺺﺧﺎﺷ ي

ﻌﺗ ﯿﯿ ﻓﺮﻇ ﻦ ﯿ ﺮﻓ ﺖ ﯾ رﺰ زا ﺮﻈﻧ ﻓﯿ ﺰﯾ ﮑ ﯽ و ﻪﺑ ﺗرﺎﺒﻋ ﯽ زا

دﯾ هﺎﮔﺪ دﺎﺼﺘﻗا ي درﻮﻣ ﻪﺟﻮﺗ ﯽﻣ ﺪﺷﺎﺑ 3 ] و 4 . [

ز داﺪﻌﺗ ﻪﭼﺮﮔا ﯾ

دﺎ ي اﺮﺑ لﺪﻣ ي ﭘ ﯿ ﺑ ﺶ ﯿﻨ ﯽ تﻻﻮﺼﺤﻣ دﺎﻤﺠﻧا نﺎﻣز

اﺬﻏ ﯽﯾ ا ﺎﺑ ﺖﺳا هﺪﺷ ﻪﺋارا ﯾ

ﻟد ﻪﺑ ،لﺎﺣ ﻦ ﯿ

ا ﻞ ﯾ اﺮﻓ ﻪﮑﻨ ﯾ دﺎﻤﺠﻧا ﺪﻨ

ﯾ ﮏ ﻪﻟﺄﺴﻣ ﺎﻫزﺮﻣ ﺎﺑ ي كﺮﺤﺘﻣ ﻪﺘﺧﺎﻨﺷ 5

ﯽﻣ دﻮﺷ ، ﻪﺑ يﺮﯿﮔرﺎﮐ

شور يﺎﻫ ﺎﭘﺎﻧ ﻞﺣ ﯾ زﺎﻓ ﮏﺗ ﺎ ي

اﺮﺑ ي ا ﻞﺣ ﯾ ﻦ ﻪﻟﺄﺴﻣ ﺐﺳﺎﻨﻣ

ﻪﺘﺧﺎﻨﺷ ﯽﻤﻧ دﻮﺷ 5] .[ رد ﻦﻤﺿ رد ، اﺮﻓ لﻮﻃ ﯾ ﺎﻣﺮﮔ ،دﺎﻤﺠﻧا ﺪﻨ ي

جرﺎﺧ لﻮﺼﺤﻣ زا دﺎﻤﺠﻧا نﺎﻬﻧ ﯽﻣ

دﻮﺷ ﻪﺑ لﻮﺼﺤﻣ دﺎﻤﺠﻧا ﻪﻄﻘﻧ و

ﻟد ﯿ ﻠﻐﺗ ﻞ ﯿ نﺎﺸﻧ ﺶﻫﺎﮐ هﺪﻧﻮﺷ ﻞﺣ داﻮﻣ ﻆ ﯽﻣ

ﺪﻫد ، ﻋ رد ﯿ لﺎﺣ ﻦ

ﺻﻮﺼﺧ ﯿ ﻓﻮﻣﺮﺗ تﺎ ﯿﺰ ﯾ ﮑ ﯽ اﺪﻫ ﻪﻠﻤﺟ زا لﻮﺼﺤﻣ ﯾ

ﺗراﺮﺣ ﺖ ﯽ ،

ﺎﻣﺮﮔ ي و ﯾ ﺴﻧاد و هﮋ ﯿ ﻧ ﻪﺘ ﯿ ﮕﺘﺴﺑاو و هدﻮﺒﻧ ﺖﺑﺎﺛ ﺰ ﯽ

ﺎﻣد ﯽﯾ نﺎﺸﻧ

ﯽﻣ ﺪﻨﻫد ا زا و ﯾ زﺎﺳ لﺪﻣ ور ﻦ ي

اﺮﻓ ﯾ دﺎﻤﺠﻧا ﺪﻨ لﻮﺼﺤﻣ

، راﻮﺷد

ﺪﺷ ﺪﻫاﻮﺧ .

ﻠﺻا شور ود عﻮﻤﺠﻣ رد ﯽ

اﺮﺑ ي ﺎﺴﻣ ﻞﺣ ﯾ ﻐﺗ ﻞ ﯿﯿ زﺎﻓ ﺮ

ﺻﻮﺗ ﯿ ﺪﻨﺗرﺎﺒﻋ ﻪﮐ ﺖﺳا هﺪﺷ ﻪ زا

: ﺣ ﻠﺤﺗ ﻞ ﯿﻠ ﯽ دﺪﻋ ﻞﺣ و ي

. ﻞﺣ

ﻠﺤﺗ ﯿﻠ ﯽ اﺮﺑ ًﻻﻮﻤﻌﻣ ي

ﺳﺪﻨﻫ لﺎﮑﺷا ﯽ

ﺒﻗ زا هدﺎﺳ ﯿ

ﺗ ﻞ ﯿ دوﺪﺤﻣﺎﻧ ﻪﻐ

،

و ﻪﻧاﻮﺘﺳا ﯾ هدﺎﻔﺘﺳا ﻞﺑﺎﻗ هﺮﮐ ﺎ ﯽﻣ

ﺪﺷﺎﺑ ﻠﮐ ﻞﮑﺷ ود ﻪﺑ و ﯽ

ﻓاﺮﮔ ﯿ ﮑ ﯽ

و ﯾ ﻌﺗ ﺪﻌﺑ نوﺪﺑ داﺪﻋا زا هدﺎﻔﺘﺳا ﺎﺑ ﺎ ﯿﯿ

ﻦ ﯽﻣ دﻮﺷ 6] .[ ﻞﺑﺎﻘﻣ رد

شور يﺎﻫ دﺪﻋ ﻞﺣ ي ا ﺮﺑ هوﻼﻋ ﯾ

ﻪﮑﻨ ﯽﻣ ﺪﻨﻧاﻮﺗ ﺎﺘﻧ ﯾ ﺠ ﯽ ﯿﻗد ﻖ يﺮﺗ

ارا ار ﯾ ﺪﻨﻫد ﻪ ﯽﻣ ﺪﻨﻧاﻮﺗ اﺮﺑ ي ﺳﺪﻨﻫ لﺎﮑﺷا ﯽ

ﻏ ﯿ ﻧ ﻢﻈﻨﻣ ﺮ ﯿ رﺎﮑﺑ ﺰ

ﺪﻧﻮﺷ ﻪﺘﻓﺮﮔ .

لﺪﻣ يﺎﻫ دﺪﻋ ي ار ﯽﻣ ناﻮﺗ ﻠﮐ ﻪﺘﺳد ﻪﺳ رد ﯽ

ﻞﺿﺎﻔﺗ

دوﺪﺤﻣ ، ﺴﻘﺗ دوﺪﺤﻣ ﻢﺠﺣ و دوﺪﺤﻣ ءاﺰﺟا ﯿ

ﺪﻨﺑ ﻢ ي دﻮﻤﻧ .

ز تﺎﻌﻟﺎﻄﻣ ﯾ

دﺎ ي زﺎﺳ لﺪﻣ صﻮﺼﺧ رد ي

رد تراﺮﺣ لﺎﻘﺘﻧا

3. Nominal freezing time 4. Effective freezing time 5. Moving boundaries problem

(3)

ﻘﻘﺤﻣ ﻂﺳﻮﺗ ﺖﺷﻮﮔ ﯿ

ﻦ ﻒﻠﺘﺨﻣ ﺖﺳا ﻪﺘﻓﺮﮔ ترﻮﺻ ﺑ

اﺮ ي لﺎﺜﻣ

Moraga and

Salinas ) 1999 ( تراﺮﺣ لﺎﻘﺘﻧا لﺪﻣ ﻪﻌﺳﻮﺗ ﻪﺑ

ﺣ رد ﯿ ﻫﺎﻣ ﺖﺷﻮﮔ دﺎﻤﺠﻧا ﻦ ﯽ

زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﺤﻔﺻ ﻞﮑﺷ ﺎﺑ نﻮﻤﻟﺎﺳ

ﺪﻨﺘﺧادﺮﭘ دوﺪﺤﻣ ﻢﺠﺣ شور 7]

.[ Sheen and Hayakawa

) 1990 ( ر لﺪﻣ ﻪﻌﺳﻮﺗ ﻪﺑ ﯾ

ﺿﺎ ﯽ اﺮﺑ ي ﺣ رد ﻢﻈﻨﻣﺎﻧ لﺎﮑﺷا ﯿ

ﻦ

ﺪﻨﺘﺧادﺮﭘ دﺎﻤﺠﻧا ﻊﻓر و دﺎﻤﺠﻧا .

ﮐﺬﻣ لﺪﻣ رد ﻐﺗ ﺮﺛا رﻮ

ﯿﯿ ﻢﺠﺣ تاﺮ

ﺷﺎﻧ ﯽ ﻧ دﺎﻤﺠﻧا زا ﯿ

لﺪﻣ رد ﺰ هﺪﻧﺎﺠﻨﮔ

دﻮﺑ هﺪﺷ 8]

.[ و Sanz

نارﺎﮑﻤﻫ ) 1999 ( زا ﯾ ر لﺪﻣ ﮏ ﯾ ﺿﺎ ﯽ دوﺪﺤﻣ ﻞﺿﺎﻔﺗ ﻞﺣ شور ﺎﺑ

اﺮﺑ ي ﺒﺷ ﯿ زﺎﺳ ﻪ ي ﺎﻣﺮﺳ ﺖﻋﺮﺳ ﯾ

ﺶ توﺎﻔﺘﻣ ﻪﻠﻀﻋ ﺢﻄﺳ رد

ﺖﺳد رﻮﻈﻨﻣ ﻪﺑ كﻮﺧ ﺖﺷﻮﮔ ﯾﺑﺎ

ﯽ ﻪﺑ ﻣ ﯿ دﺎﻤﺠﻧا ناﺰ ﺖﻬﺟ ﺮﺛﻮﻣ

ﻟﻮﺗ ﯿ ﺪ ﯾ ﮐ ﺎﺑ لﻮﺼﺤﻣ ﮏ ﯿﻔ

ﯿ ﺗ ﺎﺑ بﻮﺧ ﺖ زﻮﺗ ﻪﺑ ﻪﺟﻮ

ﯾ ﻬﺑ ﻊ ﯿ ﻪﻨ

ﺎﻫرﻮﻠﺑ ي ﯾ ﻓ جرﺎﺧ و ﻞﺧاد رد ﺦ ﯿ

ﺎﻫﺮﺒ ي ﺘﻓﺎﺑ ﯽ ﺪﻧدﺮﮐ هدﺎﻔﺘﺳا ،دﻮﺷ

9] .[ Tocci and Mascheronni )

1995 ( ﻧ ﯿ لﺪﻣ ﻪﻌﺳﻮﺗ ﻪﺑ ﺰ

رﯾ ﺿﺎ ﯽ زا هدﺎﻔﺘﺳا ﺎﺑ شور

يﺎﻫ دﺪﻋ ي اﺮﺑ ي زﺎﺳ لﺪﻣ ي دﺎﻤﺠﻧا

تراﺮﺣ و مﺮﺟ لﺎﻘﺘﻧا ﻦﺘﻓﺮﮔ ﺮﻈﻧ رد ﺎﺑ ﺖﺷﻮﮔ ﻢﻫ

نﺎﻣز ﻪﺘﺧادﺮﭘ ﺪﻧا

10] .[ رد ﯾ ﮏ ﻘﺤﺗ ﯿ د ﻖ ﯾ

،ﺮﮕ Zillo نارﺎﮑﻤﻫ و )

2018 ( ﻪﻌﺳﻮﺗ ﻪﺑ

ﯾ ﺪﻌﺑ ﻪﺳ لﺪﻣ ﮏ ي

اﺮﺑ دوﺪﺤﻣ ﻢﺠﺣ شور ﺎﺑ ي

زﺎﺳ لﺪﻣ ي

ﺳ دﺎﻤﺠﻧا ﯿ ﺪﻨﺘﺧادﺮﭘ دوﺪﺤﻣ ﻪﻧاﻮﺘﺳا ﻞﮑﺷ ﻪﺑ غﺮﻣ ﻪﻨ 11]

.[ ﺎﺘﻧ ﯾ ﺞ

ا زا ﻞﺻﺎﺣ ﯾ

ﻦ ﻖﯿﻘﺤﺗ ﺎﻫ ﮐﺎﺣ ﯽ ﺖﻗد زا لﻮﺒﻗ ﻞﺑﺎﻗ ﺎﺘﻧ

ﯾ ﺞ ﭘﯿ ﺑ ﺶ ﯿﻨ ﯽ

ﻂﺳﻮﺗ هﺪﺷ ﺎﺑ لﺪﻣ

هداد يﺎﻫ ﺑﺮﺠﺗ ﯽ دﻮﺑ .

رد لﺎﺳ يﺎﻫ ﺧا ﯿ ﺮ ﻪﺑ يﺮﯿﮔرﺎﮐ ﺎﻫاﺰﻓا مﺮﻧ ي

ﺒﻗ زا CFD ﯿ ﻞ

COMSOL 12]

،[ FLUENT 13]

،[ STAR-CCM+

11]

، [ ANSYS-CFX 14]

و [ OpenFOAM 15]

اﺮﺑ [ ي

زﺎﺳ لﺪﻣ ي اﺬﻏ داﻮﻣ دﺎﻤﺠﻧا ﯽﯾ

هدﻮﺑ ﺪﺷر ﻪﺑ ور ﺖﺳا

. ﻟو ﯽ هدﺎﻔﺘﺳا

ا زا ﯾ ا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺎﻫراﺰﻓا مﺮﻧ ﻦ ﯾ

ﺎﺴﻣ ﻞﺣ دراﺪﻧﺎﺘﺳا شور زا ﻪﮑﻨ ﯾ

ﻞ

ﻐﺗ ﯿﯿ زﺎﻓ ﺮ ) ﺘﻧآ شور ﭙﻟﺎ ﯽ ( هدﺎﻔﺘﺳا ﯽﻤﻧ ﺪﻨﻨﮐ ﺎﺑ ﺶﻟﺎﭼ ﯽﯾﺎﻫ ﻧ ﯿ وﺮﺑور ﺰ

ﺖﺳا هدﻮﺑ 16]

. [ ا رد ﯾ ﻘﺤﺗ ﻦ ﯿ ﻖ

، ﻌﺗ رﻮﻈﻨﻣ ﻪﺑ ﯿﯿ

و دﺎﻤﺠﻧا نﺎﻣز ﻦ

ﻌﺗ ﯿﯿ ﻓوﺮﭘ ﻦ ﯿ ﺎﻣد ﻞ ي ﺮﻓ رد ﺮﮔﺮﺒﻤﻫ لﻮﺼﺤﻣ ﯾ

رﺰ ، ﻠﮐ اﺪﺘﺑا ﯿ ﻪ

ﺻﻮﺼﺧ ﯿ ﻓﻮﻣﺮﺗ تﺎ ﯿﺰ ﯾ ﮑ ﯽ ﻣ ﺮﺑ ﻞﻤﺘﺸﻣ لﻮﺼﺤﻣ ﯿ

ناﺰ ﯾ ﮑﺸﺗ ﺦ ﯿ ﻞ

ﺣ رد هﺪﺷ ﯿ دﺎﻤﺠﻧا ﻦ ) ﺮﺴﮐ ﯾ ﺨ ﯽ (،

ﺴﻧاد ﯿ

،ﻪﺘ ﺎﻣﺮﮔ ي و ﯾ و هﮋ اﺪﻫ ﯾ ﺖ

ﺗراﺮﺣ ﯽ ﻌﺑﺎﺗ ناﻮﻨﻋ ﻪﺑ ﺮﮔﺮﺒﻤﻫ لﻮﺼﺤﻣ ﯽ

و تراﺮﺣ ﻪﺟرد زا

ﮐﺮﺗ ﯿ ﺷ ﺐ ﯿ ﺎﻤ ﯽﯾ هداد ﻪﻌﺳﻮﺗ لﻮﺼﺤﻣ ﺪﺷ

لﺪﻣ ود ﺪﻌﺑ ﻪﻠﺣﺮﻣ رد و

دﺪﻋ ي ﺎﻨﺒﻣ ﺮﺑ ي و دوﺪﺤﻣ ﻞﺿﺎﻔﺗ ﻞﺣ شور ءاﺰﺟا

دوﺪﺤﻣ ﺎﺑ

راﺰﻓا مﺮﻧ زا هدﺎﻔﺘﺳا COMSOL

اﺮﺑ ي زﺎﺳ لﺪﻣ ي تراﺮﺣ لﺎﻘﺘﻧا ﺣ رد

ﯿ ﻐﺗ ﻦ ﯿﯿ ارا ﺮﮔﺮﺒﻤﻫ ﻪﻧﻮﻤﻧ زﺎﻓ ﺮ ﯾ

ﻪ دﺮﮔ ﯾ ﺪ

، ﺎﻬﻧ رد ﯾ ﺎﺘﻧ ﺖ ﯾ ﻪﺑ ﺞ

زﺎﺳ لﺪﻣ شور ﺎﺑ هﺪﻣآ ﺖﺳد ي

ﺎﺘﻧ ﺎﺑ ﯾ ﺑﺮﺠﺗ ﺞ ﯽ ﺎﻘﻣ ﯾ ﺴ ﺪﺷ ﻪ ﺪﻧ .

2 - و داﻮﻣ شور

ﺎﻫ

2 - 1 - زﺎﺳ هدﺎﻣآ و داﻮﻣ ي

ﻪﻧﻮﻤﻧ ﺎﻫ

ﻪﻧﻮﻤﻧ يﺎﻫ ﺮﮔﺮﺒﻤﻫ رﺎﮑﺑ ﻪﺘﻓر رد اﯾ وﺎﺣ ﺶﻫوﮋﭘ ﻦ ي

، 75 ﺪﺻرد

ﭘ ،ﻪﻟﺎﺳﻮﮔ ﺖﺷﻮﮔ ﯿ

رﺎﺧﻮﺳ درآ ،زﺎ ي

ﻔﺼﺗ ﮏﻤﻧ ، ﯿ

ودا ،هﺪﺷ ﻪ ﯾ

ﻪ

ﺒﻃ ﯿﻌ ﯽ زا و دﻮﺑ ﻦﻏور و ﯾ

ﮑ ﯽ زا ﺖﮐﺮﺷ يﺎﻫ ﻟﻮﺗ ﯿ ﺮﮔﺮﺒﻤﻫ هﺪﻨﻨﮐ ﺪ

ﺪﻤﺠﻨﻣ ﺪﺷ بﺎﺨﺘﻧا ﻪﻤﻫ رد لﻮﺼﺤﻣ ﺖﻣﺎﺨﺿ ،

ﻪﻧﻮﻤﻧ ﺎﻫ 18 ﻣ ﯿﻠ ﯽ

و دﻮﺑ ﺮﺘﻣ اﺮﺑ ي ﻌﺗ ﯿﯿ ﻦ ﻣﯿ ناﺰ ﺑﺮﭼ ﯽ و ﺖﺑﻮﻃر ، ﺌﺗوﺮﭘ

ﯿ ﻦ ﻪﺑ ﻪﻧﻮﻤﻧ

ﺗﺮﺗ ﯿ ﺐ شور زا

،ﻪﻠﺴﮐﻮﺳ ﮏﺸﺧ

ندﺮﮐ ﺎﺑ نوآ ) 105 ﻪﺟرد

ﯽﺘﻧﺎﺳ داﺮﮔ ( شور و لاﺪﻠﮐ هدﺎﻔﺘﺳا ﺪﺷ . ﺎﺘﻧ ﯾ ﺞ ﺰﺠﺗ ﯾﻪ ﺷﯿ ﺎﻤ ﯽﯾ

ﻪﻧﻮﻤﻧ ﺎﻫ لوﺪﺟ رد 1

ﻪﺋارا هﺪﺷ ﺖﺳا 17] .[ ﺮﻫ ﯾ ﮏ زا ﺎﻣزآ ﯾ تﺎﺸ

قﻮﻓ ﻞﻗاﺪﺣ رد 3 راﺮﮑﺗ مﺎﺠﻧا ﺪﺷ و ﺎﺘﻧ ﯾ ﺞ ﻪﺑ ترﻮﺻ ﻣﯿ ﮕﻧﺎ ﯿ ﻦ

هﺪﺷ شراﺰﮔ ﺖﺳا

. اﺮﺑ ي ﻌﺗ ﯿﯿ ﻓوﺮﭘ ﻦ ﯿ ﺎﻣد ﻞ ي ﺣ رد لﻮﺼﺤﻣ ﯿ

ﻦ

زا دﺎﻤﺠﻧا 3 عﻮﻧ ﻞﭘﻮﮐﻮﻣﺮﺗ دﺪﻋ ﺗﺮﺗ ﻪﺑ ﻪﮐ K

ﯿ ﺗراﺮﺣ ﺰﮐﺮﻣ رد ﺐ ﯽ

،

ﻪﻧﻮﻤﻧ ﺢﻄﺳ ﺤﻣ و

ﯿ ﺮﻓ ﻂ ﯾ اﺮﻗ رﺰ ر ﺘﺳا دﻮﺑ هﺪﺷ هداد دﺮﮔ هدﺎﻔ

ﯾ ﺪ.

ﺎﻣزآ ﯾ رد تﺎﺸ ﯾ ﺮﻓ ﮏ ﯾ ﺎﻣزآ رﺰ ﯾ ﻫﺎﮕﺸ ﯽ ) ا ،كوﺮﮔ ﯾ ناﺮ ( ﺎﻣد ود رد ي

ﻒﻠﺘﺨﻣ 18 - و 35 - ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ ﺖﻓﺮﮔ ترﻮﺻ .

رد ﺎﻣد

ﻧﺎﻣز ﻞﺻاﻮﻓ ﯽ

ﺮﻫ ﯾ ﻗد ﮏ ﯿ ﺎﭘ ﺎﺗ ﻪﻘ ﯾ د ﻂﺳﻮﺗ دﺎﻤﺠﻧا نﺎﻣز نﺎ ﯾ

ﺮﮔﻻﺎﺘ

ﺪﺷ ﺖﺒﺛ .

2 - 2 - ﻌﺗ ﯿﯿ ﺻﻮﺼﺧ ﻦ ﯿ

ﻓﻮﻣﺮﺗ تﺎ ﯿﺰ

ﯾ ﮑ ﯽ ﻪﻧﻮﻤﻧ

ﺖﻗد ﭘﯿ ﺶ ﺑﯿﻨ ﯽ

،لﺪﻣ ﻪﻄﺑار ﻘﺘﺴﻣ ﯿﻤ ﯽ ﺑﺎ ﺖﻗد ﺮﺘﻣارﺎﭘ يﺎﻫ درﻮﻣ

هدﺎﻔﺘﺳا رد لﺪﻣ دراد ﻪﮐ ﻢﻬﻣ ﻦﯾﺮﺗ ﺎﻫﺮﺘﻣارﺎﭘ رد لﺪﻣ يﺎﻫ لﺎﻘﺘﻧا

تراﺮﺣ ﻞﻣﺎﺷ يﺎﻣﺮﮔ وﯾ اﺪﻫ ،هﮋ ﯾ ﺖ ﺗراﺮﺣ ﯽ

، ﺴﻧاد ﯿ ﻪﺘ و ﺮﺿ ﯾ ﺐ

لﺎﻘﺘﻧا تراﺮﺣ ﺢﻄﺳ رد اﺬﻏ هدﺎﻣ

ﯽﯾ ﯽﻣ ﺪﻨﺷﺎﺑ . اﺮﺑ ي ﻤﺨﺗ ﯿ و ﻦ

ﻌﺗ ﯿﯿ ﻣ ﻦ ﯿ اﺪﻫ ناﺰ ﯾ ﺗراﺮﺣ ﺖ ﯽ ﺎﻫﺎﻣد رد ﺮﮔﺮﺒﻤﻫ ي

ﻻﺎﺑ ي ﻪﺟرد ﺮﻔﺻ

ﯽﺘﻧﺎﺳ داﺮﮔ زاﻮﻣ لﺪﻣ زا

1ي اﺮﺑ و ي ﺎﻫﺎﻣد ي ز ﯾ ﻟوا دﺎﻤﺠﻧا ﻪﻄﻘﻧ ﺮ ﯿ

ﻪ

ﮐﺮﺗ لﺪﻣ زا ﯿﺒ

2ﯽ ) ﺮﺳ ي زاﻮﻣ و ي ( ﻂﺑاور و 1 ﺎﺗ 3 ﺪﺷ هدﺎﻔﺘﺳا

18] و 20 .[

) 1 (





N

i i

ki

k

1



1 Parallel model 2 Combined

(4)

) 2 (





) / (

/

i i

i x

x



 

) 3 (

   







 

  _N

B LW not i

i i

B LW W

B LW

k v v k

v k v

,

1 2



اﺮﺑ ي ﻌﺗ ﯿﯿ ﺎﻣﺮﮔ ﻦ ي و ﯾ ﻣ اﺪﺘﺑا لﻮﺼﺤﻣ هﮋ ﯿ

ﻪﺟﻮﺗ ﺎﺑ هﺪﺷ ﺪﻧﺎﺑ بآ ناﺰ

ﻪﻄﺑار ﻪﺑ ) 4 ( ﺪﺷ ﺺﺨﺸﻣ و

ﻣ ﺪﻌﺑ ﻪﻠﺣﺮﻣ رد ﯿ

ناﺰ ﯾ ﮑﺸﺗ ﺦ ﯿ هﺪﺷ ﻞ

ﺎﻫﺎﻣد رد ي ﻪﻄﺑار زا هدﺎﻔﺘﺳا ﺎﺑ ﻒﻠﺘﺨﻣ 5

- 7 ﻤﺨﺗ ﯿ ﺪﺷ هدز ﻦ 19]

.[

ﺎﻬﻧ رد ﯾ ﮐﺮﺗ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺖ ﯿ

ﺷ ﺐ ﯿﻤ ﯿﺎ ﯽﯾ ﻧ ﻣ ﻪﻧﻮﻤ ﯿ ناﺰ ﺎﻣﺮﮔ ي و ﯾ هﮋ

ﺮﻫﺎﻇ ي لﻮﺼﺤﻣ ﻪﻄﺑار ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ 8

ﻌﺗ ﯿﯿ ﺪﺷ ﻦ 20] .[

) 4(

100

) 1 . 0 3

. 0

( _P _C

B

x

x x  



) 5 (

f

i T if T T

x( )0 

) 6 (

) ( )

(T x x T

x_w  _tw _i

) 7 (

f f

B tw

i if T T

T x T

x T

x  











 



 273.15

15 . 1 273

) (

) 8 (

) ( ) ( ) ( ) ( ) ( )

( T

dT Ldx T x T Cp T x T Cp x T Cp

C_Papp _s _s _w _w  _i _i  ⁱ

2 - 2 - 1 - ﻌﺗ ﯿﯿ ﺴﻧاد ﻦ ﯿ ﻪﻧﻮﻤﻧ ﻪﺘ

اﺮﺑ ي ﻤﺨﺗ ﯿ ﻣ ﻦ ﯿ ﺴﻧاد ناﺰ ﯿ ﮐﺮﺗ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻪﻧﻮﻤﻧ ﻪﺘ ﯿ

ﺷ ﺐ ﯿﻤ ﯿﺎ ﯽﯾ

ﻪﻄﺑار زا لﻮﺼﺤﻣ 9

ﺪﺷ هدﺎﻔﺘﺳا .

) 9 (





i

xi 

 /

1

2 - 2 - 2 - ﺮﺿ ﯾ لﺎﻘﺘﻧا ﺐ ﺢﻄﺳ رد تراﺮﺣ

اﺮﺑ ي ﻌﺗ ﯿﯿ ﺮﺿ ﻦ ﯾ ﮔ هزاﺪﻧا شور زا ﺢﻄﺳ رد تراﺮﺣ لﺎﻘﺘﻧا ﺐ ﯿﺮ

ي

ﺎﭘﺎﻧ ﺖﻟﺎﺣ رد ﺎﻣد ﯾ

ﺪﺷ هدﺎﻔﺘﺳا ﺎ .

ﺪﺑ ﯾ رﻮﻈﻨﻣ ﻦ ﯾ ﻪﻌﻄﻗ ﮏ ﯽﻣﻮﯿﻨﯿﻣﻮﻟآ

رد ﺮﮔﺮﺒﻤﻫ ﻪﻧﻮﻤﻧ دﺎﻌﺑا ﻪﺑ ﯾ

ﻠﭘ ﺲﻨﺟ زا بﻮﭼرﺎﭼ ﮏ ﯽ

ﺗا ﯿ راﺮﻗ ﻦﻠ

ﮐﻮﻣﺮﺗ ود زا هدﺎﻔﺘﺳا ﺎﺑ و ﺖﻓﺮﮔ عﻮﻧ زا ﻞﭘﻮ

ﺰﮐﺮﻣ و ﺢﻄﺳ رد ﻪﮐ K

ﻐﺗ دﻮﺑ ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﻧﻮﻤﻧ ﯿﯿ

ﺣ رد ﺎﻣد تاﺮ ﯿ

ﺮﻓ رد دﺎﻤﺠﻧا ﻦ ﯾ

ﺎﺑ رﺰ زا هدﺎﻔﺘﺳا

ﯾ د ﮏ ﯾ ﺪﺷ ﺖﺒﺛ ﺮﮔﻻﺎﺘ .

ﻣﯿ ﺮﺿ ناﺰ ﯾ رد تراﺮﺣ لﺎﻘﺘﻧا ﺐ

ﭗﻣﻻ شور زا هدﺎﻔﺘﺳا ﺎﺑ ﺢﻄﺳ )

ﻓﺮﻇ ﯿ هدﺮﺸﻓ ﺖ

1( ﺪﻣآ ) ﻞﮑﺷ 1 (

21] . [ اﺮﺑ ي ﺎﻘﻣ ﯾ ﻪﺴ ﺮﺿ ﯾ تراﺮﺣ لﺎﻘﺘﻧا ﺐ شور زا هﺪﻣآ ﺖﺳد ﻪﺑ

ﻓ داﺪﻋا شور ﺎﺑ قﻮ نوﺪﺑ

ﻪﻄﺑار زا ﺪﻌﺑ )

10 ( ﺪﺷ هدﺎﻔﺘﺳا .

ا ﯾ ﻦ

هدوﺪﺤﻣ رد ﻪﻄﺑار ر دﺪﻋ

ﯾ زﺪﻟﻮﻨ ) 5/

3 - 80000 ( دراد دﺮﺑرﺎﮐ .

) 10 (

54 58

14 23

13 12

282000 1 Re

) Pr 4 . 0 ( 1

Pr Re 62 . 3 0 . 0















 









 



 Nu

Fig 1 Experimental set up used for determining of convective heat transfer coefficient

2 - 3 - تراﺮﺣ لﺎﻘﺘﻧا لﺪﻣ

ﺎﺑ ا ضﺮﻓ ﯾ ﺮﮔﺮﺒﻤﻫ ﻪﮑﻨ ﯾ

ﺖﺑﺎﺛ ﺖﻣﺎﺨﺿ ﺎﺑ دوﺪﺤﻣ ﻪﻧاﻮﺘﺳا ﮏ )

(L

عﺎﻌﺷ و ) (r ﯽﻣ ﺪﺷﺎﺑ ﺪﻌﺑ ود تراﺮﺣ لﺎﻘﺘﻧا ﻪﻟدﺎﻌﻣ ي

اﺮﺑ ي ﺖﻟﺎﺣ

اﺪﻫ ﯾ ﮕﺘﺴﺑاو ضﺮﻓ ﺎﺑ و ﺖ ﯽ

ﺻﻮﺼﺧ ﯿ ﺗراﺮﺣ تﺎ ﯽ ﺎﻣد ﻪﺑ ﺮﮔﺮﺒﻤﻫ

ﯽﻣ ناﻮﺗ ﻪﻟدﺎﻌﻣ 10 ﺖﺷﻮﻧ ار :

) 11 (



 







 



 







 



r H H T r rk r z

H H T t k t

t r z

H ( )

) 1 (

) ) ( ) (

, , (

2 - 3 - 1 - اﺮﺷ ﯾ زﺮﻣ ﻂ ي ﻪﻧﻮﻤﻧ

رﻮﺤﻣ نرﺎﻘﺗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ رد ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ي

اﺮﺑ ي لﺎﻘﺘﻧا و ﻪﻧﻮﻤﻧ

اﺮﺷ ﻪﻧﻮﻤﻧ ﺢﻄﺳ رد ﺖﻓﺮﻤﻫ شور ﻪﺑ تراﺮﺣ ﯾ

زﺮﻣ ﻂ ي ز ﯾ ﺮ

) ﻂﺑاور 12 - 11 ( اﺮﺑ ي ﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد لﺪﻣ .

اﺮﺑ ي ﻪﻧﻮﻤﻧ ﺢﻄﺳ

1. Lumped capacitance

(5)

) 12 (

) (T T_a r h

k T  



 

نرﺎﻘﺗ طﺮﺷ

) 13 (

0 ) , , 0

( 



 z t x T

2 - 3 - 2 - زﺎﺳ لﺪﻣ ي

- دوﺪﺤﻣ ﻞﺿﺎﻔﺗ

ﻠﺻا تﻻدﺎﻌﻣ ﯽ

اﺮﺷ لﺎﻤﻋا ﺎﺑ تراﺮﺣ لﺎﻘﺘﻧا ﯾ

ﻟوا ﻂ ﯿ زﺮﻣ و ﻪ ي ﻪﺑ

دﺪﻋ رﻮﻃ ي ﺎﺑ و هدﺎﻔﺘﺳا ﺎﻨﺒﻣ ﺮﺑ دوﺪﺤﻣ ﻞﺿﺎﻔﺗ شور زا ي

ﺎﻤﺷ ي

ﺮﺻ ﯾ

1ﺢ دﺮﮔ ﻞﺣ ﯾ ﺪﻧﺪ . ا رد ﯾ دﺎﻌﺑا ﻪﺑ ﺮﮔﺮﺒﻤﻫ ﻪﻧﻮﻤﻧ ﻪﻌﻟﺎﻄﻣ ﻦ 140

× 18 ﻣ ﯿﻠ ﯽ ﻪﺑ ﺮﺘﻣ 11 ﻟﻮﻃ هﺮﮔ ﯽ ﺴﻘﺗ ﯿ ﺪﺷ ﻢ . يدورو يﺎﻫ درﻮﻣ

لوﺪﺟ رد لﺪﻣ رد هدﺎﻔﺘﺳا 1

ﻮﻧ ﻪﻣﺎﻧﺮﺑ و ﺖﺳا هﺪﺷ هداد نﺎﺸﻧ ﯾ

ﺴ ﯽ

ور ﺮﺑ ي راﺰﻓا مﺮﻧ MATLAB R2016b ﺬﭘ مﺎﺠﻧا

ﯾ ﺖﻓﺮ 21] . [

ﺎﻨﺒﻣ ﺮﺑ قﻮﻓ ﻪﻟدﺎﻌﻣ ﻞﺣ زا ي

ﺎﻤﺷ ي ﺮﺻ ﯾ ﺢ ﻞﺿﺎﻔﺗ شور رد

دوﺪﺤﻣ ﯽﻣ ناﻮﺗ ﻪﻟدﺎﻌﻣ 13 اﺮﺑ ار ي ﻠﺧاد طﺎﻘﻧ ﯽ

ﻤﻧ دروآﺮﺑ ﻪﻧﻮ

اﺮﺑ ،دﻮﻤﻧ ي هﺮﮔ يﺎﻫ ﻧ ﻪﻧﻮﻤﻧ ﺢﻄﺳ و ﺰﮐﺮﻣ رد ﻊﻗاو ﯿ

ﺰ ﯽﻣ ناﻮﺗ

ﻬﺑﺎﺸﻣ تﻻدﺎﻌﻣ ﯽ

اﺮﺷ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﯾ

زﺮﻣ ﻂ ي دروآ ﺖﺳد ﻪﺑ ﻪﻧﻮﻤﻧ

22] . [

) 14 (

   

jⁱ

 

i j i j i j i j i i j

j j i

j k T T k T T

r Cp T t

T^¹ ¹ ₂  _₁_/₂( _₁ ) _₁_/₂  _₁















 

 

اﺮﺑ ي اﺰﻓا ﯾ اﺪﻫ لﺪﻌﻣ زا ،لﺪﻣ ﺖﻗد ﺶ ﯾ

ﺗراﺮﺣ ﺖ ﯽ رد هﺮﮔ ﺎﻫ ﺮـﻫ رد

ﻧﺎﻣز مﺎﮔ ﯽ ﻪﻄﺑار زا هدﺎﻔﺘﺳا ﺎﺑ 14

ﺳا ﺪﺷ هدﺎﻔﺘ .

) 15 ( 2

1 2 / 1

t j t t j

j

k

k k 

 ^ 

2

1 2 / 1

t i t t i

i

k

k k 

 ^



2 - 3 - 3 - زﺎﺳ لﺪﻣ ي - ءاﺰﺟا دوﺪﺤﻣ

اﺮﺷ و ﻢﮐﺎﺣ ﻪﻟدﺎﻌﻣ ﯾ

زﺮﻣ ﻂ ي ﻟوا و ﯿ راﺰﻓا مﺮﻧ زا هدﺎﻔﺘﺳا ﺎﺑ ﻪ 5.5

COMSOL اﺮﺑ

ي تﺎﺼﺘﺨﻣ ﻪﻧاﻮﺘﺳا

يا ﺪﻌﺑ ود ﺖﻟﺎﺣ رد و ي

ﻠﺜﻣ لﺎﮑﺷا ﺎﺑ ﮋﻧاﺮﮔﻻ مود ﻪﺟرد نﺎﻤﻟا ﺎﺑ و نرﺎﻘﺘﻣ ﺜ

ﯽ ) 1856 دﺪﻋ (

ﺎﭘ ﻊﺑﺎﺗ ناﻮﻨﻋ ﻪﺑ ﯾ

ﺪﺷ ﻞﺣ ﻪ 11]

و 13 . [

2 - 4 - ﺰﺠﺗ ﯾ ﻠﺤﺗ و ﻪ ﯿ رﺎﻣآ ﻞ ي

ﻌﻣ ود ﯿ رﺎﻣآ رﺎ ي ) ﻂﺑاور 16 - 15 ( ﺮﺿ ، ﯾ ﺗ ﺐ ﻌ ﯿﯿ ﻦ ) R² ( ر و ﯾ ﻪﺸ

ﻣﯿ ﮕﻧﺎ ﯿ ﺎﻄﺧ تﺎﻌﺑﺮﻣ ﻦ )

(RMSE اﺮﺑ ي زرا ﯾﺑﺎ ﯽ ﺑ ﺐﺳﺎﻨﺗ ﯿ ﺎﺑ لﺪﻣ ﻦ

هداد يﺎﻫ ﺑﺮﺠﺗ ﯽ ) آ ﺎﻣز ﯾ ﺸ ﯽ ( ﺖﻓﺮﮔ راﺮﻗ هدﺎﻔﺘﺳا درﻮﻣ 2]

. [

1. Explicit

) 16 (

 

_^





















 N

i

i pre i pre N

i

i i pre

T T

T T R

1

2 , , 1

2 exp, ,

2 1

) 17 (

 















 







2

1

, exp,

N T T RMSE

N

i

i pre i

ﻻﺎﺑ ﻂﺑاور رد Tpre,i

و Texp,i

ﺗﺮﺗ ﻪﺑ ﯿ ﺎﻣد ﺐ ي ﭘ ﯿ ﺑ ﺶ ﯿﻨ ﯽ هﺪﺷ

ﻂﺳﻮﺗ لﺪﻣ ﺎﻫ ﺎﻣد و ي ﺎﻣزآ ﯾ ﺸ ﯽ و داﺪﻌﺗ N هداد ﺎﻫ ﯽﻣ ﺪﺷﺎﺑ .

3 - ﺎﺘﻧ ﯾ ﺚﺤﺑ و ﺞ

3 - 1 - ﺻﻮﺼﺧ ﯿ ﻓﻮﻣﺮﺗ تﺎ ﯿﺰ

ﯾﮑ ﯽ لﻮﺼﺤﻣ

ﻞﮑﺷ 2 ﻣﯿ ناﺰ ﺴﮐ ﺮ ﯾ ﺨ ﯽ ﮑﺸﺗ ﯿ ﻌﺑﺎﺗ ناﻮﻨﻋ ﻪﺑ ﻪﻧﻮﻤﻧ رد هﺪﺷ ﻞ ﯽ

زا

نﺎﺸﻧ ار ﺎﻣد ﯽﻣ

ﺪﻫد

، ﻞﮑﺷ سﺎﺳا ﺮﺑ ﺘﺣ ﻪﮐ ﺖﺳا ﺺﺨﺸﻣ

ﯽ رد

ﺎﻣد ي 40 - ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ دوﺪﺣ 88 % لﻮﺼﺤﻣ رد دﻮﺟﻮﻣ بآ

ﻞﮑﺷ ﻪﺑ لﺎﺘﺴﯾﺮﮐ يﺎﻫ ﯾ رد ﺦ ﯽﻣ ﺪﯾآ ﻘﺑﺎﻣ و ﯽ ﺎﻣ ترﻮﺻ ﻪﺑ زﻮﻨﻫ ﯾ

ﻊ

لﻮﺼﺤﻣ ﺖﻓﺎﺑ رد ﻗﺎﺑ

ﯽ ﯽﻣ ﺪﻧﺎﻣ

، ﺸﺨﺑ ﻪﮐ ﯽ ا زا ﯾ ترﻮﺻ ﻪﺑ بآ ﻦ

ﻘﺑﺎﻣ و هﺪﺷ ﺪﻧﺎﺑ بآ ﯽ

ترﻮﺻ ﻪﺑ بآ

دﺎﻤﺠﻧا ﻞﺑﺎﻗ ﯽﻣ

ﺪﺷﺎﺑ . ﻪﺘﮑﻧ

دﯾ ﺮﮕ ي ﻪﮐ رد ﻞﮑﺷ 2 ﺎﻣد ﻪﻨﻣاد رد ،ﺖﺳا ﺺﺨﺸﻣ ﯽﯾ

ﺑﯿ ﻦ ﻪﻄﻘﻧ

ﻟوا دﺎﻤﺠﻧا ﯿ ﺎﺗ لﻮﺼﺤﻣ ﻪ 10

ﻪﺟرد ﺘﻧﺎﺳ ﯽ داﺮﮔ ﺮﺘﻤﮐ زا اﯾ ،ﻪﻄﻘﻧ ﻦ

ﺑﯿ ﺮﺘﺸ ﯾ ﻣ ﻦ ﯿ ناﺰ ﯾ دوﺪﺣ ﻪﮐ لﻮﺼﺤﻣ ﺦ 75

% لﺎﺘﺴﯾﺮﮐ يﺎﻫ ﯾ ﺖﺴﻫ ﺦ

ﮑﺸﺗ ﯿ ﻞ ﺖﺳا هﺪﺷ ﺑ ﺶﻫﺎﮐ ﺎﺑ و

ﯿ ﺎﻣد ﺮﺘﺸ ﻂﺧ ﺖﻟﺎﺣ ﻪﺑ رادﻮﻤﻧ

ﻘﻓا ﯽ دﺰﻧ ﺖﺑﺎﺛ ﯾ ﻐﺗ ﺪﻧور و هﺪﺷ ﮏ ﯿﯿ

ﮑﺸﺗ و تاﺮ ﯿ

ﻞ لﺎﺘﺴﯾﺮﮐ يﺎﻫ

ﯾ ﺦ ﺪﻨﮐ ﺮﺗ ﯽﻣ دﻮﺷ . اﯾ ﻤﻫا ﻪﺘﮑﻧ ﻦ ﯿ

ز ﺖ ﯾ دﺎ ي لﻮﺼﺤﻣ ﺖﻓﺎﺑ رد

ز ﺖﺷاد ﺪﻫاﻮﺧ ﯾ

ا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ اﺮ ﯾ

ﮑﺸﺗ ﺎﺑ ﻪﮑﻨ ﯿ

ﻞ لﺎﺘﺴﯾﺮﮐ يﺎﻫ ﯾ ﺦ

عاﻮﻧا ﺐﯿﺳآ يﺎﻫ دﺎﻤﺠﻧا ي ﺒﻗ زا ﯿ ﻠﻐﺗ ،نﺪﺷ ﮏﺸﺧ ﻞ ﯿ

ﻞﺣ داﻮﻣ ﻆ

ﺳآ و هﺪﻧﻮﺷ ﯿ

ﻧﺎﮑﻣ ﺐ ﯿ ﮑ ﯽ ﺷﺎﻧ ﯽ اﺰﻓا زا ﯾ ﻢﺠﺣ ﺶ لﺎﺘﺴﯾﺮﮐ يﺎﻫ ﯾ ﺦ

ﭘ ﻞﺑﺎﻗ ﺖﻓﺎﺑ ﺮﺑ ﯿ

ﺑ ﺶ ﯿﻨ ﯽ ﻌﺗ ،ﺖﺳا ﯿﯿ ﺧ و دورو نﺎﻣز ﻦ جوﺮ

ا رد لﻮﺼﺤﻣ ﯾ

ﻦ ﺎﻣد هزﺎﺑ ﯽﯾ ﻤﻫا ﯿ دراد ﺖ 23]

دﺎﻤﺠﻧا نﺎﻣز و [

ﻤﺳا ﯽ ﻤﻫ سﺎﺳا ﺮﺑ ﯿ

ﻌﺗ ﺺﺧﺎﺷ ﻦ ﯿﯿ

ﻦ ﻣ ﯽ ﺷ ﻮ د ) لوﺪﺟ 2 .(

(6)

Table 1 Thermo-physical data for hamburger patty

Property Value

Thermal conductivity of unfrozen product 0.47 W/m. ôC Thermal conductivity of frozen product 1.56 W/m.ôC Heat capacity of unfrozen product 3100 J/kg. ôC Heat capacity of frozen product 1500 J/kg. ôC Density of unfrozen product 1045 kg/m³

Density of frozen product 1010 kg/m³

Latent heat of fusion 333600 J/kg

Bound water 5%

Initial freezing point -2.52 ^oC

Moisture content 66.3%

Protein content 14.2%

Initial temperature 20 ^oC

Heat transfer coefficient 15 W/m^2oC Number of node in axial and radial direction 11

Table 2 Experimental test conditions and results for ground beef patty freezing

Freezing

method

Medium temperature

(^oC)

Surface heat transfer coefficient (W/m². ^oC)

Sample thickness

(mm)

Freezing rate (^oC/min)

Nominal freezing time

(min)

Effective freezing

time (min)

Air blast -18 15 18.0 0.22 77 min 113 min

Air blast -35 15 18.0 0.71 24 min 41 min

ﻐﺗ ﯿﯿ تاﺮ ﺎﻣﺮﮔ ي و ﯾ هﮋ ﻌﺑﺎﺗ ناﻮﻨﻋ ﻪﺑ ﺮﮔﺮﺒﻤﻫ ﯽ

ﺎﻣد زا ي دﺎﻤﺠﻧا ﻪﮐ

تﻻدﺎﻌﻣ زا 4

- 8 ﺪﺑ ﻞﮑﺷ رد ﺖﺳا هﺪﻣآ ﺖﺳ 1

هﺪﺷ هداد نﺎﺸﻧ

ﺖﺳا . ﻐﺗ سﺎﺳا ﺮﺑ ﯿﯿ

ﺎﻣﺮﮔ تاﺮ ي و ﯾ ﺮﻫﺎﻇ هﮋ ي دﺎﻤﺠﻧا ﻪﻄﻘﻧ ،ﻪﻧﻮﻤﻧ

ﻟوا ﯿ لﻮﺼﺤﻣ ﻪ 52

/ 2 - ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ رادﻮﻤﻧ ﺮﺜﮐاﺪﺣ و )

ﻪﻠﻗ ( ﻧﯿ ﺰ

دوﺪﺣ رد 68

/ 38 ﮐ ﯿ ﮐ ﺮﺑ لوژﻮﻠ ﯿ

ﻮﻠﮐ مﺮﮔﻮﻠ ﯾ

ﻌﺗ ﻦ ﯿﯿ ﺪﺷ ﻦ ﻪﮐ ﺎﺑ

ﺎﺘﻧ ﯾ ﻂﺳﻮﺗ هﺪﻣآ ﺖﺳد ﻪﺑ ﺞ Tavman

نارﺎﮑﻤﻫ و )

2007 (

ﺖﻬﺑﺎﺸﻣ ﺖﺷاد . ﺎﺘﻧ سﺎﺳا ﺮﺑ ﯾ

ا ﺞ ﯾ ﻘﻘﺤﻣ ﻦ ﯿ ﻣ ﻦ ﯿ دﺎﻤﺠﻧا ﻪﻄﻘﻧ ناﺰ

ﻟوا ﯿ ﺎﻣﺮﮔ ﺮﺜﮐاﺪﺣ راﺪﻘﻣ و ﻪ ي

و ﯾ ﺮﻫﺎﻇ هﮋ ي و ﺮﮔﺮﺒﻤﻫ ﻪﻧﻮﻤﻧ

ﺗﺮﺗ ﻪﺑ هدﺮﮐ خﺮﭼ ﺖﺷﻮﮔ ﯿ

ﺎﺑ ﺮﺑاﺮﺑ ﺐ 6/

2 - و 3/

2 - ﻪﺟرد

ﯽﺘﻧﺎﺳ داﺮﮔ و 3/

26 و 8/

32 ﮐ ﯿ ﮐ ﺮﺑ لوژﻮﻠ ﯿ

ﻌﺗ مﺮﮔﻮﻠ ﯿﯿ دﻮﺑ هﺪﺷ ﻦ .

ﺑ توﺎﻔﺗ ﯿ ﺎﺘﻧ ﻦ ﯾ ا ﺞ ﯾ ﻘﺤﺗ ﻦ ﯿ ﺎﺘﻧ و ﻖ ﯾ ا تﺎﻋﻼﻃا زا ﻞﺻﺎﺣ ﺞ ﯾ

ﻦ

ﻘﻘﺤﻣ ﯿ ﻦ ﯽﻣ ﺪﻧاﻮﺗ ﮐﺮﺗ رد توﺎﻔﺗ ﻪﺑ طﻮﺑﺮﻣ ﯿ

ﺷ تﺎﺒ ﯿ ﺎﻤ ﯽﯾ ﻪﻧﻮﻤﻧ ﺎﻫ

ﺪﺷﺎﺑ 24] . [ نﺎﻤﻫ رﻮﻃ و داﻮﻣ ﺶﺨﺑ رد ﻪﮐ شور

ﺎﻫ ﺑ ﯿ اﺮﺑ ،ﺪﺷ نﺎ ي

اﺪﻫ ﯾ ﺗراﺮﺣ ﺖ ﯽ ﺎﻣد رد ﻪﻧﻮﻤﻧ ي

ز ﯾ ﺗ لﺪﻣ زا دﺎﻤﺠﻧا ﻪﻄﻘﻧ ﺮ ﮐﺮ

ﯿﺒ ﯽ و

اﺮﺑ ي ﺎﻣد ي ﻻﺎﺑ ي زاﻮﻣ لﺪﻣ زا دﺎﻤﺠﻧا ﻪﻄﻘﻧ ي

ﺪﺷ هدﺎﻔﺘﺳا .

ﻪﺟﻮﺗ ﺎﺑ

ا ﻪﺑ ﯾ ﻪﮑﻨ زاﻮﻣ لﺪﻣ ي ﻣ ﺮﺜﮐاﺪﺣ ﯿ اﺪﻫ ناﺰ ﯾ ﺗراﺮﺣ ﺖ ﯽ اﺬﻏ داﻮﻣ ﯽﯾ و

ﺮﺳ لﺪﻣ ي اﺪﻫ ﻞﻗاﺪﺣ ﯾ

ﺗراﺮﺣ ﺖ ﯽ اﺬﻏ داﻮﻣ ﯽﯾ ﭘ ار ﯿ ﺑ ﺶ ﯿﻨ ﯽ

ﯽﻣ ﺪﻨﮐ

، ﮐﺮﺗ لﺪﻣ رد ﯿﺒ

ﯽ اﺪﻫ ﯾ ﺗراﺮﺣ ﺖ ﯽ اﺰﺟا ي ﻏ ﯿ ﺎﻣ ﺮ ﯾ ﻪﺑ بآ ﻊ

زاﻮﻣ ترﻮﺻ ي

و هﺪﺷ دروآﺮﺑ ﺮﺳ لﺪﻣ ﺎﺑ ﺲﭙﺳ ﺎﺑ

ي ﮐﺮﺗ ﯿ ﺐ ﯽﻣ

دﻮﺷ . اﺰﻓا ﯾ ﻣ رد ﻪﺟﻮﺗ ﻞﺑﺎﻗ ﺶ ﯿ

اﺪﻫ ناﺰ ﯾ ﺗراﺮﺣ ﺖ ﯽ رد لﻮﺼﺤﻣ

ﺎﻫﺎﻣد ي ز ﯾ ﻪﺟرد ﺮﻔﺻ ﺮ ﯽﻣ

ﺪﻧاﻮﺗ ﻪﺑ ﻣ ﯿ ناﺰ ﯾ ﮑﺸﺗ ﺦ ﯿ رد هﺪﺷ ﻞ

ﺎﻫﺎﻣد ي ز ﯾ ﺮﻔﺻ ﺮ هداد طﺎﺒﺗرا دﻮﺷ

) ﺮﺴﮐ رادﻮﻤﻧ ﯾ

ﺨ ﯽ لﻮﺼﺤﻣ (

زﯾ اﺪﻫ اﺮ ﯾ ﺗراﺮﺣ ﺖ ﯽ ﯾ ﺦ

ًﺎﺒﯾﺮﻘﺗ 4 اﺪﻫ ﺮﺑاﺮﺑ ﯾ ﺗراﺮﺣ ﺖ ﯽ بآ

ﯽﻣ ﺪﺷﺎﺑ 18] . [

ﻞﮑﺷ 3 ﻓوﺮﭘ ﯿ ﺎﻣد ﻞ ي نﺎﺸﻧ ار دﺎﻤﺠﻧا نﺎﻣز ﺮﺑاﺮﺑ رد لﻮﺼﺤﻣ

ﯽﻣ ﺪﻫد . ﻤﻬﻣ ﺶﻘﻧ دﺎﻤﺠﻧا ﺖﻋﺮﺳ ﯽ

ﮐ رد ﯿﻔ ﯿ اﺬﻏ داﻮﻣ ﺖ ﯽﯾ

و دراد

اﺰﻓا ﺎﺑ ﯾ ﻟد ﻪﺑ دﺎﻤﺠﻧا ﺖﻋﺮﺳ ﺶ ﯿ

هزاﺪﻧا ﺶﻫﺎﮐ ﻞ لﺎﺘﺴﯾﺮﮐ

يﺎﻫ ﯾ ،ﺦ

ﮐﯿ ﻔﯿ اﺬﻏ هدﺎﻣ ﺖ ﯽﯾ

دﻮﺒﻬﺑ ﯽﻣ ﺪﺑﺎﯾ . ا ﺮﺑ ﯾ ﻪﮐ رﻮﻃ نﺎﻤﻫ سﺎﺳا ﻦ

رﺎﻈﺘﻧا ﯽﻣ دور ﻣد رد دﺎﻤﺠﻧا ﺖﻋﺮﺳ ﺎ

ي 35 - ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ

دوﺪﺣ 2/

3 ﺑ ﺮﺑاﺮﺑ ﯿ ﺎﻣد زا ﺮﺘﺸ ي

18 - ﻪﺟرد ﯽﺘﻧﺎﺳ داﺮﮔ ﺖﺳا .

ﺮﻌﺗ سﺎﺳا ﺮﺑ دﺎﻤﺠﻧا ﺖﻋﺮﺳ ﯾ

ﻒ ) IIR ﻪﺴﺳﻮﻣ ﺑﯿ ﻦ ﻠﻠﻤﻟا ﯽ ﺮﺒﺗ ﯾ ﺪ (

ﻧﯿ ﻌﺗ ﺰ ﯿﯿ ﺪﺷ ﻦ . ا ﺮﺑ ﯾ ﺎﺳا ﻦ ﺎﻣد ود رد ﻪﻧﻮﻤﻧ دﺎﻤﺠﻧا ﺖﻋﺮﺳ س ي

ﺗﺮﺗ ﻪﺑ رﻮﮐﺬﻣ ﯿ

ﺐ 6/

0 و 9/

1 ﺘﻧﺎﺳ ﯽ ﻌﻣ ﺖﻋﺎﺳ ﺮﺑ ﺮﺘﻣ ﯿ

دﺮﮔ ﻦ ﯾ ﻪﮐ ﺪ

ﺗﺮﺗ ﻪﺑ ﯿ ﺎﺸﻧ ﺐ ﺪﻨﮐ دﺎﻤﺠﻧا هﺪﻨﻫد ن ﺮﺳ دﺎﻤﺠﻧا و 1

ﯾ

2ﻊ ﻣ ﯽ ﺪﺷﺎﺑ .

اﺮﺷ ﯾ ﺎﻣزآ ﻂ ﯾ ﺎﺳ و تﺎﺸ ﯾ

ﺎﺘﻧ ﺮ ﯾ ﺑ هﺪﻣآ ﺖﺳد ﻪﺑ ﺞ ﯿ

ﺎﻣد ود ﻦ ي رﺎﮑﺑ

1. Slow freezing 2. Quick freezing

(7)

لوﺪﺟ رد هﺪﺷ ﻪﺘﻓﺮﮔ 2

ﺖﺳا هﺪﺷ ﻪﺋارا 25]

.[ ﺮﺿ ﯾ لﺎﻘﺘﻧا ﺐ

ود ﺎﺑ ﺢﻄﺳ رد تراﺮﺣ ر

دﺮﮔ دروآﺮﺑ ﻒﻠﺘﺨﻣ شو ﯾ

،ﺪ دﺪﻋ راﺪﻘﻣ ي

اﯾ ﺮﺿ ﻦ ﯾ هزاﺪﻧا شور رد ﺐ ﮔﯿ

ﺮ ي دوﺪﺣ هﺪﺷ 15

ﺘﻣ ﺮﺑ تاو ﺮ

ﻪﺟرد ﻊﺑﺮﻣ ﺘﻧﺎﺳ

ﯽ داﺮﮔ شور رد و داﺪﻋا

ﺪﻌﺑ نوﺪﺑ ﻪﮐ

هدﺎﻔﺘﺳا ﺎﺑ

ﻪﻟدﺎﻌﻣ زا ) 10 ( دوﺪﺣ ﺪﺷ ﻞﺻﺎﺣ 96

/ 10 ﺮﺑ تاو ﻊﺑﺮﻣ ﺮﺘﻣ ﻪﺟرد ﺘﻧﺎﺳ

ﯽ داﺮﮔ آﺮﺑ درو ﺪﺷ ﻟد ، ﯿ ا ﻞ ﯾ فﻼﺘﺧا ﻦ ﻣ

ﯽ ﺪﻧاﻮﺗ ﻪﺑ تﺪﺷ

ﺮﺟ شﺎﺸﺘﻏا ﯾ

دﺎﻤﺠﻧا ﻪﻈﻔﺤﻣ ﻞﺧاد رد ﺖﻋﺮﺳ نﺎﺳﻮﻧ ﺮﺛا رد اﻮﻫ نﺎ

ﻂﺒﺗﺮﻣ ﺪﺷﺎﺑ . ا ﺮﺑ هوﻼﻋ ﯾ

نﺎﻤﻫ ﻦ رﻮﻃ ﻞﮑﺷ رد ﻪﮐ 3

هﺪﻫﺎﺸﻣ

ﯽﻣ دﻮﺷ

، يﺎﻣد ﺢﻄﺳ ﻪﻧﻮﻤﻧ ﻞﯿﻟد ﻪﺑ زﺮﻣ طﺮﺷ ي ﺘﻓﺮﻤﻫ ﯽ اﻮﻫ

ﻊﯾﺮﺳ ﺮﺗ زا ﺰﮐﺮﻣ ﻪﻧﻮﻤﻧ اﺰﻓا ﯾ ﺶ ﯾ ﻪﺘﻓﺎ ﺖﺳا .

Fig 2 Thermophysical properties of Hamburger patty as a function of temperature: ice fraction, apparent specific heat and thermal conductivity.

ﻞﮑﺷ 4 ﻪﺴﯾﺎﻘﻣ يا ﺑ ﯿ ﺎﺘﻧ ﻦ ﯾ ﻞﺿﺎﻔﺗ ،دوﺪﺤﻣ ءاﺰﺟا لﺪﻣ زا ﻞﺻﺎﺣ ﺞ

ﺎﺘﻧ و دوﺪﺤﻣ ﯾ

ﺑﺮﺠﺗ ﺞ ﯽ ﺖﺳا . نﺎﻤﻫ رﻮﻃ هﺪﻫﺎﺸﻣ ﻪﮐ ﯽﻣ

دﻮﺷ رد

ﮕﺘﺴﺒﻤﻫ عﻮﻤﺠﻣ ﯽ

ﺑﻮﺧ قﺎﺒﻄﻧا و ﯽ

ﺑ ﯿ ﻦ هداد يﺎﻫ دﺪﻋ لﺪﻣ ي

و

ﺎﺘﻧ ﯾ ﺑﺮﺠﺗ ﺞ ﯽ دراد دﻮﺟو .

ﻟو ﯽ ا ﯾ اﺰﻓا ﺎﺑ ،قﺎﺒﻄﻧا ﻦ ﯾ

نﺎﻣز ﺶ هﮋﯾو ﻪﺑ

ﺑ ﺶﻫﺎﮐ ﺢﻄﺳ رد ﯿ

ﺮﺘﺸ ي نﺎﺸﻧ ار ﯽﻣ ﺪﻫد ﻪﮐ ﯽﻣ ﺪﻧاﻮﺗ ﻟد ﻪﺑ ﯿ ﻞ

ﺪﭘ ﯾ ﺷﺎﻧ مﺮﺟ لﺎﻘﺘﻧا هﺪ ﯽ

ﻌﺼﺗ زا ﯿ و ﺪ ﯾ ﺨﺒﺗ ﺎ ﯿ رد ﺮﮔﺮﺒﻤﻫ بآ ﺮ

ﺮﻓ ﯾ ﺖﺳا هﺪﺸﻧ ظﺎﺤﻟ لﺪﻣ رد ﻪﮐ ﺪﺷﺎﺑ رﺰ .

ا ﺮﺑ هوﻼﻋ ﯾ ﻦ نﺎﻤﻫ رﻮﻃ

ﻞﮑﺷ زا ﻪﮐ 4

هﺪﻫﺎﺸﻣ ﯽﻣ دﻮﺷ ﺑ ﺖﻗد زا دوﺪﺤﻣ ءاﺰﺟا لﺪﻣ ﯿ

ﺮﺘﺸ ي رادرﻮﺧﺮﺑ دوﺪﺤﻣ ﻞﺿﺎﻔﺗ لﺪﻣ ﻪﺑ ﺖﺒﺴﻧ ﺎﻣد دروآﺮﺑ رد

ﯽﻣ ﺪﺷﺎﺑ و

اﯾ ﺮﻃ زا عﻮﺿﻮﻣ ﻦ ﯾ

ﻖ ﺺﺧﺎﺷ يﺎﻫ رﺎﻣآ ي ﻧ ﯿ ﻪﺑ ،ﺪﺷ هﺪﻫﺎﺸﻣ ﺰ

ﻪﮐ يرﻮﻃ ﻣ ﯿ ﮕﻧﺎ ﯿ ر ﻦ ﯾ ﻣ ﻪﺸ ﯿ ﮕﻧﺎ ﯿ ﺮﺿ و ﺎﻄﺧ تﺎﻌﺑﺮﻣ ﻦ ﯾ

ﻌﺗ ﺐ ﯿﯿ ﻦ

ﺑﯿ ﺎﺘﻧ و دوﺪﺤﻣ ءاﺰﺟا لﺪﻣ ﻦ ﯾ

ﺑﺮﺠﺗ ﺞ ﯽ ﺗﺮﺗ ﻪﺑ ﯿ ﺎﺑ ﺮﺑاﺮﺑ ﺐ 953

/1 و

96 /0 ﯽﻣ ﺪﺷﺎﺑ دﺎﻘﻣ و ﯾ اﺮﺑ قﻮﻓ ﺮ ي

ﺎﺘﻧ و دوﺪﺤﻣ ﻞﺿﺎﻔﺗ لﺪﻣ ﯾ

ﺞ

ﺑﺮﺠﺗ ﯽ ﺗﺮﺗ ﻪﺑ ﯿ ﺎﺑ ﺮﺑاﺮﺑ ﺐ 025

/ 3 و 89 / 0 ﻖﺑﺎﻄﺗ هﺪﻨﻫد نﺎﺸﻧ ﻪﮐ دﻮﺑ

ﺎﺘﻧ ﺎﺑ دوﺪﺤﻣ ءاﺰﺟا لﺪﻣ ﺮﺘﻬﺑ ﯾ

ﺑﺮﺠﺗ ﺞ ﯽ ﯽﻣ ﺪﺷﺎﺑ .

(8)

Fig 3 Temperature profile of Hamburger patties at two selected freezing medium temperature at center

and surface nodes

4 - ﺘﻧﯿ ﮔ ﻪﺠ ﯿﺮ ي

ا رد ﯾ آﺮﻓ ،ﻪﻌﻟﺎﻄﻣ ﻦ ﯾ

ﺮﮔﺮﺒﻤﻫ دﺎﻤﺠﻧا ﺪﻨ ﻌﺗ و

ﯿﯿ ﻦ دﺎﻤﺠﻧا نﺎﻣز تﺪﻣ

لﻮﺼﺤﻣ دﺪﻋ شور ود ﺎﺑ ي

ﻒﻠﺘﺨﻣ ) ءاﺰﺟا و دوﺪﺤﻣ ﻞﺿﺎﻔﺗ

دوﺪﺤﻣ ( ﺳرﺮﺑ درﻮﻣ ﯽ

ﺎﺘﻧ و ﺖﻓﺮﮔ راﺮﻗ ﯾ

ﺎﺑ ﺞ هداد يﺎﻫ ﺑﺮﺠﺗ ﯽ

ﺎﻘﻣ ﯾ ﻪﮐ ﺪﺷ ﺺﺨﺸﻣ و ﺪﺷ ﻪﺴ د ﺮﻫ ﻪﭼﺮﮔا

و ﺑﻮﺧ ﺖﻗد ﺎﺑ شور ﯽ

ﭘ ﻪﺑ ردﺎﻗ ﯿ ﺑ ﺶ ﯿﻨ ﯽ ﻃ رد لﻮﺼﺤﻣ زا ﻪﻄﻘﻧ ﺮﻫ رد ﺎﻣد ﯽ

اﺮﻓ ﯾ ﻐﺗ ﺪﻨ ﯿﯿ ﺮ

زﺎﻓ ﯽﻣ ﺪﻨﺷﺎﺑ ﻟو ﯽ ﺎﻣد ي ﭘ ﯿ ﺑ ﺶ ﯿﻨ ﯽ شور زا هدﺎﻔﺘﺳا ﺎﺑ هﺪﺷ ءاﺰﺟا

دوﺪﺤﻣ ﻖﯿﻗد ﺮﺗ ﺖﺳا دوﺪﺤﻣ ﻞﺿﺎﻔﺗ شور زا .

ﺎﺑ ﻪﺑ يﺮﯿﮔرﺎﮐ لﺪﻣ

ﻪﻌﺳﻮﺗ ﯾ ﻪﺘﻓﺎ ﯽﻣ ناﻮﺗ ﺎﻣد و دﺎﻤﺠﻧا نﺎﻣز تﺪﻣ زا ﻪﻄﻘﻧ ﺮﻫ رد

ﻌﺑﺎﺗ ناﻮﻨﻋ ﻪﺑ ار ﺮﮔﺮﺒﻤﻫ ﯽ

ﺒﻗ زا ﻒﻠﺘﺨﻣ ﻞﻣاﻮﻋ زا ﯿ

ﻪﺟرد ﻞ

تراﺮﺣ يﺎﻫ ﻒﻠﺘﺨﻣ ﺮﻓ ﯾ رﺰ ﯾ اﺮﺿ ﺎ ﯾ تراﺮﺣ لﺎﻘﺘﻧا ﻒﻠﺘﺨﻣ ﺐ

ﺘﻓﺮﻤﻫ ﯽ رد ﺮﻓ ﯾ رﺰ و ﯾ ﺎﻫﺪﺻرد ﺎﺑ ﺮﮔﺮﺑ تﻻﻮﺼﺤﻣ عاﻮﻧا ﺎ ي

ﺌﺗوﺮﭘ ﻒﻠﺘﺨﻣ ﯿ

ﻦ ﻌﺗ ار ﯿﯿ دﻮﻤﻧ ﻦ .

Fig 4 Comparison between temperature profiles of Hamburger patties between finite element and finite

difference at center and surface ﺪﻌﺑ مﺎﮔ رد

ي ا ﯾ ﻘﺘﻧا تﻻدﺎﻌﻣ ندﺮﮐ ﻞﭘﻮﮐ ﺎﺑ ﻪﻌﻟﺎﻄﻣ ﻦ مﺮﺟ لﺎ

ﺷﺎﻧ ﯽ ﻌﺼﺗ زا ﯿ رد ﺪ ﺣ ﯿ ار لﺪﻣ ﺖﻗد دﺎﻤﺠﻧا ﻦ ﯽﻣ

ناﻮﺗ اﺰﻓا ﯾ داد ﺶ .

5 - تارﺎﺼﺘﺧا و ﻢﺋﻼﻋ

Cp Specific heat (J/kg.K)

هﮋﯾو يﺎﻣﺮﮔ

) لوژ / ﻦﯾﻮﻠﮐ مﺮﮔﻮﻠﯿﮐ (

h

Averaged heat transfer coefficient at

surface (W/m².K)

تراﺮﺣ لﺎﻘﺘﻧا ﺐﯾﺮﺿ ﻦﯿﮕﻧﺎﯿﻣ ﺢﻄﺳ رد

) تاو / ﻊﺑﺮﻣ ﺮﺘﻣ ﻦﯾﻮﻠﮐ ( k Thermal conductivity

(W/m.K)

ﯽﺗراﺮﺣ ﺖﯾاﺪﻫ

) ﻦﯾﻮﻠﮐ ﺮﺘﻣ ﺮﺑ تاو (

L Latent heat of fusion (J/kg)

ﺦﯾ بوذ نﺎﻬﻧ يﺎﻣﺮﮔ

) مﺮﮔﻮﻠﯿﮐ ﺮﺑ لوژ (

r Radial coordination ﯽﻋﺎﻌﺷ تﺎﺼﺘﺨﻣ R² Determination of

coefficient ﻦﯿﯿﺒﺗ ﺐﯾﺮﺿ RMSE Root mean square of

error ﺎﻄﺧ تﺎﻌﺑﺮﻣ ﻦﯿﮕﻧﺎﯿﻣ ﻪﺸﯾر t Time (min, s) (ﻪﻘﯿﻗد - ﻪﯿﻧﺎﺛ) نﺎﻣز T Temperature (^oC, K) ( ﻦﯾﻮﻠﮐ -داﺮﮔﯽﺘﻧﺎﺳ ) ﺎﻣد x

Mass fraction of chemical composition of

hamburger

ﯽﯾﺎﯿﻤﯿﺷ ياﺰﺟا ﯽﻣﺮﺟ ﺮﺴﮐ ﺮﮔﺮﺒﻤﻫ Z Axial coordination ﯽﻟﻮﻃ تﺎﺼﺘﺨﻣ

Greek letters ﯽﻧﺎﻧﻮﯾ فوﺮﺣ

ν Volume fraction ﯽﻤﺠﺣ ﺮﺴﮐ

ρ Density (kg/m³) ﺐﻌﮑﻣ ﺮﺘﻣ ﺮﺑ مﺮﮔﻮﻠﯿﮐ ﻪﺘﯿﺴﻧاد Subscript ﺲﯾﻮﻧ ﺮﯾز

B Bound هﺪﺷ ﺪﻧﺎﺑ

c Carbohydrate تارﺪﯿﻫﻮﺑﺮﮐ

exp Experimental ﯽﺸﯾﺎﻣزآ

f Freezing temperature دﺎﻤﺠﻧا يﺎﻣد

i Chemical

composition, ice ﺦﯾ - ﯽﯾﺎﯿﻤﯿﺷ ياﺰﺟا LW Water in liquid state ﻊﯾﺎﻣ ﺖﻟﺎﺣ رد بآ

p Protein ﻦﯿﺌﺗوﺮﭘ

pre Predicted هﺪﺷ ﯽﻨﯿﺑ ﺶﯿﭘ

s Solid materials ﺪﻣﺎﺟ داﻮﻣ

tw Total water بآ ﻞﮐ

w Water بآ

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6 - ﻊﺑﺎﻨﻣ

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Comparison of two different numerical modeling for predicting the temperature of hamburger patty during freezing process.

Dalvi Isfahan, M. ¹, Daraei Garmakhany, A. ^2*

1. Assistant professor, Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Jahrom, Iran.

2. Assistant professor, Department of Food Science and Technology, Tuyserkan Faculty of Engineering & Natural Resources, Bu-Ali Sina University, Hamedan, Iran.

ABSTRACT ARTIClE INFO

Article History:

Received 2020/ 10/ 09 Accepted 2021/ 02/ 27 Keywords:

Finite Element, Heat transfer, Freezing, Finite difference, Hamburger.

Hamburgers are one of the most widely consumed meat products in the world. The shelf life of this product is rather short, therefore the freezing process is commonly used to reduce water activity and prevent the growth of microorganisms. Accurate temperature prediction during freezing is important in designing optimum cooling procedures and to avoid quality deterioration. Models for predicting freezing times range from relatively simple analytical equations to the more complicated numerical methods which require a lot of computing time and a sophisticated computer. In this research, thermal properties of hamburger, including ice fraction, thermal conductivity and specific heat were determined mathematically and then the freezing process of hamburger patty was investigated by two different numerical models (finite difference& finite element). The results were compared with experimental data and it was found that although both two models could reasonably forecast the temperature of hamburger patties during freezing, the finite element model demonstrated better goodness of fit than finite difference model. This study shows that the use of CFD packages such as COMSOL software can be considered as a suitable option for the estimation of freezing time of meat products.

DOI: 10.29252/fsct.18.06.28

*Corresponding Author E-Mail:

[email protected]

Iranian Journal of Food Science and Technology

Homepage:www.fsct.modares.ir

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