‫ﺑﺴﻤﻪ ﺗﻌﺎﻟﻲ‬ ‫داﻧﺸﮕﺎه آزاد اﺳﻼﻣﻲ واﺣﺪ ﭘﺮﻧﺪ‬

‫ﻋﻨﻮان درس‪ :‬اﻧﺘﻘﺎل ﺣﺮارت ‪1‬‬

‫ﻧﻴﻤﺴﺎل‪ :‬ﺗﺎﺑﺴﺘﺎن ‪93‬‬

‫‪Home Work 3‬‬

‫ﻣﻘﻄﻊ‪ :‬ﻛﺎرﺷﻨﺎﺳﻲ ﻣﻬﻨﺪﺳﻲ ﻣﻜﺎﻧﻴﻚ‬

‫ﻧﺎم اﺳﺘﺎد‪ :‬ﻣﻮﻣﻨﻲ ﻣﻮﺣﺪ‬

‫‪100ºC‬‬ ‫‪1m‬‬

‫‪1‬‬

‫ﻳﻚ ورق ﻓﻮﻻدي ﺑﻪ ﻃﻮل ﻳﻚ ﻣﺘﺮ و ﺿﺮﻳﺐ ﻫﺪاﻳﺖ ‪ 50W/m.K‬ﻛﻪ از‬ ‫ﻃﺮﻓﻴﻦ ﻛﺎﻣﻼ ﻋﺎﻳﻘﻜﺎري ﺷﺪه را در ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﺳﻄﺢ ﺑﺎﻻﻳﻲ اﻳﻦ ورق در‬ ‫‪85ºC‬‬ ‫دﻣﺎي ‪ 100ºC‬ﻗﺮار داﺷﺘﻪ و ﺳﻄﺢ ﭘﺎﻳﻴﻨﻲ ﺗﺤﺖ ﺳﺮﻣﺎﻳﺶ ﺟﺎﺑﺠﺎﻳﻲ ﺑﺎ‬ ‫ﺳﻴﺎﻟﻲ ﺑﻪ دﻣﺎي ‪ 20ºC‬ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ‪ .‬در ﺷﺮاﻳﻂ داﺋﻢ و ﺑﺪون ﺗﻮﻟﻴﺪ‬ ‫اﻧﺮژي‪ ،‬ﺗﺮﻣﻮﻛﻮﭘﻞ واﻗﻊ در وﺳﻂ ورق‪ ،‬دﻣﺎي ‪ 85ºC‬را ﻣﻲﺧﻮاﻧﺪ‪ .‬ﻣﻘﺪار‬ ‫ﺿﺮﻳﺐ ﺟﺎﺑﺠﺎﻳﻲ در ﺳﻄﺢ ﭘﺎﻳﻴﻨﻲ ﭼﻘﺪر اﺳﺖ؟‬

‫‪T∞=20ºC, h‬‬

‫ﻫﻮاي داﺧﻞ ﻳﻚ ﻣﺤﻔﻈﻪ ﺑﺎ دﻣﺎي ‪ T∞,i=50ºC‬ﺗﺤﺖ ﮔﺮﻣﺎﻳﺶ ﺟﺎﺑﺠﺎﻳﻲ ﺑﻪ ﺿﺮﻳﺐ ‪ hi=20W/m².K‬ﺑﺎ دﻳﻮاري‬ ‫ﺑﻪ ﺿﺨﺎﻣﺖ ‪ 200 mm‬ﺿﺮﻳﺐ ﻫﺪاﻳﺖ ‪ 4 W/m.K‬و ﺗﻮﻟﻴﺪ ﮔﺮﻣﺎي ﻳﻜﻨﻮاﺧﺖ ‪ 1000 W/m³‬ﻗﺮار دارد‪ .‬ﺑﻪ ﻣﻨﻈﻮر‬ ‫ﺟﻠﻮﮔﻴﺮي از ﺑﻴﺮون رﻓﺘﻦ ﮔﺮﻣﺎي ﺗﻮﻟﻴﺪ ﺷﺪه ﺑﻪ ﺧﺎرج ﻣﺤﻔﻈﻪ ﻛﻪ داراي دﻣﺎي ‪ T∞,o=25ºC‬و ﺻﺮﻳﺐ ﺟﺎﺑﺠﺎﻳﻲ‬ ‫‪ ho=5W/m².K‬اﺳﺖ ﮔﺮﻣﻜﻦ اﻟﻜﺘﺮﻳﻜﻲ ﺑﺴﻴﺎر ﻧﺎزﻛﻲ روي دﻳﻮار ﺑﻴﺮوﻧﻲ ﻛﺎر ﮔﺬاﺷﺘﻪ ﺷﺪه اﺳﺖ ﻛﻪ ﺷﺎر ﮔﺮﻣﺎي‬ ‫ﻳﻜﻨﻮاﺧﺖ ً‪ qo‬را ﺗﻮﻟﻴﺪ ﻣﻲﻛﻨﺪ‪.‬‬

‫‪2‬‬

‫اﻟﻒ( ﺗﻮزﻳﻊ دﻣﺎي دﻳﻮار را روي ﻣﺨﺘﺼﺎت ‪ T-x‬ﺑﺮاي ﺷﺮاﻳﻄﻲ رﺳﻢ ﻛﻨﻴﺪ ﻛﻪ ﮔﺮﻣﺎي ﺗﻮﻟﻴﺪ ﺷﺪه ﺑﻪ ﺑﻴﺮون از ﻣﺤﻔﻈﻪ‬ ‫ﻣﻨﺘﻘﻞ ﻧﻤﻲﺷﻮد‪.‬‬ ‫ب( ﺑﺮاي ﺷﺮاﻳﻂ ﻗﺴﻤﺖ اﻟﻒ‪ ،‬دﻣﺎي ﻣﺮزﻫﺎي دﻳﻮار‪ T(0) ،‬و )‪ T(L‬را ﭘﻴﺪا ﻛﻨﻴﺪ‪.‬‬ ‫ج( ﻣﻘﺪار ً‪ qo‬ﺟﻘﺪر ﺑﺎﺷﺪ ﺗﺎ ﺗﻤﺎﻣﻲ ﮔﺮﻣﺎي ﺗﻮﻟﻴﺪ ﺷﺪه در دﻳﻮار ﺑﻪ داﺧﻞ ﻣﺤﻔﻈﻪ ﻣﻨﺘﻘﻞ ﺷﻮد‪.‬‬ ‫د( اﮔﺮ ﺗﻮﻟﻴﺪ ﮔﺮﻣﺎ در دﻳﻮار ﻗﻄﻊ ﺷﻮد و در ﻫﻤﺎن ﺣﺎل ﺷﺎر ﮔﺮﻣﺎ در ﮔﺮﻣﻜﻦ ﺛﺎﺑﺖ ﺑﻤﺎﻧﺪ‪ ،‬دﻣﺎي داﺋﻢ در ﺳﻄﺢ ﺧﺎرﺟﻲ‬ ‫دﻳﻮار )‪ ،T(0‬ﭼﻘﺪر ﺧﻮاﻫﺪ ﺷﺪ؟‬

‫ﻣﻮﻓﻖ ﺑﺎﺷﻴﺪ ‪ -‬ﻣﻮﻣﻨﻲ‬

1 > : Home Work 3 : 93 : @> 50W/mK ...

20ºC . > > > <@. @ > <. 85ºC . = >. 1. 2. T∞=20ºC, h. 85ºC. 100ºC. 1 m. @ > > @. T∞,i=50ºC hi=20W/m².K. @ >. 200 mm. 4 W/m.K. @. 1000 W/m³. > > . @ > @ > > @ @. T∞,o=25ºC ho=5W/m².K. > @. @. @ qo . (. > @ > @ >. T-x. @ @. > . (. < > @ @ > < @. T(0). T(L) . > (. @ qo. > > > > @ . > (. > > @ > < > > > > >. > T(0). = <

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