‫ﺑﺴﻤﻪ ﺗﻌﺎﻟﻲ‬ ‫داﻧﺸﮕﺎه آزاد اﺳﻼﻣﻲ واﺣﺪ ﭘﺮﻧﺪ‬

‫ﻋﻨﻮان درس‪ :‬اﻧﺘﻘﺎل ﺣﺮارت ‪1‬‬ ‫ﻧﺎم اﺳﺘﺎد‪ :‬ﻣﻮﻣﻨﻲ ﻣﻮﺣﺪ‬

‫‪Home Work 2‬‬

‫ﻧﻴﻤﺴﺎل‪ :‬ﺗﺎﺑﺴﺘﺎن ‪93‬‬ ‫ﻣﻘﻄﻊ‪ :‬ﻛﺎرﺷﻨﺎﺳﻲ ﻣﻬﻨﺪﺳﻲ ﻣﻜﺎﻧﻴﻚ‬

‫‪1‬‬

‫ﺳﻄﺤﻲ ﺑﻪ دﻣﺎي ‪ 400˚C‬ﺗﻮﺳﻂ ﻻﻳﻪاي از ﻋﺎﻳﻖ ﺑﻪ ﺿﺨﺎﻣﺖ ‪ 25 mm‬و ﺿﺮﻳﺐ ﻫﺪاﻳﺖ ‪ 0.1W/m.K‬از ﺟﺮﻳﺎن‬ ‫ﻫﻮا ﺟﺪا ﺷﺪه اﺳﺖ‪ .‬اﮔﺮ دﻣﺎي ﻫﻮا ‪ 35˚C‬و ﺿﺮﻳﺐ ﺟﺎﺑﺠﺎﻳﻲ ﺑﻴﻦ ﻫﻮا و ﺳﻄﺢ ﺧﺎرﺟﻲ ﻋﺎﻳﻖ ‪ 500 W/m².K‬ﺑﺎﺷﺪ‪،‬‬ ‫دﻣﺎي ﺳﻄﺢ ﺧﺎرﺟﻲ را ﺑﻴﺎﺑﻴﺪ‪.‬‬

‫‪2‬‬

‫در ﻳﻚ ﻟﺤﻈﻪ ﻣﺸﺨﺺ‪ ،‬ﺗﻮزﻳﻊ دﻣﺎ در ﻳﻚ ﺟﺴﻢ ﻫﻤﮕﻦ ﻧﺎﻣﺤﺪود ﺗﻮﺳﻂ ﺗﺎﺑﻊ زﻳﺮ داده ﺷﺪه اﺳﺖ‪:‬‬ ‫‪T(x,y,z)= 5x-20xy+z²-xy+2yz‬‬ ‫ﻓﺮض ﻛﻨﻴﺪ ﺧﻮاص ﺟﺴﻢ ﺛﺎﺑﺖ ﺑﻮده و ﺗﻮﻟﻴﺪ داﺧﻠﻲ ﮔﺮﻣﺎ وﺟﻮد ﻧﺪارد‪ .‬ﻧﺎﺣﻴﻪﻫﺎﻳﻲ را ﭘﻴﺪا ﻛﻨﻴﺪ ﻛﻪ در آﻧﻬﺎ دﻣﺎ ﺑﺎ زﻣﺎن‬ ‫ﺗﻐﻴﻴﺮ ﻣﻲﻛﻨﺪ‪.‬‬

‫‪3‬‬

‫ﺗﻮزﻳﻊ دﻣﺎي داﺋﻢ در ﻳﻚ دﻳﻮار ﻳﻚ ﺑﻌﺪي ﺑﺎ ﺿﺮﻳﺐ ﻫﺪاﻳﺖ ‪ 50 W/m.K‬و ﺿﺨﺎﻣﺖ ‪ 50 mm‬ﺑﺮاﺑﺮ‬ ‫‪ T(˚C)=ax+b/x‬اﻧﺪازهﮔﻴﺮي ﺷﺪه اﺳﺖ ﻛﻪ در آن ‪ b=-2000˚C/m² ،a=200˚C‬و ‪ x‬ﺑﺮ ﺣﺴﺐ ﻣﺘﺮ اﺳﺖ‪.‬‬ ‫اﻟﻒ( ﻧﺮخ ﺗﻮﻟﻴﺪ ﮔﺮﻣﺎ‪ ، q& ،‬در دﻳﻮار ﭼﻘﺪر اﺳﺖ؟‬ ‫ب( ﺷﺎر ﮔﺮﻣﺎ روي دو ﺳﻄﺢ دﻳﻮار را ﻣﺤﺎﺳﺒﻪ ﻛﻨﻴﺪ‪ .‬راﺑﻄﻪ ﺷﺎر ﮔﺮﻣﺎ ﺑﺎ ﻧﺮخ ﺗﻮﻟﻴﺪ ﮔﺮﻣﺎ ﺑﻪ ﭼﻪ ﺻﻮرت اﺳﺖ؟‬ ‫ﻳﻚ ﭘﻮﺳﺘﻪ ﻛﺮوي ﺑﺎ ﺷﻌﺎع داﺧﻠﻲ ‪ ri‬و ﺷﻌﺎع ﺧﺎرﺟﻲ ‪ ، ro‬ﺣﺎوي ﻋﻨﺎﺻﺮ ﭘﺨﺶ ﮔﺮﻣﺎ ﺑﻮده و در ﻳﻚ ﻟﺤﻈﻪ ﺧﺎص‬ ‫ﺗﻮزﻳﻊ ﮔﺮﻣﺎ در ﭘﻮﺳﺘﻪ ﺑﻪ ﺷﻜﻞ زﻳﺮ اﺳﺖ‪:‬‬

‫‪4‬‬

‫‪C1‬‬ ‫‪+ C2‬‬ ‫‪r‬‬

‫= ) ‪T (r‬‬

‫ﺗﻌﻴﻴﻦ ﻛﻨﻴﺪ ﺷﺮاﻳﻂ داﺋﻢ ﻳﺎ ﻏﻴﺮ داﺋﻢ اﺳﺖ؟ ﻧﺤﻮه ارﺗﺒﺎط ﺷﺎر ﮔﺮﻣﺎ و ﻧﺮخ ﮔﺮﻣﺎ ﺑﻪ ﺷﻌﺎع ﭼﮕﻮﻧﻪ اﺳﺖ؟‬

‫‪5‬‬

‫ﭼﻨﺎﻧﭽﻪ در ﻳﻚ دﻳﻮار ﺗﻮﻟﻴﺪ ﺣﺮارت وﺟﻮد ﻧﺪاﺷﺘﻪ ﺑﺎﺷﺪ و دو ﻃﺮف دﻳﻮار در دﻣﺎﻫﺎي ‪ T1‬و ‪ T2‬ﻗﺮار داﺷﺘﻪ ﺑﺎﺷﻨﺪ‪،‬‬ ‫ﺗﺎﺑﻊ ﺗﻮزﻳﻊ دﻣﺎ در داﺧﻞ دﻳﻮار ﭼﮕﻮﻧﻪ اﺳﺖ؟ ﺛﺎﺑﺖ ﻛﻨﻴﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﭼﻨﺎﻧﭽﻪ ﺷﺎر ﺗﻮﻟﻴﺪ ﮔﺮﻣﺎ در داﺧﻞ دﻳﻮار ﻣﻘﺪاري‬ ‫ﺛﺎﺑﺖ ﺑﺮاﺑﺮ &‪ q‬ﺑﺎﺷﺪ‪ ،‬ﺗﺎﺑﻊ ﺗﻮزﻳﻊ دﻣﺎ را ﺑﺪﺳﺖ آورﻳﺪ‪.‬‬

‫ﻣﻮﻓﻖ ﺑﺎﺷﻴﺪ ‪ -‬ﻣﻮﻣﻨﻲ‬

Heat Transfer_2_t93.pdf

400˚C. @. 25 mm. 0.1W/m.K . @ >. 35˚C. 500 W/m².K. <. @ > . > > > > > > <. : T(x,y,z)= 5x-20xy+z²-xy+2yz. > > > > . > > . @ > > > @ >. 50 W/m.K. 50 mm. T(˚C)=ax+b/x. > @ a=200˚C. < b=-2000˚C/m² x . (. < > qx. = > > <. (. > > @ . = > >. > @ ir o r. > > @ <. > : 2. 1. )( C r. C. rT. +. = = > = > >. @ > > > > > > > >. 1. T. 2. T. < >.
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