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fins-2 - Fins-2 If the pot from previous lecture is made of...

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Fins-2 If the pot from previous lecture is made of other materials other than the aluminum, what will be the temperature distribution? Try stainless steel (k=15 W/m.K) and copper (385 W/m.K). Recall: h=5 W/ m 2 ° C, P=2W+2t=2(0.03+0.005)=0.07(m) A C =Wt=0.00015(m 2 ), L=0.2(m) Therefore, m ss =(hP/kA C ) 1/2 =12.47, m cu =2.46 M ss = (hPk ss A C ) (T b -T )=0.028(100-25)=2.1(W) M cu = (hPk ss A C ) θ b =0.142(100-25)=10.66(W) For stainless steel, - T x T T T m L x mL T x T x x ss b b ss ss ( ) cosh ( ) cosh cosh[ .47( . )] cosh( .47* . ) , ( ) . * cosh[ .47( . )] - = = - - - = - = + - θ θ 25 100 25 12 0 2 12 0 2 25 12 3 12 0 2
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Fins-2 (cont.) For copper, - T x T T T m L x mL T x T x x cu b b cu cu ( ) cosh ( ) cosh cosh[ .46( . )] cosh( .46 * . ) , ( ) . * cosh[ .46( . )] - = = - - - = - = + - θ θ 25 100 25 2 0 2 2 0 2 25 66 76 2 0 2 0 0.04 0.08 0.12 0.16 0.2 75 80 85 90 95 100 T( ) x T ss ( ) x T cu ( ) x x copper aluminum stainless steel
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Fins-2 (cont.) Inside the handle of the stainless steel pot, temperature drops quickly. Temperature at the end of the handle is 37.3 ° C. This is because the stainless steel has low thermal conductivity and heat can not penetrate easily into the handle.
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