# sm3_22 - PROBLEM 3.22 KNOWN Temperatures and convection...

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Unformatted text preview: PROBLEM 3.22 KNOWN: Temperatures and convection coefﬁcients associated with ﬂuids at inner and outer surfaces of a composite wall. Contact resistance, dimensions, and thermal conductivities associated with wall materials. FIND: (a) Rate of heat transfer through the wall, (b) Temperature distribution. SCH EMATIC: Hg'l-L -I-l a-oosw/m-K LJ=2000C T T T T hg=IaWﬁnLK I Tm ML “R a. E? k,=0.1W/m-K— . ‘1- 31 t= 755: EA a2 w n.5,": Eﬁ‘mc Handsome-KM "" “'1 a.=2ow1m:1< L,=aai..,1.,.aozm ASSUMPTIONS: (I) Steady-state conditions, (2) One-dimensional heat transfer, (3) Negligible radiation, (4) Constant properties. ANALYSIS: (a) Calculate the total resistance to ﬁnd the heat rate, tot—L'l' LA +th+ LB +L hlA kAA 5 kBA th l 0.01 0.3 0.02 1 K le— + + + + 10x5 0.]x5 5 0.04x5 20x5 W R101 2 [0.02+0.02+0.06+ 0.10+0.01]£= 0.21i W W Tm J00; _ (200—40)°C q= = 762 w. Rtot 0.21 10w (b) It follows that T51=Tm pi: 200°c— 7’62 w =1s4.s°c ' * hlA 50 W11; qLA , Tszw x 0.01m , TA = T591——=184.8 C——=169.6 c “A 0.1 w >1st m - K a K a TB ZTA ‘qu: 2169.6 C—TGZWxCIﬂG—z 123.8 C w qLB , 762w x 0.0211: , T52 =TB——=123.8 C——=4?.6 c * 1-. A W 2 B 0.04 K XSm m. aszw = 40I’C q '3 T = T —— = 41.6 c — “”2 5’2 th 1110wa ...
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