heat_3_52 - PROBLEM 3.52 KNOWN: Inner surface temperature...

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PROBLEM 3.52 KNOWN: Inner surface temperature of insulation blanket comprised of two semi-cylindrical shells of different materials. Ambient air conditions. FIND: (a) Equivalent thermal circuit, (b) Total heat loss and material outer surface temperatures. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional, radial conduction, (3) Infinite contact resistance between materials, (4) Constant properties. ANALYSIS: (a) The thermal circuit is, conv,A conv,B 2 RR1 / r h π ʹʹ == () 21 cond A A ln r / r R k ʹ = < 2i cond B ln r / r R k ʹ = B The conduction resistances follow from Section 3.3.1 and Eq. 3.28. Each resistance is larger by a factor of 2 than the result of Eq. 3.28 due to the reduced area. (b) Evaluating the thermal resistances and the heat rate AB q=q q , ʹ + ( ) 1 2 conv R 0.1m 25 W/m K 0.1273 m K/W ʹ = × × = cond A cond B cond A ln 0.1m/0.05m R0 . 1 1 0 3 m K / W R 8 R 0 . 8 8 2 5 m K / W 2 W/m K
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