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HomeworkSolutions_C8 - Problem#1 Consider a circular steel...

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Problem #1: Consider a circular steel pipe having an inner diameter of 2.067 in., and wall thickness of 0.154 in. The pipe carrying steam is insulted with 2 in. of 85% magnesia covered in turn with 2 in. of cork. Estimate the heat loss per hour per foot of pipe if the inner surface of the pipe is at 250 o F and the outer surface of the cork is at 90 o F. The thermal conductivities (in Btu/hr.ft.F) of the substances concerned are: steel, 26.1; 85% magnesia, 0.04; cork, 0.03. Answer: See Example 10.6-1 (or 9.6-1) in the textbook, 2 nd (or 1 st ) edition, for the notation and the derivation of the energy equations in terms of temperature for individual layers. The final forms of these equations are as follow: ( ) ( ) ( ) 1 0 01 0 0 0 1 0 0 01 2 1 12 0 0 1 2 0 0 12 3 2 23 0 0 2 3 0 0 23 Zone 01 (steel): Zone 12 (magnesia): Zone 23 (cor k): ln ln ln r r dT k r r q T T r q dr k r r dT k r r q T T r q dr k r r dT k r r q T T r q dr k = = = = = = Addition of these above equation gives ( ) ( ) ( ) 0 3 0 0 1 0 2 1 3 2 01 12 23 ln ln ln T T r q r r r r r r k k k = + + Thus, the heat loss over the inner surface of the pipe with an area of 0 2 Lr π
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