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Solution_HW6 - Solutions for homework Set#6 Problem#1 Solve...

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Solutions for homework Set #6: Problem #1 : Solve problem 10.A.1 in BSL Answer: See Example 10.6-1 in BSL 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 ( ) ( ) ( ) ( ) 0 3 0 0 0 1 0 2 1 3 2 01 12 23 2 2 ln ln ln L T T Q Lr q r r r r r r k k k π π = = + + Or the heat loss per hour per foot of the pipe
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