The exhaust duct from a heater has an inside diameter of 114.3 mm with ceramic walls 6.4 mm thick. The average k = 1.52 W/mK. Outside this wall, an insulation of rock wool 102 mm thick is installed. The thermal conductivity of the rock wool is k = 0.046+1.56*10-4T (°C) (W/mK). The inside surface temperature of the ceramic is T1= 588.7 K, and the outside surface temperature of the insulation is T3= 311 K. Calculate the heat loss for 1.5 m of duct and the interface temperature T2between the ceramic and the insulation.Assumesteady heat transfer.Hint: The correct value of km for insulation is that evaluated at the mean temperature of T2+T3/2. Hence, for the first trial assume a mean temperature of, say, 448 K. Then, calculate the heat loss and T2. Using this new T2, calculate a new mean temperature and proceed as before.

Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
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Author:Raymond A. Serway, John W. Jewett
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Chapter19: Temperature
Section: Chapter Questions
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The exhaust duct from a heater has an inside diameter of 114.3 mm with ceramic walls 6.4 mm thick. The average k = 1.52 W/mK. Outside this wall, an insulation of rock wool 102 mm thick is installed. The thermal conductivity of the rock wool is k = 0.046+1.56*10-4T (°C) (W/mK). The inside surface temperature of the ceramic is T1= 588.7 K, and the outside surface temperature of the insulation is T3= 311 K. Calculate the heat loss for 1.5 m of duct and the interface temperature T2between the ceramic and the insulation.Assumesteady heat transfer.Hint: The correct value of km for insulation is that evaluated at the mean temperature of T2+T3/2. Hence, for the first trial assume a mean temperature of, say, 448 K. Then, calculate the heat loss and T2. Using this new T2, calculate a new mean temperature and proceed as before.

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