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Transport Phenomena - Heat Transfer Problem :
Minimum thickness for a composite furnace wall


Problem.

The wall of a furnace comprises three layers as shown in the figure. The first layer is refractory (whose maximum allowable temperature is 1400oC) while the second layer is insulation (whose maximum allowable temperature is 1093oC). The third layer is a plate of 6.35 mm thickness of steel [thermal conductivity = 45 W/(m K)]. Assume the layers to be in very good thermal contact.

figure : Layers in a composite furnace wall
Figure. Layers in a composite furnace wall.

The temperature T0 on the inside of the refractory is 1370oC, while the temperature T3 on the outside of the steel plate is 37.8oC. The heat loss through the furnace wall is expected to be 15800 W/m2. Determine the thickness of refractory and insulation that results in the minimum total thickness of the wall.

Given thermal conductivities in W/(m K):
Layerk at 37.8oCk at 1093oC
Refractory3.126.23
Insulation1.563.12


Solution.

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