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Question

A carpenter builds an outer house wall with a layer of wood 2.0 cm thick on the outside and a layer of an insulator 3.5 cm thick as the inside wall surface. The wood has k=0.03 W/mK and the insulation has k=0.01W/mK. The interior surface temperature is 19C and the exterior surface temperature is 10C. What is the temperature at the plane where the wood meets the insulation ?(in K)

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Solution

At steady state, constant heat current will flow through the wall. Hence,

K1Al1(TTout)=K2Al2(TinT)

0.032(T+10)=0.013.5(19T)

10.5(T+10)=2(19T)

12.5T=67

T=5.360C

Answer is 5.360C.

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