Question

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

Answer 1

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

$\frac{K_{1}A}{l_1}(T-T_{out})=\frac{K_{2}A}{l_2}(T_{in}-T)$

$\frac{0.03}{2}(T+10)=\frac{0.01}{3.5}(19-T)$

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

$12.5T=-67$

$T={-5.36}^{0}C$

Answer is ${-5.36}^{0}C$.