Question

A carpenter builds an exterior house wall with a layer of wood 2.8 cm thick on the outside and a layer of Styrofoam insulation 2.3 cm thick on the inside wall surface. The wood has k=0.080W/(m⋅K), and the Styrofoam has k= 0.010 W/(m⋅K). The interior surface temperature is 19.0 ∘C , and the exterior surface temperature is -11.0 ∘C .

**Part A**

What is the temperature at the plane where the wood meets the Styrofoam?

**Part B**

What is the rate of heat flow per square meter through this wall?

Answer #1

Thermal conductivity of wood = K_{1} = 0.08 W/(m.K)

Thermal conductivity of styrofoam = K_{2} = 0.01
W/(m.K)

Thickness of the wood layer = L_{1} = 2.8 cm = 0.028
m

Thickness of the styrofoam insulation = L_{2} = 2.3 cm =
0.023 m

Exterior surface temperature (Wood) = T_{1} = -11
^{o}C

Interior surface temperature (Styrofoam) = T_{2} = 19
^{o}C

Temperature at the interface between wood and styrofoam =
T_{3}

The rate of heat flow per square meter through the wooden layer is equal to that through the styrofoam.

6.571(T_{3} + 11) = 19 - T_{3}

7.571T_{3} = -53.281

T_{3} = -7.037 ^{o}C

Rate of heat flow per square meter through the wall = Q

Q = 11.322 W/m^{2}

A) Temperature at the plane where wood meets the styrofoam =
-7.037 ^{o}C

B) Rate of heat flow per square meter through this wall = 11.322
W/m^{2}

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