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 = K₁ = 0.08 W/(m.K)

Thermal conductivity of styrofoam = K₂ = 0.01 W/(m.K)

Thickness of the wood layer = L₁ = 2.8 cm = 0.028 m

Thickness of the styrofoam insulation = L₂ = 2.3 cm = 0.023 m

Exterior surface temperature (Wood) = T₁ = -11 ^oC

Interior surface temperature (Styrofoam) = T₂ = 19 ^oC

Temperature at the interface between wood and styrofoam = T₃

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

6.571(T₃ + 11) = 19 - T₃

7.571T₃ = -53.281

T₃ = -7.037 ^oC

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

Q = 11.322 W/m²

A) Temperature at the plane where wood meets the styrofoam = -7.037 ^oC

B) Rate of heat flow per square meter through this wall = 11.322 W/m²