Question

# A carpenter builds an exterior house wall with a layer of wood 2.8 cm thick on...

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?

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.