Question

A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2.4 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 20.0 ∘C , and the exterior surface temperature is -14.0 ∘C .

Part A

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

Express your answer using two significant figures

Part B

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

Express your answer using two significant figures. (please please i need to get a correct answer for this problem because i got many worng answers for it that did not help me at all and show the work and everything thank u )

Answer 1

a = 0.03 m thickness of the wood layer

kw = 0.08 W/mK thermal conductivity of wood

To = - 14 degree C = 259 K outside temperature

b = 0.024 m thickness of styrofoam

ks = 0.01 W/mK thermal conductivity of styrofoam

Ti = 20 degree C = 293 K inside temperature

Tx = temperature at contact point wood - styrofoam

The rate of heat transfer must be the same through the wood and styrofoam layers :

ks ( Ti - Tx ) / b = kw ( Tx - To ) / a

Tx ( kw/a + ks/b) = ks Ti/b + kw To/a

Tx = ( 0.01*293/0.024+ 0.08*259/0.03 ) / ( 0.08/0.03 + 0.01/0.024 ) = 264 K

Tx = - 9 degree C

The rate of heat flow per square meter is :

Φ = delta(T )/ R ; where R is total thermal resistance of the wall R = Rw + Rs

Rw thermal resistance of wood layer Rw = a / A*kw = 0.03 / 0.08 = 0.375 K/W

Rs thermal resistance of styro layer Rs = b / A*ks = 0.024 / 0.01 = 2.4 K/W

A = 1 square meter

R = 2.775 K/W

Delta(T) = 20 - (-14) = 34 K

Φ = 34 / 2.775 = 12.25 W