An insulated wall consists of an exterior wood layer of thickness 3.0 cm and an

Question

An insulated wall consists of an exterior wood layer of thickness 3.0 cm  and an interior layer of foam insulation of thickness 2.0 cm . For the wood, k=0.080W/(mK), and for the foam insulation k=0.010 W/(mK). The outer surface of the wood is at a constant -14.0 C , and the inner surface of the foam insulation is at a constant 20.0 C .

Part A

Calculate the temperature where the wood and foam insulation are in contact.

Express your answer using two significant figures.

T = ? deg C

Part B

Calculate the heat flow per unit area through the two-layer wall.

Express your answer using two significant figures.

H = ? W/m^2

Explanation / Answer

Part A: Problem is similar to two rods of different lengths and different materials maintained at different temperatures are coupled together. Under steady state condition heat current through wood will be equal to heat current through foam insulation. Let the temperature of the junction is T.

Therefore, using relation for H = kwood Awood(Twood - T) / Lwood = kfoam Afoam(T - Tfoam) / Lfoam. Using Awood = Afoam we get T = (kwood* Twood*Lfoam + kfoam * Tfoam * Lwood) / (kwood * Lfoam + kfoam * Lwood) [equation 1]. On substituting values we get T = 264 K or - 9 degree celsius.

Part B) Substituting expression for T given by equation 1 into H relation we find H/A = kwood* kfoam * (Twood - Tfoam) / (kwood * Lfoam + kfoam * Lwood) = 14.31 W/m2

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