Question

A carpenter builds an exterior house wall with a layer of wood 3.1 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 -15.0 ∘C.A.)What is the temperature at the plane where the wood meets the Styrofoam?
B.)What is the rate of heat flow per square meter through this wall?

Answer 1

Answer: T = -0.213°c

Heat flow = 38.2 w/m²

Explanation:

given data:

Wood = 0.031m thick

Styrofoam = 0.023m thick

Wood = k ( 0.080W/m.k)

Styrofoam = k (0.010W/m.k)

Temperature of wood = -15°c

Temperature of styrofoam = 19°c

(a) heat flow in wood and styrofoam must be equal

KAdT/ L = KAdT/ L

0.080 * A * ( T - ( -15) ) / 0.031 = 0.010 * A * ( T - ( 19°c) ) / 0.023

T = -0.213°c

(b) heat flow

H = KAdT / L

H = 0.080 * A * ( -0.213°c - ( -15°c) ) / 0.031

= 38.2 w/m²