Question

# The thermal conductivity of a sheet of rigid,extruded insulation is k = 0.020 W/(m*K). The measured...

The thermal conductivity of a sheet of rigid,extruded insulation is k = 0.020 W/(m*K). The measured temperature difference across a 30-mm-thick sheet of the material is T1-T2=10 C.

a.) Assuming 1-D, steady state conditions withouth thermal energy generation in the material, what is the heat flux through a 2 m x 3 m sheet of the insulation?

b.) What would be the effect on the rate of heat transfer through the sheet if a material with a relatively higher thermal conductivity were to be chosen?

From the Fouriers law of heat conduction

Rate of heat transfer

Negative sign shows that the temperature is decreased with increase in the thickness.

Part a

Rate of heat transfer

Q = kA(T1 - T2) /t

= 0.020 W/(m*K) x 2m x 3m x (10 C) / (30 mm x 1m/1000mm)

= 40 W

Heat flux = Q/A

= 40 W / (2m x 3m)

= 6.66 W/m2

Part b

if a material with a relatively higher thermal conductivity were to be chosen then rate of heat transfer will increase.

Q is directly proportional to the thermal conductivity k

Higher k will lead to the higher rate of heat transfer.