Question

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?

Answer 1

From the Fouriers law of heat conduction

Rate of heat transfer

Q = - kAdT/dt

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.