A wall has thickness L = 0.05 m, cross-sectional area A = 2.0 m^2, thermal conductivity k = 0.8 W/m·K, and ΔT = 20 K across it. What is the rate of heat transfer by conduction?

A wall has thickness L = 0.05 m, cross-sectional area A = 2.0 m^2, thermal conductivity k = 0.8 W/m·K, and ΔT = 20 K across it. What is the rate of heat transfer by conduction?

• A. 320 W
• B. 800 W
• C. 640 W
• D. 1280 W

Answer: (C)

Heat conduction through a plane wall follows Fourier's law: the rate of heat transfer is proportional to the thermal conductivity, the cross-sectional area, and the temperature difference, and inversely proportional to the thickness. Mathematically, Qdot = k A ΔT / L. Plugging in the values: kA = 0.8 × 2.0 = 1.6 W/K. Times ΔT = 20 gives 32 W. Dividing by L = 0.05 m yields 32 / 0.05 = 640 W. So the rate of heat transfer by conduction is 640 watts. This shows how increasing conductivity, area, or temperature difference raises the rate, while increasing thickness lowers it.

Heat conduction through a plane wall follows Fourier's law: the rate of heat transfer is proportional to the thermal conductivity, the cross-sectional area, and the temperature difference, and inversely proportional to the thickness. Mathematically, Qdot = k A ΔT / L.

Plugging in the values: kA = 0.8 × 2.0 = 1.6 W/K. Times ΔT = 20 gives 32 W. Dividing by L = 0.05 m yields 32 / 0.05 = 640 W.

So the rate of heat transfer by conduction is 640 watts. This shows how increasing conductivity, area, or temperature difference raises the rate, while increasing thickness lowers it.