Heat conduction worksheet with answers

Free printable Heat conduction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Concrete, k = 1.450 mm20 °C-13 °CQ̇ = ?

A wall of concrete is 50 mm thick and has an area of 15 m². Its faces are held at 20 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 15 m²T1 = 20 °CT2 = -13 °C
Q̇ = W
2.Easy
Glass, k = 0.96250 mm16 °C4 °Cq″ = ?

A wall of glass is 250 mm thick and has an area of 20 m². Its faces are held at 16 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 250 mmA = 20 m²T1 = 16 °CT2 = 4 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.03550 mmGlass, k = 0.96100 mm20 °C1 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 100 mm of glass, with an area of 4 m². The outer faces are at 20 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 20 °CT3 = 1 °C
Ti = °C
4.Medium
Wood, k = 0.17250 mmGlass, k = 0.9625 mm16 °C-5 °CQ̇ = ?

A wall is made of 250 mm of wood and 25 mm of glass, with an area of 12 m². The outer faces are at 16 °C and -5 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 12 m²T1 = 16 °CT3 = -5 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.04250 mmWood, k = 0.1750 mmroom 22 °Coutside -7 °CQ̇ = ?

A wall of 250 mm mineral wool and 50 mm wood separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -7 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.035200 mmMineral wool, k = 0.04150 mmroom 21 °Coutside -3 °CQ̇ = ?

A wall of 200 mm expanded polystyrene and 150 mm mineral wool separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -3 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 13860 W
  2. 2. q″ = 46.08 W/m²
  3. 3. Ti = 2.291 °C
  4. 4. Q̇ = 168.4 W
  5. 5. Q̇ = 86.26 W
  6. 6. Q̇ = 49.58 W

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