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
Expanded polystyrene, k = 0.035250 mm17 °C8 °CQ̇ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 20 m². Its faces are held at 17 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 20 m²T1 = 17 °CT2 = 8 °C
Q̇ = W
2.Easy
Wood, k = 0.1750 mm23 °C-9 °CQ̇ = ?

A wall of wood is 50 mm thick and has an area of 15 m². Its faces are held at 23 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 15 m²T1 = 23 °CT2 = -9 °C
Q̇ = W
3.Medium
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.035100 mm22 °C-15 °CTi​ = ?Q̇

A wall is made of 200 mm of glass and 100 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 22 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 22 °CT3 = -15 °C
Ti = °C
4.Medium
Brick, k = 0.72100 mmMineral wool, k = 0.0475 mm18 °C2 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 75 mm of mineral wool, with an area of 15 m². The outer faces are at 18 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 18 °CT3 = 2 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0450 mmroom 21 °Coutside -1 °CQ̇

A wall of 50 mm expanded polystyrene and 50 mm mineral wool separates a room at 21 °C from outside air at -1 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -1 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4200 mmMineral wool, k = 0.04100 mmroom 20 °Coutside -6 °CTs​ = ?Q̇

A wall of 200 mm concrete and 100 mm mineral wool separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -6 °C
Ts = °C

Answer key

  1. 1. Q̇ = 25.2 W
  2. 2. Q̇ = 1632 W
  3. 3. Ti = 19.49 °C
  4. 4. Ti = 16.9 °C
  5. 5. U = 0.3548 W/(m²·K)
  6. 6. Ts = 18.48 °C

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