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 = 0.035100 mm19 °C-15 °CQ̇ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 10 m². Its faces are held at 19 °C and -15 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 10 m²T1 = 19 °CT2 = -15 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03520 mm24 °C0 °CQ̇ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 15 m². Its faces are held at 24 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 15 m²T1 = 24 °CT2 = 0 °C
Q̇ = W
3.Medium
Brick, k = 0.72200 mmExpanded polystyrene, k = 0.035100 mm20 °C2 °CTi​ = ?Q̇

A wall is made of 200 mm of brick and 100 mm of expanded polystyrene, with an area of 8 m². The outer faces are at 20 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 8 m²T1 = 20 °CT3 = 2 °C
Ti = °C
4.Medium
Concrete, k = 1.4250 mmMineral wool, k = 0.0450 mm24 °C0 °CQ̇ = ?

A wall is made of 250 mm of concrete and 50 mm of mineral wool, with an area of 8 m². The outer faces are at 24 °C and 0 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 8 m²T1 = 24 °CT3 = 0 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.04250 mmWood, k = 0.1750 mmroom 21 °Coutside 1 °CTs​ = ?Q̇

A wall of 250 mm mineral wool and 50 mm wood separates a room at 21 °C from outside air at 1 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 1 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17100 mmConcrete, k = 1.425 mmroom 20 °Coutside 2 °CQ̇

A wall of 100 mm gypsum board and 25 mm concrete separates a room at 20 °C from outside air at 2 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 2 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 119 W
  2. 2. Q̇ = 630 W
  3. 3. Ti = 18.41 °C
  4. 4. Q̇ = 134.4 W
  5. 5. Ts = 20.51 °C
  6. 6. U = 1.23 W/(m²·K)

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