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
Wood, k = 0.17250 mm23 °C-12 °CQ̇ = ?

A wall of wood is 250 mm thick and has an area of 12 m². Its faces are held at 23 °C and -12 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 12 m²T1 = 23 °CT2 = -12 °C
Q̇ = W
2.Easy
Wood, k = 0.1750 mm15 °C10 °Cq″ = ?

A wall of wood is 50 mm thick and has an area of 4 m². Its faces are held at 15 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 4 m²T1 = 15 °CT2 = 10 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04150 mmWood, k = 0.17150 mm21 °C8 °CQ̇ = ?

A wall is made of 150 mm of mineral wool and 150 mm of wood, with an area of 6 m². The outer faces are at 21 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 21 °CT3 = 8 °C
Q̇ = W
4.Medium
Concrete, k = 1.4200 mmExpanded polystyrene, k = 0.03575 mm17 °C1 °CTi​ = ?Q̇

A wall is made of 200 mm of concrete and 75 mm of expanded polystyrene, with an area of 10 m². The outer faces are at 17 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 10 m²T1 = 17 °CT3 = 1 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035250 mmWood, k = 0.17100 mmroom 22 °Coutside -11 °CQ̇

A wall of 250 mm expanded polystyrene and 100 mm wood separates a room at 22 °C from outside air at -11 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -11 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4100 mmGlass, k = 0.96100 mmroom 21 °Coutside -1 °CQ̇

A wall of 100 mm concrete and 100 mm glass separates a room at 21 °C from outside air at -1 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 285.6 W
  2. 2. q″ = 17 W/m²
  3. 3. Q̇ = 16.84 W
  4. 4. Ti = 16 °C
  5. 5. U = 0.1269 W/(m²·K)
  6. 6. U = 2.952 W/(m²·K)

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