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 = 0.03510 mm16 °C-14 °CQ̇ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 8 m². Its faces are held at 16 °C and -14 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 8 m²T1 = 16 °CT2 = -14 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.035250 mm20 °C-13 °Cq″ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 12 m². Its faces are held at 20 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 12 m²T1 = 20 °CT2 = -13 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4200 mmWood, k = 0.17150 mm21 °C3 °CTi​ = ?Q̇

A wall is made of 200 mm of concrete and 150 mm of wood, with an area of 8 m². The outer faces are at 21 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 21 °CT3 = 3 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04100 mmConcrete, k = 1.425 mm17 °C-14 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 25 mm of concrete, with an area of 4 m². The outer faces are at 17 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 4 m²T1 = 17 °CT3 = -14 °C
Ti = °C
5.Hard
Brick, k = 0.72150 mmWood, k = 0.17150 mmroom 20 °Coutside -11 °CQ̇

A wall of 150 mm brick and 150 mm wood separates a room at 20 °C from outside air at -11 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -11 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4200 mmMineral wool, k = 0.0475 mmroom 21 °Coutside -3 °CQ̇ = ?

A wall of 200 mm concrete and 75 mm mineral wool separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -3 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 840 W
  2. 2. q″ = 4.62 W/m²
  3. 3. Ti = 18.49 °C
  4. 4. Ti = −13.78 °C
  5. 5. U = 0.8126 W/(m²·K)
  6. 6. Q̇ = 66.02 W

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