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 mm24 °C-11 °CQ̇ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 12 m². Its faces are held at 24 °C and -11 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 12 m²T1 = 24 °CT2 = -11 °C
Q̇ = W
2.Easy
Concrete, k = 1.450 mm21 °C-9 °Cq″ = ?

A wall of concrete is 50 mm thick and has an area of 12 m². Its faces are held at 21 °C and -9 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 12 m²T1 = 21 °CT2 = -9 °C
q″ = W/m²
3.Medium
Brick, k = 0.7250 mmConcrete, k = 1.4100 mm24 °C3 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of concrete, with an area of 15 m². The outer faces are at 24 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 24 °CT3 = 3 °C
Ti = °C
4.Medium
Mineral wool, k = 0.0450 mmGypsum board, k = 0.1750 mm19 °C4 °CQ̇ = ?

A wall is made of 50 mm of mineral wool and 50 mm of gypsum board, with an area of 8 m². The outer faces are at 19 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 19 °CT3 = 4 °C
Q̇ = W
5.Hard
Wood, k = 0.17150 mmBrick, k = 0.7250 mmroom 22 °Coutside 4 °CQ̇

A wall of 150 mm wood and 50 mm brick separates a room at 22 °C from outside air at 4 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = 4 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.04100 mmroom 22 °Coutside -6 °CQ̇ = ?

A wall of 50 mm expanded polystyrene and 100 mm mineral wool separates a room at 22 °C from outside air at -6 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -6 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 1470 W
  2. 2. q″ = 840 W/m²
  3. 3. Ti = 13.65 °C
  4. 4. Q̇ = 77.71 W
  5. 5. U = 0.9215 W/(m²·K)
  6. 6. Q̇ = 68.23 W

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