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
Concrete, k = 1.410 mm19 °C-14 °CQ̇ = ?

A wall of concrete is 10 mm thick and has an area of 15 m². Its faces are held at 19 °C and -14 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 15 m²T1 = 19 °CT2 = -14 °C
Q̇ = W
2.Easy
Concrete, k = 1.4250 mm24 °C-8 °CQ̇ = ?

A wall of concrete is 250 mm thick and has an area of 4 m². Its faces are held at 24 °C and -8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 4 m²T1 = 24 °CT2 = -8 °C
Q̇ = W
3.Medium
Concrete, k = 1.450 mmGlass, k = 0.9650 mm23 °C-6 °CTi​ = ?Q̇

A wall is made of 50 mm of concrete and 50 mm of glass, with an area of 8 m². The outer faces are at 23 °C and -6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 8 m²T1 = 23 °CT3 = -6 °C
Ti = °C
4.Medium
Brick, k = 0.7250 mmWood, k = 0.1775 mm19 °C-1 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 75 mm of wood, with an area of 15 m². The outer faces are at 19 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 19 °CT3 = -1 °C
Ti = °C
5.Hard
Brick, k = 0.72150 mmGypsum board, k = 0.1725 mmroom 20 °Coutside -6 °CQ̇

A wall of 150 mm brick and 25 mm gypsum board separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0450 mmroom 22 °Coutside -7 °CTs​ = ?Q̇

A wall of 50 mm expanded polystyrene and 50 mm mineral wool separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -7 °C
Ts = °C

Answer key

  1. 1. Q̇ = 69300 W
  2. 2. Q̇ = 716.8 W
  3. 3. Ti = 11.2 °C
  4. 4. Ti = 16.28 °C
  5. 5. U = 1.748 W/(m²·K)
  6. 6. Ts = 20.68 °C

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