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 = 0.1750 mm20 °C10 °CQ̇ = ?

A wall of wood is 50 mm thick and has an area of 10 m². Its faces are held at 20 °C and 10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 10 m²T1 = 20 °CT2 = 10 °C
Q̇ = W
2.Easy
Concrete, k = 1.4100 mm23 °C10 °Cq″ = ?

A wall of concrete is 100 mm thick and has an area of 4 m². Its faces are held at 23 °C and 10 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 4 m²T1 = 23 °CT2 = 10 °C
q″ = W/m²
3.Medium
Brick, k = 0.72200 mmGypsum board, k = 0.17100 mm25 °C9 °CTi​ = ?Q̇

A wall is made of 200 mm of brick and 100 mm of gypsum board, with an area of 4 m². The outer faces are at 25 °C and 9 °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 = 0.17 W/(m·K)A = 4 m²T1 = 25 °CT3 = 9 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmGlass, k = 0.9650 mm15 °C-5 °CTi​ = ?Q̇

A wall is made of 100 mm of concrete and 50 mm of glass, with an area of 12 m². The outer faces are at 15 °C and -5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 12 m²T1 = 15 °CT3 = -5 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17250 mmWood, k = 0.1775 mmroom 22 °Coutside -9 °CQ̇

A wall of 250 mm gypsum board and 75 mm wood separates a room at 22 °C from outside air at -9 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -9 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.17100 mmMineral wool, k = 0.04150 mmroom 22 °Coutside -7 °CQ̇ = ?

A wall of 100 mm gypsum board and 150 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 heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 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
Q̇ = W

Answer key

  1. 1. Q̇ = 340 W
  2. 2. q″ = 182 W/m²
  3. 3. Ti = 19.87 °C
  4. 4. Ti = 3.434 °C
  5. 5. U = 0.4792 W/(m²·K)
  6. 6. Q̇ = 25.67 W

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