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 = 0.03550 mm25 °C-1 °CQ̇ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 12 m². Its faces are held at 25 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 12 m²T1 = 25 °CT2 = -1 °C
Q̇ = W
2.Easy
Brick, k = 0.72200 mm25 °C-5 °CQ̇ = ?

A wall of brick is 200 mm thick and has an area of 6 m². Its faces are held at 25 °C and -5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 6 m²T1 = 25 °CT2 = -5 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035150 mmConcrete, k = 1.425 mm21 °C-3 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 25 mm of concrete, with an area of 15 m². The outer faces are at 21 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 21 °CT3 = -3 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.03550 mmWood, k = 0.1725 mm19 °C10 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 25 mm of wood, with an area of 8 m². The outer faces are at 19 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 19 °CT3 = 10 °C
Ti = °C
5.Hard
Glass, k = 0.96250 mmMineral wool, k = 0.04150 mmroom 22 °Coutside -2 °CQ̇

A wall of 250 mm glass and 150 mm mineral wool separates a room at 22 °C from outside air at -2 °C. The convection coefficients are 8 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 = 250 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -2 °C
U = W/(m²·K)
6.Hard
Mineral wool, k = 0.04200 mmGypsum board, k = 0.17150 mmroom 22 °Coutside -7 °CQ̇ = ?

A wall of 200 mm mineral wool and 150 mm gypsum board separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -7 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 218.4 W
  2. 2. Q̇ = 648 W
  3. 3. Ti = −2.9 °C
  4. 4. Ti = 10.84 °C
  5. 5. U = 0.2399 W/(m²·K)
  6. 6. Q̇ = 19.26 W

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