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 mm25 °C-3 °Cq″ = ?

A wall of wood is 50 mm thick and has an area of 20 m². Its faces are held at 25 °C and -3 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 20 m²T1 = 25 °CT2 = -3 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035150 mm22 °C-4 °CQ̇ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 4 m². Its faces are held at 22 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 4 m²T1 = 22 °CT2 = -4 °C
Q̇ = W
3.Medium
Brick, k = 0.72200 mmConcrete, k = 1.4150 mm24 °C3 °CTi​ = ?Q̇

A wall is made of 200 mm of brick and 150 mm of concrete, with an area of 12 m². The outer faces are at 24 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 24 °CT3 = 3 °C
Ti = °C
4.Medium
Glass, k = 0.96250 mmGypsum board, k = 0.1725 mm16 °C-4 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 25 mm of gypsum board, with an area of 8 m². The outer faces are at 16 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 16 °CT3 = -4 °C
Ti = °C
5.Hard
Brick, k = 0.72250 mmGypsum board, k = 0.17150 mmroom 22 °Coutside -2 °CQ̇

A wall of 250 mm brick and 150 mm gypsum board separates a room at 22 °C from outside air at -2 °C. The convection coefficients are 6 W/(m²·K) inside and 25 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 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -2 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035150 mmGypsum board, k = 0.17150 mmroom 22 °Coutside -9 °CQ̇

A wall of 150 mm expanded polystyrene and 150 mm gypsum board separates a room at 22 °C from outside air at -9 °C. The convection coefficients are 7.7 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 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -9 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 95.2 W/m²
  2. 2. Q̇ = 24.27 W
  3. 3. Ti = 8.845 °C
  4. 4. Ti = 3.218 °C
  5. 5. U = 0.6963 W/(m²·K)
  6. 6. U = 0.1876 W/(m²·K)

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