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 = 0.035200 mm20 °C-3 °Cq″ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 6 m². Its faces are held at 20 °C and -3 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 6 m²T1 = 20 °CT2 = -3 °C
q″ = W/m²
2.Easy
Concrete, k = 1.410 mm18 °C-7 °CQ̇ = ?

A wall of concrete is 10 mm thick and has an area of 15 m². Its faces are held at 18 °C and -7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 15 m²T1 = 18 °CT2 = -7 °C
Q̇ = W
3.Medium
Wood, k = 0.1750 mmGlass, k = 0.96150 mm17 °C3 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 150 mm of glass, with an area of 6 m². The outer faces are at 17 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 6 m²T1 = 17 °CT3 = 3 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmWood, k = 0.17150 mm22 °C-10 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 150 mm of wood, with an area of 8 m². The outer faces are at 22 °C and -10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 22 °CT3 = -10 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17150 mmWood, k = 0.17150 mmroom 22 °Coutside 4 °CQ̇ = ?

A wall of 150 mm gypsum board and 150 mm wood 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 6 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = 4 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.035250 mmGypsum board, k = 0.1750 mmroom 21 °Coutside 2 °CQ̇ = ?

A wall of 250 mm expanded polystyrene and 50 mm gypsum board separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 2 °C
Q̇ = W

Answer key

  1. 1. q″ = 4.025 W/m²
  2. 2. Q̇ = 52500 W
  3. 3. Ti = 7.857 °C
  4. 4. Ti = 6 °C
  5. 5. Q̇ = 56.9 W
  6. 6. Q̇ = 37.5 W

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