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
Glass, k = 0.9620 mm19 °C-2 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 12 m². Its faces are held at 19 °C and -2 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 12 m²T1 = 19 °CT2 = -2 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03550 mm23 °C-12 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 15 m². Its faces are held at 23 °C and -12 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 15 m²T1 = 23 °CT2 = -12 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17200 mmExpanded polystyrene, k = 0.03550 mm20 °C-13 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 50 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 20 °C and -13 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 20 °CT3 = -13 °C
Q̇ = W
4.Medium
Wood, k = 0.17200 mmExpanded polystyrene, k = 0.035150 mm18 °C5 °CTi​ = ?Q̇

A wall is made of 200 mm of wood and 150 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 18 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 18 °CT3 = 5 °C
Ti = °C
5.Hard
Concrete, k = 1.4100 mmWood, k = 0.17150 mmroom 20 °Coutside 1 °CQ̇

A wall of 100 mm concrete and 150 mm wood separates a room at 20 °C from outside air at 1 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 1 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4200 mmGlass, k = 0.96100 mmroom 21 °Coutside -1 °CQ̇

A wall of 200 mm concrete and 100 mm glass separates a room at 21 °C from outside air at -1 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 1008 W/m²
  2. 2. q″ = 24.5 W/m²
  3. 3. Q̇ = 253.4 W
  4. 4. Ti = 15.2 °C
  5. 5. U = 0.8992 W/(m²·K)
  6. 6. U = 2.157 W/(m²·K)

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