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
Gypsum board, k = 0.17150 mm23 °C-13 °Cq″ = ?

A wall of gypsum board is 150 mm thick and has an area of 8 m². Its faces are held at 23 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 8 m²T1 = 23 °CT2 = -13 °C
q″ = W/m²
2.Easy
Wood, k = 0.1710 mm20 °C1 °Cq″ = ?

A wall of wood is 10 mm thick and has an area of 6 m². Its faces are held at 20 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 6 m²T1 = 20 °CT2 = 1 °C
q″ = W/m²
3.Medium
Brick, k = 0.72200 mmWood, k = 0.1750 mm25 °C-2 °CTi​ = ?Q̇

A wall is made of 200 mm of brick and 50 mm of wood, with an area of 6 m². The outer faces are at 25 °C and -2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 25 °CT3 = -2 °C
Ti = °C
4.Medium
Brick, k = 0.72200 mmExpanded polystyrene, k = 0.035150 mm21 °C1 °CQ̇ = ?

A wall is made of 200 mm of brick and 150 mm of expanded polystyrene, with an area of 4 m². The outer faces are at 21 °C and 1 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 4 m²T1 = 21 °CT3 = 1 °C
Q̇ = W
5.Hard
Brick, k = 0.72150 mmMineral wool, k = 0.0425 mmroom 20 °Coutside -12 °CTs​ = ?Q̇

A wall of 150 mm brick and 25 mm mineral wool separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -12 °C
Ts = °C
6.Hard
Concrete, k = 1.4200 mmGypsum board, k = 0.1750 mmroom 20 °Coutside -4 °CQ̇ = ?

A wall of 200 mm concrete and 50 mm gypsum board separates a room at 20 °C from outside air at -4 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -4 °C
Q̇ = W

Answer key

  1. 1. q″ = 40.8 W/m²
  2. 2. q″ = 323 W/m²
  3. 3. Ti = 11.89 °C
  4. 4. Q̇ = 17.53 W
  5. 5. Ts = 16.03 °C
  6. 6. Q̇ = 452.1 W

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