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
Brick, k = 0.72200 mm25 °C7 °Cq″ = ?

A wall of brick is 200 mm thick and has an area of 10 m². Its faces are held at 25 °C and 7 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 10 m²T1 = 25 °CT2 = 7 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1710 mm22 °C8 °Cq″ = ?

A wall of gypsum board is 10 mm thick and has an area of 20 m². Its faces are held at 22 °C and 8 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 20 m²T1 = 22 °CT2 = 8 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4100 mmExpanded polystyrene, k = 0.03550 mm15 °C-10 °CQ̇ = ?

A wall is made of 100 mm of concrete and 50 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 15 °C and -10 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 15 °CT3 = -10 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035250 mmMineral wool, k = 0.0450 mm22 °C-1 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 50 mm of mineral wool, with an area of 6 m². The outer faces are at 22 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 6 m²T1 = 22 °CT3 = -1 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04250 mmGypsum board, k = 0.17100 mmroom 20 °Coutside -15 °CQ̇

A wall of 250 mm mineral wool and 100 mm gypsum board separates a room at 20 °C from outside air at -15 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -15 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4100 mmGypsum board, k = 0.1775 mmroom 20 °Coutside 4 °CQ̇ = ?

A wall of 100 mm concrete and 75 mm gypsum board separates a room at 20 °C from outside air at 4 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 4 °C
Q̇ = W

Answer key

  1. 1. q″ = 64.8 W/m²
  2. 2. q″ = 238 W/m²
  3. 3. Q̇ = 250 W
  4. 4. Ti = 2.426 °C
  5. 5. U = 0.1426 W/(m²·K)
  6. 6. Q̇ = 279.2 W

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