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 = 0.035250 mm19 °C4 °CQ̇ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 8 m². Its faces are held at 19 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 8 m²T1 = 19 °CT2 = 4 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03550 mm24 °C-9 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 4 m². Its faces are held at 24 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 4 m²T1 = 24 °CT2 = -9 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.0450 mmWood, k = 0.17150 mm15 °C-14 °CQ̇ = ?

A wall is made of 50 mm of mineral wool and 150 mm of wood, with an area of 15 m². The outer faces are at 15 °C and -14 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 15 °CT3 = -14 °C
Q̇ = W
4.Medium
Wood, k = 0.17150 mmBrick, k = 0.72150 mm25 °C-6 °CTi​ = ?Q̇

A wall is made of 150 mm of wood and 150 mm of brick, with an area of 4 m². The outer faces are at 25 °C and -6 °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 = 0.72 W/(m·K)A = 4 m²T1 = 25 °CT3 = -6 °C
Ti = °C
5.Hard
Brick, k = 0.7250 mmMineral wool, k = 0.0425 mmroom 22 °Coutside -13 °CQ̇

A wall of 50 mm brick and 25 mm mineral wool separates a room at 22 °C from outside air at -13 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -13 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.17150 mmExpanded polystyrene, k = 0.035150 mmroom 22 °Coutside -15 °CQ̇ = ?

A wall of 150 mm wood and 150 mm expanded polystyrene separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -15 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 16.8 W
  2. 2. q″ = 23.1 W/m²
  3. 3. Q̇ = 204 W
  4. 4. Ti = −0.07865 °C
  5. 5. U = 1.166 W/(m²·K)
  6. 6. Q̇ = 139.6 W

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