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 = 0.7210 mm24 °C-10 °CQ̇ = ?

A wall of brick is 10 mm thick and has an area of 4 m². Its faces are held at 24 °C and -10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 4 m²T1 = 24 °CT2 = -10 °C
Q̇ = W
2.Easy
Concrete, k = 1.450 mm16 °C-5 °CQ̇ = ?

A wall of concrete is 50 mm thick and has an area of 8 m². Its faces are held at 16 °C and -5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 8 m²T1 = 16 °CT2 = -5 °C
Q̇ = W
3.Medium
Concrete, k = 1.4100 mmGypsum board, k = 0.1750 mm20 °C-2 °CQ̇ = ?

A wall is made of 100 mm of concrete and 50 mm of gypsum board, with an area of 20 m². The outer faces are at 20 °C and -2 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 20 °CT3 = -2 °C
Q̇ = W
4.Medium
Glass, k = 0.96200 mmWood, k = 0.1775 mm21 °C-15 °CTi​ = ?Q̇

A wall is made of 200 mm of glass and 75 mm of wood, with an area of 20 m². The outer faces are at 21 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 21 °CT3 = -15 °C
Ti = °C
5.Hard
Brick, k = 0.7250 mmMineral wool, k = 0.0450 mmroom 22 °Coutside -15 °CTs​ = ?Q̇

A wall of 50 mm brick and 50 mm mineral wool separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -15 °C
Ts = °C
6.Hard
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.03575 mmroom 21 °Coutside -12 °CQ̇

A wall of 200 mm glass and 75 mm expanded polystyrene separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -12 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 9792 W
  2. 2. Q̇ = 4704 W
  3. 3. Q̇ = 1204 W
  4. 4. Ti = 9.453 °C
  5. 5. Ts = 18.76 °C
  6. 6. U = 0.3974 W/(m²·K)

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