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 = 0.9650 mm25 °C-7 °CQ̇ = ?

A wall of glass is 50 mm thick and has an area of 20 m². Its faces are held at 25 °C and -7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 20 m²T1 = 25 °CT2 = -7 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03510 mm22 °C4 °CQ̇ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 8 m². Its faces are held at 22 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 8 m²T1 = 22 °CT2 = 4 °C
Q̇ = W
3.Medium
Brick, k = 0.72200 mmGypsum board, k = 0.1775 mm23 °C8 °CTi​ = ?Q̇

A wall is made of 200 mm of brick and 75 mm of gypsum board, with an area of 20 m². The outer faces are at 23 °C and 8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 23 °CT3 = 8 °C
Ti = °C
4.Medium
Glass, k = 0.96150 mmExpanded polystyrene, k = 0.03550 mm16 °C10 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 50 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 16 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 16 °CT3 = 10 °C
Ti = °C
5.Hard
Mineral wool, k = 0.0450 mmGypsum board, k = 0.1750 mmroom 21 °Coutside -4 °CQ̇

A wall of 50 mm mineral wool and 50 mm gypsum board separates a room at 21 °C from outside air at -4 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -4 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside -5 °CTs​ = ?Q̇

A wall of 200 mm glass and 150 mm expanded polystyrene separates a room at 20 °C from outside air at -5 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -5 °C
Ts = °C

Answer key

  1. 1. Q̇ = 12288 W
  2. 2. Q̇ = 504 W
  3. 3. Ti = 17.2 °C
  4. 4. Ti = 15.41 °C
  5. 5. U = 0.5961 W/(m²·K)
  6. 6. Ts = 19.12 °C

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