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
Concrete, k = 1.450 mm25 °C-2 °CQ̇ = ?

A wall of concrete is 50 mm thick and has an area of 10 m². Its faces are held at 25 °C and -2 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 10 m²T1 = 25 °CT2 = -2 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.0410 mm16 °C-9 °CQ̇ = ?

A wall of mineral wool is 10 mm thick and has an area of 6 m². Its faces are held at 16 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 10 mmA = 6 m²T1 = 16 °CT2 = -9 °C
Q̇ = W
3.Medium
Mineral wool, k = 0.04150 mmExpanded polystyrene, k = 0.03525 mm15 °C-7 °CQ̇ = ?

A wall is made of 150 mm of mineral wool and 25 mm of expanded polystyrene, with an area of 4 m². The outer faces are at 15 °C and -7 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 4 m²T1 = 15 °CT3 = -7 °C
Q̇ = W
4.Medium
Glass, k = 0.9650 mmBrick, k = 0.7275 mm23 °C-5 °CTi​ = ?Q̇

A wall is made of 50 mm of glass and 75 mm of brick, with an area of 4 m². The outer faces are at 23 °C and -5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 4 m²T1 = 23 °CT3 = -5 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035200 mmGypsum board, k = 0.17150 mmroom 20 °Coutside -6 °CQ̇

A wall of 200 mm expanded polystyrene and 150 mm gypsum board separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.17150 mmConcrete, k = 1.475 mmroom 22 °Coutside -1 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 75 mm concrete separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -1 °C
Ts = °C

Answer key

  1. 1. Q̇ = 7560 W
  2. 2. Q̇ = 600 W
  3. 3. Q̇ = 19.71 W
  4. 4. Ti = 13.67 °C
  5. 5. U = 0.1477 W/(m²·K)
  6. 6. Ts = 19.88 °C

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