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
Gypsum board, k = 0.1710 mm15 °C-1 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 12 m². Its faces are held at 15 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 12 m²T1 = 15 °CT2 = -1 °C
Q̇ = W
2.Easy
Concrete, k = 1.420 mm19 °C-15 °Cq″ = ?

A wall of concrete is 20 mm thick and has an area of 6 m². Its faces are held at 19 °C and -15 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 20 mmA = 6 m²T1 = 19 °CT2 = -15 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04100 mmGypsum board, k = 0.1725 mm21 °C0 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 25 mm of gypsum board, with an area of 6 m². The outer faces are at 21 °C and 0 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 21 °CT3 = 0 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17100 mmExpanded polystyrene, k = 0.03525 mm18 °C-1 °CTi​ = ?Q̇

A wall is made of 100 mm of gypsum board and 25 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 18 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 18 °CT3 = -1 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17200 mmExpanded polystyrene, k = 0.035150 mmroom 22 °Coutside 0 °CQ̇

A wall of 200 mm gypsum board and 150 mm expanded polystyrene separates a room at 22 °C from outside air at 0 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 0 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.17250 mmWood, k = 0.1775 mmroom 20 °Coutside -10 °CTs​ = ?Q̇

A wall of 250 mm gypsum board and 75 mm wood separates a room at 20 °C from outside air at -10 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -10 °C
Ts = °C

Answer key

  1. 1. Q̇ = 3264 W
  2. 2. q″ = 2380 W/m²
  3. 3. Ti = 1.167 °C
  4. 4. Ti = 9.419 °C
  5. 5. U = 0.1761 W/(m²·K)
  6. 6. Ts = 17.64 °C

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