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 = 0.17100 mm17 °C-8 °Cq″ = ?

A wall of gypsum board is 100 mm thick and has an area of 8 m². Its faces are held at 17 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 8 m²T1 = 17 °CT2 = -8 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.0450 mm25 °C1 °CQ̇ = ?

A wall of mineral wool is 50 mm thick and has an area of 4 m². Its faces are held at 25 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 50 mmA = 4 m²T1 = 25 °CT2 = 1 °C
Q̇ = W
3.Medium
Concrete, k = 1.4100 mmWood, k = 0.17150 mm25 °C7 °CTi​ = ?Q̇

A wall is made of 100 mm of concrete and 150 mm of wood, with an area of 8 m². The outer faces are at 25 °C and 7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 25 °CT3 = 7 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035200 mmWood, k = 0.17100 mm18 °C-9 °CQ̇ = ?

A wall is made of 200 mm of expanded polystyrene and 100 mm of wood, with an area of 12 m². The outer faces are at 18 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 12 m²T1 = 18 °CT3 = -9 °C
Q̇ = W
5.Hard
Glass, k = 0.9650 mmGypsum board, k = 0.1750 mmroom 20 °Coutside 0 °CQ̇

A wall of 50 mm glass and 50 mm gypsum board separates a room at 20 °C from outside air at 0 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 0 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96250 mmMineral wool, k = 0.0425 mmroom 21 °Coutside -1 °CQ̇

A wall of 250 mm glass and 25 mm mineral wool separates a room at 21 °C from outside air at -1 °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 = 250 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 42.5 W/m²
  2. 2. Q̇ = 76.8 W
  3. 3. Ti = 23.65 °C
  4. 4. Q̇ = 51.41 W
  5. 5. U = 1.901 W/(m²·K)
  6. 6. U = 0.952 W/(m²·K)

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