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 = 0.96150 mm20 °C-3 °CQ̇ = ?

A wall of glass is 150 mm thick and has an area of 6 m². Its faces are held at 20 °C and -3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 150 mmA = 6 m²T1 = 20 °CT2 = -3 °C
Q̇ = W
2.Easy
Wood, k = 0.1750 mm23 °C1 °Cq″ = ?

A wall of wood is 50 mm thick and has an area of 4 m². Its faces are held at 23 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 4 m²T1 = 23 °CT2 = 1 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4150 mmWood, k = 0.1725 mm25 °C0 °CQ̇ = ?

A wall is made of 150 mm of concrete and 25 mm of wood, with an area of 4 m². The outer faces are at 25 °C and 0 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 25 °CT3 = 0 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.0450 mmGypsum board, k = 0.17150 mm15 °C-11 °CTi​ = ?Q̇

A wall is made of 50 mm of mineral wool and 150 mm of gypsum board, with an area of 8 m². The outer faces are at 15 °C and -11 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 15 °CT3 = -11 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.03550 mmGypsum board, k = 0.1725 mmroom 22 °Coutside 0 °CQ̇

A wall of 50 mm expanded polystyrene and 25 mm gypsum board 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 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 0 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.17250 mmConcrete, k = 1.4150 mmroom 22 °Coutside -6 °CQ̇

A wall of 250 mm wood and 150 mm concrete separates a room at 22 °C from outside air at -6 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -6 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 883.2 W
  2. 2. q″ = 74.8 W/m²
  3. 3. Q̇ = 393.4 W
  4. 4. Ti = −0.2414 °C
  5. 5. U = 0.5579 W/(m²·K)
  6. 6. U = 0.5722 W/(m²·K)

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