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 = 1.4200 mm21 °C10 °CQ̇ = ?

A wall of concrete is 200 mm thick and has an area of 8 m². Its faces are held at 21 °C and 10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 8 m²T1 = 21 °CT2 = 10 °C
Q̇ = W
2.Easy
Glass, k = 0.9650 mm24 °C9 °Cq″ = ?

A wall of glass is 50 mm thick and has an area of 12 m². Its faces are held at 24 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 12 m²T1 = 24 °CT2 = 9 °C
q″ = W/m²
3.Medium
Brick, k = 0.72100 mmGypsum board, k = 0.17150 mm16 °C-2 °CQ̇ = ?

A wall is made of 100 mm of brick and 150 mm of gypsum board, with an area of 6 m². The outer faces are at 16 °C and -2 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 16 °CT3 = -2 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04250 mmWood, k = 0.17150 mm16 °C9 °CTi​ = ?Q̇

A wall is made of 250 mm of mineral wool and 150 mm of wood, with an area of 20 m². The outer faces are at 16 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 16 °CT3 = 9 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17150 mmGlass, k = 0.9650 mmroom 22 °Coutside -13 °CQ̇

A wall of 150 mm gypsum board and 50 mm glass separates a room at 22 °C from outside air at -13 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -13 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4100 mmGlass, k = 0.96100 mmroom 20 °Coutside 5 °CQ̇

A wall of 100 mm concrete and 100 mm glass separates a room at 20 °C from outside air at 5 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 5 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 616 W
  2. 2. q″ = 288 W/m²
  3. 3. Q̇ = 105.8 W
  4. 4. Ti = 9.866 °C
  5. 5. U = 0.8815 W/(m²·K)
  6. 6. U = 2.662 W/(m²·K)

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