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
Brick, k = 0.72100 mm15 °C8 °CQ̇ = ?

A wall of brick is 100 mm thick and has an area of 10 m². Its faces are held at 15 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 100 mmA = 10 m²T1 = 15 °CT2 = 8 °C
Q̇ = W
2.Easy
Concrete, k = 1.4250 mm18 °C-13 °CQ̇ = ?

A wall of concrete is 250 mm thick and has an area of 10 m². Its faces are held at 18 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 10 m²T1 = 18 °CT2 = -13 °C
Q̇ = W
3.Medium
Wood, k = 0.1750 mmBrick, k = 0.72100 mm15 °C-15 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 100 mm of brick, with an area of 6 m². The outer faces are at 15 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 6 m²T1 = 15 °CT3 = -15 °C
Ti = °C
4.Medium
Wood, k = 0.17200 mmMineral wool, k = 0.0425 mm23 °C-15 °CQ̇ = ?

A wall is made of 200 mm of wood and 25 mm of mineral wool, with an area of 4 m². The outer faces are at 23 °C and -15 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²T1 = 23 °CT3 = -15 °C
Q̇ = W
5.Hard
Glass, k = 0.96250 mmWood, k = 0.1775 mmroom 21 °Coutside 2 °CQ̇

A wall of 250 mm glass and 75 mm wood separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 2 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.450 mmBrick, k = 0.72100 mmroom 21 °Coutside 3 °CQ̇

A wall of 50 mm concrete and 100 mm brick separates a room at 21 °C from outside air at 3 °C. The convection coefficients are 8 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 = 50 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 3 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 504 W
  2. 2. Q̇ = 1736 W
  3. 3. Ti = −5.377 °C
  4. 4. Q̇ = 84.38 W
  5. 5. U = 1.147 W/(m²·K)
  6. 6. U = 3.004 W/(m²·K)

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