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
Mineral wool, k = 0.04250 mm22 °C-5 °CQ̇ = ?

A wall of mineral wool is 250 mm thick and has an area of 20 m². Its faces are held at 22 °C and -5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 250 mmA = 20 m²T1 = 22 °CT2 = -5 °C
Q̇ = W
2.Easy
Glass, k = 0.96250 mm18 °C-15 °Cq″ = ?

A wall of glass is 250 mm thick and has an area of 20 m². Its faces are held at 18 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 250 mmA = 20 m²T1 = 18 °CT2 = -15 °C
q″ = W/m²
3.Medium
Brick, k = 0.72250 mmGlass, k = 0.96150 mm18 °C-4 °CTi​ = ?Q̇

A wall is made of 250 mm of brick and 150 mm of glass, with an area of 10 m². The outer faces are at 18 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 10 m²T1 = 18 °CT3 = -4 °C
Ti = °C
4.Medium
Concrete, k = 1.4150 mmGlass, k = 0.96150 mm20 °C8 °CTi​ = ?Q̇

A wall is made of 150 mm of concrete and 150 mm of glass, with an area of 12 m². The outer faces are at 20 °C and 8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 12 m²T1 = 20 °CT3 = 8 °C
Ti = °C
5.Hard
Mineral wool, k = 0.0450 mmWood, k = 0.17150 mmroom 21 °Coutside -2 °CQ̇ = ?

A wall of 50 mm mineral wool and 150 mm wood separates a room at 21 °C from outside air at -2 °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 heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -2 °C
Q̇ = W
6.Hard
Glass, k = 0.9650 mmMineral wool, k = 0.0425 mmroom 21 °Coutside -1 °CQ̇

A wall of 50 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 20 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 86.4 W
  2. 2. q″ = 126.7 W/m²
  3. 3. Ti = 2.828 °C
  4. 4. Ti = 15.12 °C
  5. 5. Q̇ = 59.17 W
  6. 6. U = 1.174 W/(m²·K)

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