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 = 0.04200 mm20 °C-8 °CQ̇ = ?

A wall of mineral wool is 200 mm thick and has an area of 15 m². Its faces are held at 20 °C and -8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 15 m²T1 = 20 °CT2 = -8 °C
Q̇ = W
2.Easy
Concrete, k = 1.4100 mm18 °C4 °Cq″ = ?

A wall of concrete is 100 mm thick and has an area of 15 m². Its faces are held at 18 °C and 4 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 15 m²T1 = 18 °CT2 = 4 °C
q″ = W/m²
3.Medium
Wood, k = 0.17100 mmGypsum board, k = 0.1725 mm17 °C5 °CQ̇ = ?

A wall is made of 100 mm of wood and 25 mm of gypsum board, with an area of 4 m². The outer faces are at 17 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 17 °CT3 = 5 °C
Q̇ = W
4.Medium
Concrete, k = 1.4100 mmGlass, k = 0.9675 mm22 °C5 °CTi​ = ?Q̇

A wall is made of 100 mm of concrete and 75 mm of glass, with an area of 10 m². The outer faces are at 22 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 10 m²T1 = 22 °CT3 = 5 °C
Ti = °C
5.Hard
Wood, k = 0.1750 mmMineral wool, k = 0.04100 mmroom 20 °Coutside -14 °CQ̇ = ?

A wall of 50 mm wood and 100 mm mineral wool separates a room at 20 °C from outside air at -14 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -14 °C
Q̇ = W
6.Hard
Concrete, k = 1.4200 mmBrick, k = 0.7225 mmroom 21 °Coutside 2 °CQ̇

A wall of 200 mm concrete and 25 mm brick separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 2 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 84 W
  2. 2. q″ = 196 W/m²
  3. 3. Q̇ = 65.28 W
  4. 4. Ti = 13.88 °C
  5. 5. Q̇ = 136.3 W
  6. 6. U = 2.934 W/(m²·K)

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