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 = 1.4150 mm23 °C1 °CQ̇ = ?

A wall of concrete is 150 mm thick and has an area of 10 m². Its faces are held at 23 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 10 m²T1 = 23 °CT2 = 1 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.04200 mm20 °C-12 °Cq″ = ?

A wall of mineral wool is 200 mm thick and has an area of 10 m². Its faces are held at 20 °C and -12 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 10 m²T1 = 20 °CT2 = -12 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.1750 mmConcrete, k = 1.475 mm20 °C6 °CTi​ = ?Q̇

A wall is made of 50 mm of gypsum board and 75 mm of concrete, with an area of 15 m². The outer faces are at 20 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 20 °CT3 = 6 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmMineral wool, k = 0.04150 mm21 °C1 °CQ̇ = ?

A wall is made of 100 mm of concrete and 150 mm of mineral wool, with an area of 20 m². The outer faces are at 21 °C and 1 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 20 m²T1 = 21 °CT3 = 1 °C
Q̇ = W
5.Hard
Expanded polystyrene, k = 0.035250 mmConcrete, k = 1.450 mmroom 22 °Coutside -15 °CTs​ = ?Q̇

A wall of 250 mm expanded polystyrene and 50 mm concrete separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -15 °C
Ts = °C
6.Hard
Mineral wool, k = 0.0450 mmGypsum board, k = 0.1775 mmroom 21 °Coutside -7 °CQ̇

A wall of 50 mm mineral wool and 75 mm gypsum board separates a room at 21 °C from outside air at -7 °C. The convection coefficients are 6 W/(m²·K) inside and 25 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 = 0.04 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -7 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 2053 W
  2. 2. q″ = 6.4 W/m²
  3. 3. Ti = 8.157 °C
  4. 4. Q̇ = 104.7 W
  5. 5. Ts = 21.37 °C
  6. 6. U = 0.5269 W/(m²·K)

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