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 = 0.04100 mm25 °C1 °Cq″ = ?

A wall of mineral wool is 100 mm thick and has an area of 6 m². Its faces are held at 25 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 100 mmA = 6 m²T1 = 25 °CT2 = 1 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.04200 mm17 °C8 °Cq″ = ?

A wall of mineral wool is 200 mm thick and has an area of 20 m². Its faces are held at 17 °C and 8 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 20 m²T1 = 17 °CT2 = 8 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17100 mmGlass, k = 0.96100 mm16 °C-4 °CQ̇ = ?

A wall is made of 100 mm of gypsum board and 100 mm of glass, with an area of 10 m². The outer faces are at 16 °C and -4 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 10 m²T1 = 16 °CT3 = -4 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04150 mmConcrete, k = 1.475 mm18 °C-10 °CTi​ = ?Q̇

A wall is made of 150 mm of mineral wool and 75 mm of concrete, with an area of 20 m². The outer faces are at 18 °C and -10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 20 m²T1 = 18 °CT3 = -10 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04200 mmBrick, k = 0.7225 mmroom 20 °Coutside -12 °CQ̇

A wall of 200 mm mineral wool and 25 mm brick separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -12 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035100 mmWood, k = 0.1775 mmroom 20 °Coutside -13 °CQ̇ = ?

A wall of 100 mm expanded polystyrene and 75 mm wood separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -13 °C
Q̇ = W

Answer key

  1. 1. q″ = 9.6 W/m²
  2. 2. q″ = 1.8 W/m²
  3. 3. Q̇ = 288.8 W
  4. 4. Ti = −9.606 °C
  5. 5. U = 0.1918 W/(m²·K)
  6. 6. Q̇ = 95.01 W

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