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
Gypsum board, k = 0.17200 mm17 °C-7 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 4 m². Its faces are held at 17 °C and -7 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 4 m²T1 = 17 °CT2 = -7 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03520 mm19 °C-8 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 4 m². Its faces are held at 19 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 4 m²T1 = 19 °CT2 = -8 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035250 mmGypsum board, k = 0.17100 mm20 °C-9 °CQ̇ = ?

A wall is made of 250 mm of expanded polystyrene and 100 mm of gypsum board, with an area of 6 m². The outer faces are at 20 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 20 °CT3 = -9 °C
Q̇ = W
4.Medium
Gypsum board, k = 0.1750 mmConcrete, k = 1.425 mm25 °C-15 °CTi​ = ?Q̇

A wall is made of 50 mm of gypsum board and 25 mm of concrete, with an area of 8 m². The outer faces are at 25 °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 = 25 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 25 °CT3 = -15 °C
Ti = °C
5.Hard
Concrete, k = 1.4200 mmMineral wool, k = 0.04150 mmroom 21 °Coutside -6 °CQ̇

A wall of 200 mm concrete and 150 mm mineral wool separates a room at 21 °C from outside air at -6 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96100 mmConcrete, k = 1.450 mmroom 21 °Coutside -13 °CQ̇

A wall of 100 mm glass and 50 mm concrete separates a room at 21 °C from outside air at -13 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -13 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 20.4 W/m²
  2. 2. q″ = 47.25 W/m²
  3. 3. Q̇ = 22.51 W
  4. 4. Ti = −12.71 °C
  5. 5. U = 0.2468 W/(m²·K)
  6. 6. U = 2.805 W/(m²·K)

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