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
Glass, k = 0.9650 mm20 °C-10 °CQ̇ = ?

A wall of glass is 50 mm thick and has an area of 8 m². Its faces are held at 20 °C and -10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 8 m²T1 = 20 °CT2 = -10 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1710 mm20 °C-1 °Cq″ = ?

A wall of gypsum board is 10 mm thick and has an area of 12 m². Its faces are held at 20 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 12 m²T1 = 20 °CT2 = -1 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17150 mmConcrete, k = 1.450 mm24 °C8 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 50 mm of concrete, with an area of 6 m². The outer faces are at 24 °C and 8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 24 °CT3 = 8 °C
Ti = °C
4.Medium
Wood, k = 0.17100 mmMineral wool, k = 0.0475 mm18 °C-6 °CQ̇ = ?

A wall is made of 100 mm of wood and 75 mm of mineral wool, with an area of 10 m². The outer faces are at 18 °C and -6 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 18 °CT3 = -6 °C
Q̇ = W
5.Hard
Glass, k = 0.96150 mmGypsum board, k = 0.1750 mmroom 21 °Coutside 2 °CQ̇

A wall of 150 mm glass and 50 mm gypsum board separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 2 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035250 mmConcrete, k = 1.450 mmroom 20 °Coutside -8 °CQ̇

A wall of 250 mm expanded polystyrene and 50 mm concrete separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -8 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 4608 W
  2. 2. q″ = 357 W/m²
  3. 3. Ti = 8.622 °C
  4. 4. Q̇ = 97.43 W
  5. 5. U = 1.587 W/(m²·K)
  6. 6. U = 0.1362 W/(m²·K)

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