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
Expanded polystyrene, k = 0.035200 mm23 °C6 °CQ̇ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 12 m². Its faces are held at 23 °C and 6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 12 m²T1 = 23 °CT2 = 6 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1750 mm25 °C-10 °Cq″ = ?

A wall of gypsum board is 50 mm thick and has an area of 20 m². Its faces are held at 25 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 20 m²T1 = 25 °CT2 = -10 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04150 mmGypsum board, k = 0.1725 mm20 °C-12 °CTi​ = ?Q̇

A wall is made of 150 mm of mineral wool and 25 mm of gypsum board, with an area of 8 m². The outer faces are at 20 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 20 °CT3 = -12 °C
Ti = °C
4.Medium
Wood, k = 0.1750 mmConcrete, k = 1.4100 mm15 °C-12 °CQ̇ = ?

A wall is made of 50 mm of wood and 100 mm of concrete, with an area of 12 m². The outer faces are at 15 °C and -12 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 15 °CT3 = -12 °C
Q̇ = W
5.Hard
Brick, k = 0.72200 mmWood, k = 0.1775 mmroom 20 °Coutside -2 °CQ̇ = ?

A wall of 200 mm brick and 75 mm wood separates a room at 20 °C from outside air at -2 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -2 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.03550 mmGlass, k = 0.96150 mmroom 20 °Coutside -4 °CQ̇ = ?

A wall of 50 mm expanded polystyrene and 150 mm glass separates a room at 20 °C from outside air at -4 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -4 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 35.7 W
  2. 2. q″ = 119 W/m²
  3. 3. Ti = −10.79 °C
  4. 4. Q̇ = 886.3 W
  5. 5. Q̇ = 99.55 W
  6. 6. Q̇ = 109.7 W

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