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 mm24 °C10 °Cq″ = ?

A wall of glass is 50 mm thick and has an area of 8 m². Its faces are held at 24 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 8 m²T1 = 24 °CT2 = 10 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03520 mm15 °C-10 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 20 m². Its faces are held at 15 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 20 m²T1 = 15 °CT2 = -10 °C
q″ = W/m²
3.Medium
Wood, k = 0.1750 mmBrick, k = 0.72150 mm21 °C-3 °CQ̇ = ?

A wall is made of 50 mm of wood and 150 mm of brick, with an area of 6 m². The outer faces are at 21 °C and -3 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 6 m²T1 = 21 °CT3 = -3 °C
Q̇ = W
4.Medium
Glass, k = 0.9650 mmWood, k = 0.1775 mm21 °C-7 °CTi​ = ?Q̇

A wall is made of 50 mm of glass and 75 mm of wood, with an area of 4 m². The outer faces are at 21 °C and -7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 21 °CT3 = -7 °C
Ti = °C
5.Hard
Glass, k = 0.9650 mmWood, k = 0.1750 mmroom 22 °Coutside -13 °CTs​ = ?Q̇

A wall of 50 mm glass and 50 mm wood separates a room at 22 °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 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -13 °C
Ts = °C
6.Hard
Mineral wool, k = 0.04200 mmGypsum board, k = 0.17150 mmroom 20 °Coutside -5 °CQ̇ = ?

A wall of 200 mm mineral wool and 150 mm gypsum board separates a room at 20 °C from outside air at -5 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -5 °C
Q̇ = W

Answer key

  1. 1. q″ = 268.8 W/m²
  2. 2. q″ = 43.75 W/m²
  3. 3. Q̇ = 286.6 W
  4. 4. Ti = 18.04 °C
  5. 5. Ts = 11.64 °C
  6. 6. Q̇ = 41.1 W

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