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
Concrete, k = 1.410 mm21 °C10 °Cq″ = ?

A wall of concrete is 10 mm thick and has an area of 6 m². Its faces are held at 21 °C and 10 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 6 m²T1 = 21 °CT2 = 10 °C
q″ = W/m²
2.Easy
Wood, k = 0.17100 mm25 °C0 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 20 m². Its faces are held at 25 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 20 m²T1 = 25 °CT2 = 0 °C
Q̇ = W
3.Medium
Brick, k = 0.7250 mmWood, k = 0.17100 mm17 °C3 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of wood, with an area of 8 m². The outer faces are at 17 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 17 °CT3 = 3 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.03550 mmWood, k = 0.17100 mm23 °C-15 °CQ̇ = ?

A wall is made of 50 mm of expanded polystyrene and 100 mm of wood, with an area of 15 m². The outer faces are at 23 °C and -15 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 23 °CT3 = -15 °C
Q̇ = W
5.Hard
Expanded polystyrene, k = 0.035100 mmGypsum board, k = 0.1750 mmroom 20 °Coutside -7 °CQ̇

A wall of 100 mm expanded polystyrene and 50 mm gypsum board separates a room at 20 °C from outside air at -7 °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 = 100 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -7 °C
U = W/(m²·K)
6.Hard
Mineral wool, k = 0.04150 mmConcrete, k = 1.475 mmroom 22 °Coutside -3 °CTs​ = ?Q̇

A wall of 150 mm mineral wool and 75 mm concrete separates a room at 22 °C from outside air at -3 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -3 °C
Ts = °C

Answer key

  1. 1. q″ = 1540 W/m²
  2. 2. Q̇ = 850 W
  3. 3. Ti = 15.52 °C
  4. 4. Q̇ = 282.6 W
  5. 5. U = 0.3002 W/(m²·K)
  6. 6. Ts = 20.96 °C

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