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 = 0.03520 mm17 °C-13 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 15 m². Its faces are held at 17 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 15 m²T1 = 17 °CT2 = -13 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4100 mm22 °C-4 °CQ̇ = ?

A wall of concrete is 100 mm thick and has an area of 12 m². Its faces are held at 22 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 12 m²T1 = 22 °CT2 = -4 °C
Q̇ = W
3.Medium
Brick, k = 0.72250 mmWood, k = 0.1750 mm16 °C-7 °CTi​ = ?Q̇

A wall is made of 250 mm of brick and 50 mm of wood, with an area of 8 m². The outer faces are at 16 °C and -7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 16 °CT3 = -7 °C
Ti = °C
4.Medium
Glass, k = 0.96150 mmConcrete, k = 1.4150 mm21 °C-1 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 150 mm of concrete, with an area of 8 m². The outer faces are at 21 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 21 °CT3 = -1 °C
Ti = °C
5.Hard
Gypsum board, k = 0.1750 mmExpanded polystyrene, k = 0.03575 mmroom 21 °Coutside 2 °CQ̇ = ?

A wall of 50 mm gypsum board and 75 mm expanded polystyrene separates a room at 21 °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 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 2 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.035250 mmWood, k = 0.1750 mmroom 20 °Coutside -5 °CQ̇

A wall of 250 mm expanded polystyrene and 50 mm wood separates a room at 20 °C from outside air at -5 °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 = 250 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 = -5 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 52.5 W/m²
  2. 2. Q̇ = 4368 W
  3. 3. Ti = 3.548 °C
  4. 4. Ti = 7.949 °C
  5. 5. Q̇ = 29.21 W
  6. 6. U = 0.1313 W/(m²·K)

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