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 mm17 °C-12 °CQ̇ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 20 m². Its faces are held at 17 °C and -12 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 20 m²T1 = 17 °CT2 = -12 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.17200 mm18 °C-15 °CQ̇ = ?

A wall of gypsum board is 200 mm thick and has an area of 12 m². Its faces are held at 18 °C and -15 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 12 m²T1 = 18 °CT2 = -15 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035250 mmGypsum board, k = 0.1725 mm21 °C6 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 25 mm of gypsum board, with an area of 4 m². The outer faces are at 21 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 21 °CT3 = 6 °C
Ti = °C
4.Medium
Brick, k = 0.72100 mmWood, k = 0.17100 mm21 °C-11 °CQ̇ = ?

A wall is made of 100 mm of brick and 100 mm of wood, with an area of 12 m². The outer faces are at 21 °C and -11 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 12 m²T1 = 21 °CT3 = -11 °C
Q̇ = W
5.Hard
Wood, k = 0.17200 mmExpanded polystyrene, k = 0.03575 mmroom 20 °Coutside -15 °CQ̇ = ?

A wall of 200 mm wood and 75 mm expanded polystyrene separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -15 °C
Q̇ = W
6.Hard
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.03525 mmroom 22 °Coutside -1 °CQ̇

A wall of 100 mm brick and 25 mm expanded polystyrene separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 8 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 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 101.5 W
  2. 2. Q̇ = 336.6 W
  3. 3. Ti = 6.303 °C
  4. 4. Q̇ = 528.1 W
  5. 5. Q̇ = 150.5 W
  6. 6. U = 0.9726 W/(m²·K)

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