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 = 0.035100 mm18 °C-1 °CQ̇ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 8 m². Its faces are held at 18 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 8 m²T1 = 18 °CT2 = -1 °C
Q̇ = W
2.Easy
Brick, k = 0.7250 mm24 °C9 °CQ̇ = ?

A wall of brick is 50 mm thick and has an area of 4 m². Its faces are held at 24 °C and 9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 50 mmA = 4 m²T1 = 24 °CT2 = 9 °C
Q̇ = W
3.Medium
Brick, k = 0.72100 mmWood, k = 0.1725 mm20 °C-15 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 25 mm of wood, with an area of 8 m². The outer faces are at 20 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 20 °CT3 = -15 °C
Ti = °C
4.Medium
Concrete, k = 1.4200 mmGlass, k = 0.9650 mm22 °C-15 °CTi​ = ?Q̇

A wall is made of 200 mm of concrete and 50 mm of glass, with an area of 4 m². The outer faces are at 22 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 22 °CT3 = -15 °C
Ti = °C
5.Hard
Gypsum board, k = 0.1750 mmGlass, k = 0.9625 mmroom 21 °Coutside -3 °CQ̇

A wall of 50 mm gypsum board and 25 mm glass separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96150 mmBrick, k = 0.7275 mmroom 22 °Coutside -4 °CQ̇

A wall of 150 mm glass and 75 mm brick separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -4 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 53.2 W
  2. 2. Q̇ = 864 W
  3. 3. Ti = 3 °C
  4. 4. Ti = −5.115 °C
  5. 5. U = 2.061 W/(m²·K)
  6. 6. U = 2.141 W/(m²·K)

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