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
Wood, k = 0.1710 mm21 °C-1 °Cq″ = ?

A wall of wood is 10 mm thick and has an area of 6 m². Its faces are held at 21 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 6 m²T1 = 21 °CT2 = -1 °C
q″ = W/m²
2.Easy
Wood, k = 0.1720 mm23 °C0 °CQ̇ = ?

A wall of wood is 20 mm thick and has an area of 12 m². Its faces are held at 23 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 12 m²T1 = 23 °CT2 = 0 °C
Q̇ = W
3.Medium
Wood, k = 0.17150 mmExpanded polystyrene, k = 0.03575 mm15 °C9 °CTi​ = ?Q̇

A wall is made of 150 mm of wood and 75 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 15 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 15 °CT3 = 9 °C
Ti = °C
4.Medium
Glass, k = 0.96200 mmConcrete, k = 1.450 mm20 °C-3 °CTi​ = ?Q̇

A wall is made of 200 mm of glass and 50 mm of concrete, with an area of 6 m². The outer faces are at 20 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 20 °CT3 = -3 °C
Ti = °C
5.Hard
Glass, k = 0.9650 mmBrick, k = 0.7250 mmroom 20 °Coutside -12 °CQ̇

A wall of 50 mm glass and 50 mm brick separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -12 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4100 mmExpanded polystyrene, k = 0.03550 mmroom 21 °Coutside -11 °CQ̇

A wall of 100 mm concrete and 50 mm expanded polystyrene separates a room at 21 °C from outside air at -11 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -11 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 374 W/m²
  2. 2. Q̇ = 2346 W
  3. 3. Ti = 13.25 °C
  4. 4. Ti = 0.3659 °C
  5. 5. U = 3.924 W/(m²·K)
  6. 6. U = 0.5825 W/(m²·K)

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