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
Brick, k = 0.7210 mm23 °C9 °Cq″ = ?

A wall of brick is 10 mm thick and has an area of 8 m². Its faces are held at 23 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 8 m²T1 = 23 °CT2 = 9 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4250 mm21 °C6 °CQ̇ = ?

A wall of concrete is 250 mm thick and has an area of 4 m². Its faces are held at 21 °C and 6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 4 m²T1 = 21 °CT2 = 6 °C
Q̇ = W
3.Medium
Wood, k = 0.17100 mmBrick, k = 0.72150 mm20 °C2 °CTi​ = ?Q̇

A wall is made of 100 mm of wood and 150 mm of brick, with an area of 12 m². The outer faces are at 20 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 12 m²T1 = 20 °CT3 = 2 °C
Ti = °C
4.Medium
Glass, k = 0.96100 mmBrick, k = 0.72150 mm21 °C-4 °CQ̇ = ?

A wall is made of 100 mm of glass and 150 mm of brick, with an area of 10 m². The outer faces are at 21 °C and -4 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 10 m²T1 = 21 °CT3 = -4 °C
Q̇ = W
5.Hard
Brick, k = 0.72200 mmGlass, k = 0.96150 mmroom 21 °Coutside -4 °CQ̇

A wall of 200 mm brick and 150 mm glass separates a room at 21 °C from outside air at -4 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -4 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.17250 mmExpanded polystyrene, k = 0.03575 mmroom 22 °Coutside -15 °CQ̇

A wall of 250 mm wood and 75 mm expanded polystyrene separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -15 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 1008 W/m²
  2. 2. Q̇ = 336 W
  3. 3. Ti = 6.708 °C
  4. 4. Q̇ = 800 W
  5. 5. U = 1.537 W/(m²·K)
  6. 6. U = 0.2647 W/(m²·K)

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