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 = 0.17250 mm21 °C-15 °Cq″ = ?

A wall of wood is 250 mm thick and has an area of 20 m². Its faces are held at 21 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 20 m²T1 = 21 °CT2 = -15 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4150 mm25 °C-12 °Cq″ = ?

A wall of concrete is 150 mm thick and has an area of 20 m². Its faces are held at 25 °C and -12 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 20 m²T1 = 25 °CT2 = -12 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.03550 mmConcrete, k = 1.4150 mm15 °C-5 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 150 mm of concrete, with an area of 10 m². The outer faces are at 15 °C and -5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 15 °CT3 = -5 °C
Ti = °C
4.Medium
Brick, k = 0.7250 mmWood, k = 0.17100 mm25 °C-15 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of wood, with an area of 12 m². The outer faces are at 25 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 12 m²T1 = 25 °CT3 = -15 °C
Ti = °C
5.Hard
Brick, k = 0.7250 mmExpanded polystyrene, k = 0.03550 mmroom 20 °Coutside -3 °CQ̇ = ?

A wall of 50 mm brick and 50 mm expanded polystyrene separates a room at 20 °C from outside air at -3 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -3 °C
Q̇ = W
6.Hard
Wood, k = 0.17250 mmBrick, k = 0.7225 mmroom 22 °Coutside -1 °CQ̇ = ?

A wall of 250 mm wood and 25 mm brick separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -1 °C
Q̇ = W

Answer key

  1. 1. q″ = 24.48 W/m²
  2. 2. q″ = 345.3 W/m²
  3. 3. Ti = −3.605 °C
  4. 4. Ti = 20.78 °C
  5. 5. Q̇ = 141 W
  6. 6. Q̇ = 80.92 W

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