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
Gypsum board, k = 0.17200 mm21 °C9 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 12 m². Its faces are held at 21 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 12 m²T1 = 21 °CT2 = 9 °C
q″ = W/m²
2.Easy
Brick, k = 0.7210 mm16 °C0 °Cq″ = ?

A wall of brick is 10 mm thick and has an area of 20 m². Its faces are held at 16 °C and 0 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 20 m²T1 = 16 °CT2 = 0 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4150 mmWood, k = 0.1775 mm17 °C-14 °CQ̇ = ?

A wall is made of 150 mm of concrete and 75 mm of wood, with an area of 10 m². The outer faces are at 17 °C and -14 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 17 °CT3 = -14 °C
Q̇ = W
4.Medium
Wood, k = 0.1750 mmExpanded polystyrene, k = 0.03525 mm15 °C-7 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 25 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 15 °C and -7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 15 °CT3 = -7 °C
Ti = °C
5.Hard
Wood, k = 0.17150 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside 5 °CQ̇ = ?

A wall of 150 mm wood and 150 mm expanded polystyrene separates a room at 20 °C from outside air at 5 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 5 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.1750 mmWood, k = 0.17150 mmroom 20 °Coutside -1 °CQ̇ = ?

A wall of 50 mm gypsum board and 150 mm wood separates a room at 20 °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 10 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -1 °C
Q̇ = W

Answer key

  1. 1. q″ = 10.2 W/m²
  2. 2. q″ = 1152 W/m²
  3. 3. Q̇ = 565.4 W
  4. 4. Ti = 8.583 °C
  5. 5. Q̇ = 22.64 W
  6. 6. Q̇ = 155.4 W

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