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 = 0.72250 mm16 °C-5 °Cq″ = ?

A wall of brick is 250 mm thick and has an area of 15 m². Its faces are held at 16 °C and -5 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 250 mmA = 15 m²T1 = 16 °CT2 = -5 °C
q″ = W/m²
2.Easy
Brick, k = 0.72150 mm17 °C10 °Cq″ = ?

A wall of brick is 150 mm thick and has an area of 12 m². Its faces are held at 17 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 150 mmA = 12 m²T1 = 17 °CT2 = 10 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17250 mmGlass, k = 0.9650 mm16 °C-6 °CTi​ = ?Q̇

A wall is made of 250 mm of gypsum board and 50 mm of glass, with an area of 8 m². The outer faces are at 16 °C and -6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 8 m²T1 = 16 °CT3 = -6 °C
Ti = °C
4.Medium
Wood, k = 0.17250 mmConcrete, k = 1.4100 mm17 °C1 °CTi​ = ?Q̇

A wall is made of 250 mm of wood and 100 mm of concrete, with an area of 6 m². The outer faces are at 17 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 17 °CT3 = 1 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17250 mmBrick, k = 0.7275 mmroom 21 °Coutside -14 °CQ̇

A wall of 250 mm gypsum board and 75 mm brick separates a room at 21 °C from outside air at -14 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -14 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.17250 mmWood, k = 0.1775 mmroom 22 °Coutside 0 °CQ̇ = ?

A wall of 250 mm gypsum board and 75 mm wood separates a room at 22 °C from outside air at 0 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = 0 °C
Q̇ = W

Answer key

  1. 1. q″ = 60.48 W/m²
  2. 2. q″ = 33.6 W/m²
  3. 3. Ti = −5.247 °C
  4. 4. Ti = 1.741 °C
  5. 5. U = 0.5754 W/(m²·K)
  6. 6. Q̇ = 129.1 W

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