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 mm23 °C-3 °Cq″ = ?

A wall of wood is 250 mm thick and has an area of 6 m². Its faces are held at 23 °C and -3 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 6 m²T1 = 23 °CT2 = -3 °C
q″ = W/m²
2.Easy
Brick, k = 0.72200 mm23 °C8 °CQ̇ = ?

A wall of brick is 200 mm thick and has an area of 20 m². Its faces are held at 23 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 20 m²T1 = 23 °CT2 = 8 °C
Q̇ = W
3.Medium
Mineral wool, k = 0.04100 mmWood, k = 0.17150 mm24 °C9 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 150 mm of wood, with an area of 20 m². The outer faces are at 24 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 24 °CT3 = 9 °C
Ti = °C
4.Medium
Brick, k = 0.7250 mmConcrete, k = 1.4100 mm19 °C9 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of concrete, with an area of 8 m². The outer faces are at 19 °C and 9 °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 = 1.4 W/(m·K)A = 8 m²T1 = 19 °CT3 = 9 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17100 mmBrick, k = 0.7275 mmroom 20 °Coutside -8 °CQ̇ = ?

A wall of 100 mm gypsum board and 75 mm brick separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -8 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.17250 mmConcrete, k = 1.425 mmroom 20 °Coutside -11 °CQ̇ = ?

A wall of 250 mm gypsum board and 25 mm concrete separates a room at 20 °C from outside air at -11 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -11 °C
Q̇ = W

Answer key

  1. 1. q″ = 17.68 W/m²
  2. 2. Q̇ = 1080 W
  3. 3. Ti = 12.91 °C
  4. 4. Ti = 14.07 °C
  5. 5. Q̇ = 201.8 W
  6. 6. Q̇ = 376.5 W

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