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
Mineral wool, k = 0.04200 mm23 °C-12 °CQ̇ = ?

A wall of mineral wool is 200 mm thick and has an area of 12 m². Its faces are held at 23 °C and -12 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 12 m²T1 = 23 °CT2 = -12 °C
Q̇ = W
2.Easy
Brick, k = 0.72250 mm25 °C5 °Cq″ = ?

A wall of brick is 250 mm thick and has an area of 20 m². Its faces are held at 25 °C and 5 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 250 mmA = 20 m²T1 = 25 °CT2 = 5 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17150 mmConcrete, k = 1.4100 mm23 °C3 °CQ̇ = ?

A wall is made of 150 mm of gypsum board and 100 mm of concrete, with an area of 20 m². The outer faces are at 23 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 20 m²T1 = 23 °CT3 = 3 °C
Q̇ = W
4.Medium
Wood, k = 0.17250 mmMineral wool, k = 0.0475 mm24 °C1 °CTi​ = ?Q̇

A wall is made of 250 mm of wood and 75 mm of mineral wool, with an area of 8 m². The outer faces are at 24 °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 = 75 mm, k2 = 0.04 W/(m·K)A = 8 m²T1 = 24 °CT3 = 1 °C
Ti = °C
5.Hard
Wood, k = 0.17150 mmGypsum board, k = 0.17150 mmroom 20 °Coutside -8 °CQ̇

A wall of 150 mm wood and 150 mm gypsum board separates a room at 20 °C from outside air at -8 °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 overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -8 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035100 mmMineral wool, k = 0.04150 mmroom 22 °Coutside -9 °CQ̇ = ?

A wall of 100 mm expanded polystyrene and 150 mm mineral wool separates a room at 22 °C from outside air at -9 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -9 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 84 W
  2. 2. q″ = 57.6 W/m²
  3. 3. Q̇ = 419.4 W
  4. 4. Ti = 13.89 °C
  5. 5. U = 0.52 W/(m²·K)
  6. 6. Q̇ = 18.22 W

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