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
Concrete, k = 1.4100 mm22 °C-12 °CQ̇ = ?

A wall of concrete is 100 mm thick and has an area of 4 m². Its faces are held at 22 °C and -12 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 4 m²T1 = 22 °CT2 = -12 °C
Q̇ = W
2.Easy
Glass, k = 0.96200 mm18 °C-1 °Cq″ = ?

A wall of glass is 200 mm thick and has an area of 15 m². Its faces are held at 18 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 200 mmA = 15 m²T1 = 18 °CT2 = -1 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.0450 mmWood, k = 0.17150 mm17 °C5 °CQ̇ = ?

A wall is made of 50 mm of mineral wool and 150 mm of wood, with an area of 4 m². The outer faces are at 17 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 17 °CT3 = 5 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035150 mmMineral wool, k = 0.0475 mm16 °C-3 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 75 mm of mineral wool, with an area of 8 m². The outer faces are at 16 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 8 m²T1 = 16 °CT3 = -3 °C
Ti = °C
5.Hard
Wood, k = 0.1750 mmExpanded polystyrene, k = 0.03575 mmroom 20 °Coutside -11 °CQ̇ = ?

A wall of 50 mm wood and 75 mm expanded polystyrene separates a room at 20 °C from outside air at -11 °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 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -11 °C
Q̇ = W
6.Hard
Wood, k = 0.17150 mmBrick, k = 0.7225 mmroom 20 °Coutside -3 °CQ̇ = ?

A wall of 150 mm wood and 25 mm brick separates a room at 20 °C from outside air at -3 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -3 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 1904 W
  2. 2. q″ = 91.2 W/m²
  3. 3. Q̇ = 22.51 W
  4. 4. Ti = 2.783 °C
  5. 5. Q̇ = 144.7 W
  6. 6. Q̇ = 261.1 W

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