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 = 0.0450 mm15 °C-4 °Cq″ = ?

A wall of mineral wool is 50 mm thick and has an area of 8 m². Its faces are held at 15 °C and -4 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 50 mmA = 8 m²T1 = 15 °CT2 = -4 °C
q″ = W/m²
2.Easy
Wood, k = 0.17100 mm17 °C4 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 8 m². Its faces are held at 17 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 8 m²T1 = 17 °CT2 = 4 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.17200 mmWood, k = 0.17100 mm24 °C6 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 100 mm of wood, with an area of 6 m². The outer faces are at 24 °C and 6 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 24 °CT3 = 6 °C
Q̇ = W
4.Medium
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.03575 mm15 °C-14 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 75 mm of expanded polystyrene, with an area of 8 m². The outer faces are at 15 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 8 m²T1 = 15 °CT3 = -14 °C
Ti = °C
5.Hard
Glass, k = 0.96250 mmBrick, k = 0.7225 mmroom 22 °Coutside 2 °CQ̇ = ?

A wall of 250 mm glass and 25 mm brick separates a room at 22 °C from outside air at 2 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 2 °C
Q̇ = W
6.Hard
Wood, k = 0.1750 mmMineral wool, k = 0.04100 mmroom 22 °Coutside -11 °CQ̇ = ?

A wall of 50 mm wood and 100 mm mineral wool separates a room at 22 °C from outside air at -11 °C. The convection coefficients are 7.7 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 = 50 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -11 °C
Q̇ = W

Answer key

  1. 1. q″ = 15.2 W/m²
  2. 2. Q̇ = 176.8 W
  3. 3. Q̇ = 61.2 W
  4. 4. Ti = 13.23 °C
  5. 5. Q̇ = 510.5 W
  6. 6. Q̇ = 89.27 W

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